Comparative Analysis of Parameters of Pulsars With Breaking Indices n>0 and n<0

Comparative Analysis of Parameters of Pulsars With Breaking Indices n>0 and n<0 | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Comparative Analysis of Parameters of Pulsars With Breaking Indices n>0 and n<0 Chika Onuchukwu, E Leghara This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3961027/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 7 You are reading this latest preprint version Abstract We analyzed the timing parameters (the rotational frequency \(\nu\) , the first \(\left(\dot{\nu }\right)\) and second \(\left(\ddot{\nu }\right)\) time-derivative of frequency) and the derived parameters of a sample of pulsars that have their values of \(\ddot{\nu }\) (470 pulsars) recorded in the Australian Telescope National Facility (ATNF) pulsar catalogue. We formed various subsamples, those with breaking index \(n0\) , glitching and non-glitching pulsars. Our statistical analyses of the timing and derived parameters indicated some level of differences and similarities in the parameters analyzed. Glitching pulsars appear to have higher rotational frequency of pulsars than non-glitching pulsars, and pulsars with \(n>0\) appear to rotate faster than those with \(n0\) than for subsample with \(n<0\) . pulsar: general Method: Data Analysis - Statistical Glitches Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction The braking index of pulsar, n , is the parameter which describes how the pulsar spin-down rate varies with its rotation frequency and it is fundamental to a better understanding of the pulsar electrodynamics (Yue et al. 2007 , Chukwude et al., 2010 ). The current understanding of pulsars is that they are rapidly rotating, highly magnetized neutron stars powered by their rotational kinetic energy (Goldreich & Julian 1969 ; Manchester & Taylor 1977 ; Shapiro & Teukolsky 1983 , Chukwude et al., 2010 ; Onuchukwu & Chukwude 2016 ). The standard model of pulsar theory assumes that pure magnetic dipole radiation is the dominant process responsible for energy losses by pulsars (Pacini 1967 ; Manchester & Taylor 1977 ). In the standard model, the spin-down of a pulsar should follow a simple power-law relation between the spin frequency \(\left(\nu \right)\) and its first time-derivative \(\left(\dot{\nu }\right)\) given as (e.g. Manchester & Taylor 1977 , Chukwude et al., 2010 ) \(\dot{\nu }=-k{\nu }^{n}\) 1 \(k\) is a positive constant, \(n=3\) is the braking index for pure magnetic dipole energy loss process. Differentiating Eq. (1), and making \(n\) the subject, we have \(n=\frac{\nu \ddot{\nu }}{{\dot{\nu }}^{2}}\) 2 Equation (2) implies that once the second time derivative of a measured, pulsar \(n\) can be easily estimated. There are \(\sim4170\) known pulsars and only \(\sim470\) of the known pulsars have their values of \(\ddot{\nu }\) measured and are not given as zero (Manchester et al., 2005 ; ATNF pulsar catalogue, 2024). The values of \(n\) estimated for the pulsars with recorded values of \(\ddot{\nu }\) using Eq. (2) ranges from \(-2\times {10}^{12}\le n\le 1.1\times {10}^{11}\) , with only \(\sim12\) having \(-3\le n\le 3.\) Johnston and Galloway ( 1999 ) suggested that it will take about hundreds of years of pulsar timing to get a better measurement of \(\ddot{\nu }\) , since different effects tend to dominate the values of \(\ddot{\nu }\) over that expected from spin-down alone. These effects include pulsars glitches and timing activities (Lyne et al., 1988 ; Kaspi, et al., 1994 ; Shemar & Lyne 1996 ; Lyne et al., 1996 ; Lyne & Graham-Smith 1998 ; Camilo et al., 2000 ; Lorimer & Kramer, 2005 ; Livingstone et al., 2006 , 2007 ; Hobbs, et al., 2006 ; Chukwude et al., 2010 ) which lead to discontinuities in both frequency and first frequency time-derivative, making it very difficult to phase connect over the glitch and the recovery from a glitch in which the measurement of \(\dot{\nu }\) reflects the recovery rather than the intrinsic spin-down. Furthermore, the pulsar timing activities contaminate the deterministic spin parameters and the measurement of \(\ddot{\nu }\) from pulsar timing seem most affected, perhaps due to its small values (Chukwude, 2007 ) and changes in the signs of \(\ddot{\nu }\) ( \(+/-\) ), whereas \(\dot{\nu }\) is always negative. Moreover, microglitches with all possible sign combination ( \(+/+, +/-, -/-, -/+),\) thus, are even difficult to understand (Cordes et al. 1988; D’ Alessandro 1996, Chukwude et al. 2010 ) and model, these add to the difficulties associated with estimating the true value of \(\ddot{\nu }\) . Melatos et al. ( 2008 ) and Onuchukwu & Chukwude ( 2016 ) assumed that glitches and microglicthes phenomena in pulsars may be interpreted in terms of self-organized critical state systems (SOCS), which show behaviors that are collective, scale invariant, discrete and randomly interaction dominated events. For such systems, like Johnston and Galloway ( 1999 ), suggested, it may take hundreds of years for a reasonable value of \(\ddot{\nu }\) to be measured. Consequently, we want to statistically study pulsar parameters that have glitched at least once, whose \(\ddot{\nu }\) has been determined and breaking index using Eq. (2) can be evaluated. This study we believe, will add to the general understanding of pulsars and whether the derived and timing parameters statistics of pulsars with \(n>0\) are different from those with \(n<0\) 2. Data Analyses, Result and Discussion The data used for this study were obtained http://www.jb.man.ac.uk/pulsar/glitches.html (Basu et al., 2022 ) and Manchester et al., ( 2005 - ATNF pulsar catalogue, 2024). There are 471 pulsars whose \(\ddot{\nu }\) were non-zero or given and thus, \(n\) can be estimated from Eq. (2), amongst 471 pulsars, 114 pulsars have record that it has glitched at least once, 56 pulsars have records that they have glitches at least 3 times or more. There were 275 pulsars that have \(n>0\) , while 196 have \(n<0\) in our sample (both glitching and non-glitching pulsars). There are 36 pulsars that have glitched once in our sample \(n0,\) among them, 29 pulsars have glitched at least 3 times. Table 1 , shows the median and the mean with standard deviation of pulsar parameters (timing and some derived) we studied with \(n>0 \text{a}\text{n}\text{d} n<0\) for a sample of pulsars where \(n\) can be estimated and for a subsample of pulsars that have glitched at least once. Table 1 is the average values (Table 1 a – median and 1b – mean with standard error) of the timing and derived parameters of various subsamples of pulsars. Table 1 suggest that glitching pulsars have lower values of \(n\) , and is it lower for subsample with \(n>0\) than for subsample with \(n<0\) . For pulsars with \(n0\) , the median value is for \(G=0, {n}_{med}={1.1\times 10}^{3}\) , for \(G\ge 1, {n}_{med}={4.6\times 10}^{1},\) for \(G\ge 3, {n}_{med}={4.1\times 10}^{1}\) . Table 1 a: The Median Values of Pulsar Parameters of Various Subsamples \(\varvec{\nu }\) \(\dot{\varvec{\nu }}\) \(\ddot{\varvec{\nu }}\) \(\varvec{n}\) \(\varvec{P}\) \(\dot{\varvec{P}}\) \(\varvec{D}\varvec{M}\) \(\varvec{R}\varvec{M}\) \({\varvec{S}}_{400}\) \({\varvec{S}}_{1400}\) All \(\varvec{n}0\) 2.3 -1.3E-14 5.8E-26 2.7E + 2 0.4 5.0E-15 102.7 10.1 13.5 1.4 \(\varvec{G}\ge 1\) \(\varvec{n}0\) 3.3 -6.6E-13 4.5E-24 4.6E + 1 0.3 4.4E-14 142.1 10.1 16.1 1.5 \(\varvec{G}\ge 3\) \(\varvec{n}0\) 6.9 -4.8E-12 1.5E-22 4.1E + 1 0.1 9.6E-14 194.2 5.3 25.1 1.2 \(\varvec{G}=0\) \(\varvec{n}0\) 1.9 -5.6E-15 1.9E-26 1. 1E + 3 0.5 2.6E-15 86.9 9.9 13.1 1.2 \(\varvec{D}\) \(\varvec{R}\) \({\varvec{R}}_{14}\) \(\varvec{\tau }\) \({\varvec{B}}_{\varvec{s}}\) \(\dot{\varvec{E}}\) \(\ddot{\varvec{E}}\) \({\varvec{P}}_{\varvec{T}}\) \({\varvec{V}}_{\varvec{T}}\) \({\varvec{B}}_{\varvec{L}\varvec{C}}\) All \(\varvec{n}0\) 3.3 90.6 15.2 2.0E + 6 1.7E + 12 1.4E + 33 2.1E + 32 17.1 214.9 123 \(\varvec{G}\ge 1\) \(\varvec{n}0\) 3.2 93.1 17.2 1.1E + 5 3.1E + 12 5.8E + 34 6.3E + 33 17.5 233.9 1115 \(\varvec{G}\ge 3\) \(\varvec{n}0\) 3.6 112.8 17.1 2.6E + 4 3.6E + 12 2.0E + 36 8.7E + 34 19.1 199.2 12000 \(\varvec{G}=0\) \(\varvec{n}0\) 3.5 88.1 13.9 4.7E + 06 1.3E + 12 6.6E + 32 5.6E + 31 17.1 211.8 57.2 Note : \(\varvec{\nu }\) is the frequency in Hz; \(\dot{\varvec{\nu }}\) is the first time-derivative of frequency in \({\varvec{s}}^{-2}\) ; \(\ddot{\varvec{\nu }}\) is the second time-derivative of frequency in \({\varvec{s}}^{-3}; \varvec{n}\) is the breaking index; \(\varvec{P}\) is the period in \(\varvec{s}\) ; \(\dot{\varvec{P}}\) is the first time-derivative of the period; \(\varvec{D}\varvec{M}\) is the dispersion measure in \({\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c}\) ; \(\varvec{R}\varvec{M}\) is the rotation measure in \(\varvec{r}\varvec{a}\varvec{d} {\varvec{m}}^{-2}\) ; \({\varvec{S}}_{400}\) is the mean flux density at 400 MHz in mJy; \({\varvec{S}}_{1400}\) is the mean flux density at 1400 MHz in mJy; \(\varvec{D}\) is the distance in kpc; \(\varvec{R}\) is the Radio luminosity at 400 MHz in mJy kpc 2 ; \({\varvec{R}}_{14}\) is the Radio luminosity at 1400 MHz in mJy kpc 2 ; \(\varvec{\tau }=\frac{\varvec{P}}{2\dot{\varvec{P}}}\) is the spin-down age in years; \({\varvec{B}}_{\varvec{s}}\) is the surface magnetic flux density in Gauss; \(\dot{\varvec{E}}\) is the spin down energy loss rate in ergs/s; \(\ddot{\varvec{E}}\) is the energy flux at the Sun in ergs/kpc 2 /s; \({\varvec{P}}_{\varvec{T}}\) is the total proper motion in mas/yr; \({\varvec{V}}_{\varvec{T}}\) is the transverse velocity - based on \(\varvec{D}\) in km/s; \({\varvec{B}}_{\varvec{L}\varvec{C}}\) is the magnetic field at light cylinder in Gauss; G is number of glitches. Table 1 b: The Mean Values of Pulsar Parameters of Various Subsamples \(\varvec{\nu }\) \(\dot{\varvec{\nu }}\) \(\ddot{\varvec{\nu }}\) \(\varvec{n}\) \(\varvec{P}\) \(\dot{\varvec{P}}\) \(\varvec{D}\varvec{M}\) \(\varvec{R}\varvec{M}\) \({\varvec{S}}_{400}\) \({\varvec{S}}_{1400}\) All \(\varvec{n}<0\) 31.2 \(\pm\) 50.3 -4.8 \(\pm\) 8.3E-13 -7.1 \(\pm\) 15.5E-22 -1.2 \(\pm\) 2.4E + 10 0.9 \(\pm\) 0.8 3.2 \(\pm\) 6.3E-12 158.8 \(\pm\) 138.8 -374.4 \(\pm\) 830.3 32.1 \(\pm\) 32.8 4.8 \(\pm\) 5.6 \(\varvec{n}>0\) 25.8 \(\pm\) 41.3 -4.6 \(\pm\) 7.9E-12 2.1 \(\pm\) 3.6E-22 4.6 \(\pm\) 9.1E + 7 0.7 \(\pm\) 0.5 1.4 \(\pm\) 2.3E-13 172.3 \(\pm\) 136.1 21.9 \(\pm\) 161.5 81.2 \(\pm\) 109.1 12.1 \(\pm\) 17.4 \(\varvec{G}\ge 1\) \(\varvec{n}0\) 6.1 \(\pm\) 4.8 -1.4 \(\pm\) 2.2E-11 5.5 \(\pm\) 9.0E-22 1.1 \(\pm\) 1.7E + 3 0.5 \(\pm\) 0.4 2.5 \(\pm\) 3.4E-13 216.9 \(\pm\) 158.7 28.2 \(\pm\) 184.2 161.1 \(\pm\) 246.2 22.3 \(\pm\) 35.4 \(\varvec{G}\ge 3\) \(\varvec{n}<0\) 4.9 \(\pm\) 3.5 -2.2 \(\pm\) 2.4E-12 -2.1 \(\pm\) 2.9E-22 -6.5 \(\pm\) 9.5E + 2 2.3 \(\pm\) 3.3 5.6 \(\pm\) 9.0E-12 281.2 \(\pm\) 193.2 -134.9 \(\pm\) 283.9 115.0 \(\pm\) 120.7 5.1 \(\pm\) 5.1 \(\varvec{n}>0\) 9.6 \(\pm\) 7.2 -2.8 \(\pm\) 3.9E-11 1.1 \(\pm\) 1.4E-21 9.9 \(\pm\) 11.1E + 1 0.3 \(\pm\) 0.2 2.5 \(\pm\) 2.8E-13 249.6 \(\pm\) 163.3 -5.2 \(\pm\) 263.3 421.3 \(\pm\) 627.7 51.3 \(\pm\) 86.1 \(G=0\) \(\varvec{n}0\) 33.6± 55.7 -7.8 13.1E-12 6.3E-23± 1.2E-22 6.5E + 7± 1.3E + 8 0.7± 0.5 9.9± 17.1E-13 154.7± 124.8 19.1± 151.6 53.8± 64.1 7.3± 9.8 \(\varvec{D}\) \(\varvec{R}\) \({\varvec{R}}_{14}\) \(\varvec{\tau }\) \({\varvec{B}}_{\varvec{s}}\) \(\dot{\varvec{E}}\) \(\ddot{\varvec{E}}\) \({\varvec{P}}_{\varvec{T}}\) \({\varvec{V}}_{\varvec{T}}\) \({\varvec{B}}_{\varvec{L}\varvec{C}}\) All \(\varvec{n}0\) 4.4± 2.7 539.5± 689.8 115.9± 163.6 7.5± 12.2E + 8 4.7± 5.3E + 12 4.7 ± 8.6E + 36 8.3 ± 15.2E + 36 29.4± 22.9 323.6± 227.9 2.5± 4.2E3 \(\varvec{G}\ge 1\) \(\varvec{n}0\) 4.9± 3.7 671.1± 889.8 142.0± 205.4 2.7± 4.1E + 6 5.5 ± 4.6E + 12 1.6 ± 2.8E + 37 2.7 ± 5.1E + 36 33.8± 25.5 333.6± 235.6 53.4± 87.1E3 \(\varvec{G}\ge 3\) \(\varvec{n}0\) 5.3± 4.1 827.2± 1098.5 248.6± 401.8 2.4± 3.3E + 5 5.6 ± 3.8E + 12 3.6 ± 6.1E + 37 7.1 ± 13.1E + 37 36.7± 29.5 264.2± 179.4 12.5± 19.2E4 \(G=0\) \(\varvec{n}0\) 4.2± 2.4 494.4± 617.9 104.0± 145.1 1.1± 1.6E + 8 4.4 5.4E + 12 2.± 3.7E + 35 3.1± 5.3E + 34 27.4± 21.3 319.2± 223.1 1.4± 2.3E4 Table 1 also suggests that the average value of pulsar rotational frequency seems higher for pulsars that have glitched once \(\varvec{\nu }=3.1 Hz \left(for n0\right)\) , and gets larger for more glitching pulsars (for pulsars with \(G\ge 3\) , \(\varvec{\nu }=4.1 Hz \left(for n0\right)\) as against when all the glitching pulsars in our sample were considered \(\varvec{\nu }=1.9 Hz \left(for n0\right)\) and \(\varvec{\nu }=1.9 Hz \left(for n0\right)\) – for completeness – for pulsars that have no record of glitching. It can be inferred from this analysis, that glitching increases the rotational frequency of pulsars, and pulsars with \(n>0\) appear to rotate faster than those with \(n<0\) . This trend is similar if the period derivative \(\dot{P},\) the absolute values of \(\dot{\nu }\) and \(\ddot{\nu }\) are considered Thus, one can infer the glitching in pulsars increases the values of the timing activity parameters and perhaps the magnitude of the timing noise associated with these parameters. Chukwude (2003) reported an exceptionally strong correlation between the magnitude of the observed second derivative of the pulse rotation frequency and phase residuals from 2nd-and 3rd-order polynomial models and conclude that standard timing technique, is reasonably contaminated by effects attributable to pulsar timing irregularity, implying that effective measurement of \(n\) is on how deterministic spin-down effects are decoupled from dominant timing activities. Carrying similar analysis for the derived parameters, the median values of the dispersion measure and rotation measure showed that pulsars with \(n>0\) or \(n<0\) are located in similar environment, though if we consider only glitching pulsars, the median value \(DM = 184.7 {\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c} and 205.5 {\varvec{c}\varvec{m}}^{-3} \varvec{p}\varvec{c}\) for \(n0\) for \(G=1\) and \(G=3\) respectively; a marginal difference. The median values of the mean flux density at 400 MHz ( \({\varvec{S}}_{400}\) ) and 1400 MHz ( \({\varvec{S}}_{1400}\) ) seems to suggest higher fluxes from pulsars with \(n0\) . This is also seen is the radio luminosity at measure 400 MHz and at 1400 MHz, while the reverse is the case for non-glitching pulsars. The median values of the characteristic age of pulsars indicate that non-glitching pulsars are older, and as G increases, the characteristic age of pulsars decreases, also for also the subsamples, the median characteristic age of pulsars indicates that pulsars with \(n0\) , while it appears that the surface magnetic field of pulsars with \(n>0\) are greater that those with \(n<\) 0, also, the median values of the magnetic field of glitching pulsars surface are greater than the median values of non-glitching pulsars in our sample. Table 1 indicates that the spin down energy loss rate, the energy flux at the Sun and the magnetic field at light cylinder are greater in glitching pulsars than non-glitching pulsars and are higher for pulsars with \(n>0\) than pulsars with \(n<0\) for all the subsamples. Furthermore, the median values of the total proper motion and the transverse velocity - based on \(D\) indicated that \({P}_{T}\) and \({V}_{T}\) follow similar trend in our subsamples, higher for pulsars with \(n0\) and increases as the number of glitches increases for each subsample. The estimated median value of the distance parameter \(D\) (kpc), seems to suggest that in glitching pulsars, pulsars with \(n0,\) (for \(G\ge 1\) , \(n0, D=3.2 kpc; \text{f}\text{o}\text{r} G\ge 3, n0, D=3.6 kpc,\) while for non-glitching pulsars, \(n0, D=3.5\) . We also investigated the seemingly trend observed in the distance \(D\) of pulsars using other distance measure e.g. the parallax ( \(PX\) ), the distance from the Galactic plane ( \(ZZ\) ), the \(X\) -distance in the \(X-Y-Z\) Galactic coordinate system and the \(Y\) -distance in the \(X-Y-Z\) Galactic coordinate system. The calculated median (we used absolute values, because we are interested in distances away from the galactic plane) values were shown in Table 2 . Table 2 seems to suggest that glitching pulsars exhibit more parallax than non-glitching pulsars (higher values of \(PX\) as \(G\) increases for both \(n>0\) and \(n0\) and \(n<0\) subsamples). The XX values indicate increasing values as G increases for pulsars with \(n0\) , while YY values showed decreasing values as G increases for both pulsars with \(n0\) . The median values of YY and ZZ are similar for both pulsars with \(n0\) , XX values of subsample with \(n0\) , while PX values are higher for subsample with \(n>0\) (similar trend was observed in the D parameter). Table 2 Average values of Distance parameters of various subsamples of pulsars in our sample PX abs ZZ abs XX abs YY PX abs ZZ abs XX abs YY mas kpc kpc kpc mas kpc kpc kpc \(n0\) ALL 0.29 0.19 1.41 6.89 0.28 0.14 1.55 6.62 \(G=0\) 0.24 0.24 1.07 6.94 0.23 0.20 1.74 6.62 \(G\ge 1\) 0.44 0.07 2.10 5.72 0.48 0.06 1.26 5.90 \(G\ge 3\) 1.20 0.03 2.21 4.81 2.21 0.04 1.11 5.07 Using the mean values, similar trends observed for the various subsamples with the median values were difficult to observe because of large standard errors associated with the mean values due to extreme large values measured or derived in pulsar parameters. We believe that the trends observed in the subsamples using the median values may be significant to pulsar research. Figure 1 is the distribution plot of \(\left|n\right|.\) The plot indicates that the distribution of all the subsamples are lognormal with the peak values of the subsamples with \(n>0\) generally less than the peak values of the subsamples with \(n<0\) . Table 3 shows the correlation coefficient results between the braking index and the timing/derived parameters of pulsars. It seems the values of braking indices of pulsars do not depend on any of the measured values of the timing parameters nor the derived parameters. Though the correlation coefficient result between the characteristic age of pulsars and the braking index of pulsars suggests an inverse relationship for pulsars with \(n0\) , this is simply due to the opposite signs in the values of breaking index. Using the absolute values, the correlation between \(\tau\) and \(\left|n\right|\) follow the similar trends for \(n0\) . Also, Table 3 shows that there is no correlation between braking index and pulsar’s glitch parameters for all the subsamples. This null correlation between \(n\) and pulsar parameters indicates that \(n\) values obtained by Eq. 2, may be affected by different factors (for instance, the difficulty in measuring \(\ddot{\nu }\) used in Eq. 2 to estimate \(n\) (Johnston and Galloway, 1999 ; Alpar and Baykal 2006 ); pulsar timing activities and timing effects \(\) (Chukwude, 2003; Chukwude, 2007 ; Zou et al., 2008 ; Hobbs et al., 2006 ); pulsars as SOCS (Melatos et al. 2008 ; Onuchukwu & Chukwude 2016 ) are expected to have random values of glitch parameters and randomness in timing noises parameters). We also plotted the scatter diagram of \({\text{log}}_{10}\left|n\right|\) and logarithm of the derived parameters. the log-log plots are shown in Figs. 2 –8. Table 3 Correlation Coefficient \(\varvec{n}<0\) \(\varvec{n}<0\) \(\varvec{n}<0\) \(\varvec{n}0\) \(\varvec{n}>0\) \(\varvec{n}>0\) \(\varvec{n}>0\) All \(\varvec{G}=0\) \(\varvec{G}\ge 1\) \(\varvec{G}\ge 3\) All \(\varvec{G}=0\) \(\varvec{G}\ge 1\) \(\varvec{G}\ge 3\) \(\varvec{n}/\varvec{G}\) 0.12 n/a 0.12 0.18 -0.16 n/a -0.16 -0.08 \(\varvec{n}/\varvec{P}\) 0.05 0.07 0.07 0.06 0.01 0.00 0.27 0.34 \(\varvec{n}/\dot{\varvec{P}}\) 0.01 0.01 0.07 0.08 -0.01 -0.01 -0.08 -0.13 \(\varvec{n}/\varvec{\nu }\) -0.11 -0.10 0.19 0.24 0.01 0.01 -0.16 -0.23 \(\varvec{n}/\dot{\varvec{\nu }}\) -0.01 -0.01 -0.14 -0.26 0.01 0.02 0.09 0.16 \(\varvec{n}/\ddot{\varvec{\nu }}\) -0.01 -0.01 -0.13 -0.14 -0.01 -0.01 -0.10 -0.16 \(\varvec{n}/\varvec{D}\varvec{M}\) 0.00 -0.01 0.16 0.13 0.17 0.23 -0.13 0.06 \(\varvec{n}/\varvec{R}\varvec{M}\) -0.03 -0.03 -0.14 -0.30 0.25 0.32 0.13 -0.23 \(\varvec{n}/{\varvec{S}}_{400}\) 0.05 0.05 0.25 0.49 -0.01 -0.02 -0.08 -0.05 \(\varvec{n}/{\varvec{S}}_{1400}\) 0.03 0.03 0.14 0.22 -0.01 -0.01 -0.04 0.19 \(\varvec{n}/\varvec{D}\) -0.06 -0.07 -0.75 -0.64 0.08 0.13 -0.08 -0.11 \(\varvec{n}/\varvec{R}\) 0.03 0.03 -0.86 -0.98 -0.03 -0.03 -0.09 0.83 \(\varvec{n}/{\varvec{R}}_{14}\) 0.03 0.03 -0.55 -0.01 0.01 0.02 -0.02 0.87 \(\varvec{n}/\varvec{\tau }\) -0.99 -0.99 -0.43 -0.88 0.15 0.15 0.65 0.94 \(\varvec{n}/{\varvec{B}}_{\varvec{s}}\) 0.01 0.01 0.08 0.08 -0.02 -0.02 -0.10 -0.08 \(\varvec{n}/\dot{\varvec{E}}\) 0.01 0.02 0.15 0.26 -0.01 -0.02 -0.07 -0.14 \(\varvec{n}/\ddot{\varvec{E}}\) 0.01 0.01 0.17 0.16 -0.01 -0.01 -0.06 -0.11 \(\varvec{n}/{\varvec{P}}_{\varvec{T}}\) 0.08 0.08 0.37 0.47 -0.06 -0.06 -0.14 0.02 \(\varvec{n}/{\varvec{V}}_{\varvec{T}}\) 0.09 0.09 0.20 0.74 -0.04 -0.04 -0.13 -0.35 \(\varvec{n}/{\varvec{B}}_{\varvec{L}\varvec{C}}\) 0.01 0.01 0.00 0.24 -0.01 -0.02 -0.07 -0.14 \(\varvec{n}/\varvec{\varDelta }\varvec{T}\) 0.09 -0.16 0.01 -0.09 \(\varvec{n}/\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) -0.11 -0.03 -0.05 0.03 \(\varvec{n}/\left|\varvec{\varDelta }\dot{\varvec{\nu }}/\dot{\varvec{\nu }}\right|\) -0.06 -0.01 -0.02 0.01 \(\varvec{\varDelta }\varvec{T}/\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) 0.05 0.00 0.01 -0.03 \(\varvec{\varDelta }\varvec{T}/\left|\varvec{\varDelta }\dot{\varvec{\nu }}/\dot{\varvec{\nu }}\right|\) -0.06 -0.03 -0.02 -0.03 Note : \(\varvec{\varDelta }\varvec{T}\) is the waiting time estimated for sources that have glitched for more than once; \(\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) is the magnitude of the glitch size in frequency; \(\left|\varvec{\varDelta }\dot{\varvec{\nu }}/\dot{\varvec{\nu }}\right|\) \(\left|\varvec{\varDelta }\varvec{\nu }/\varvec{\nu }\right|\) is the magnitude of the glitch size in first-time derivative of frequency. Figure 6 : Plot of log-log values of \({\varvec{P}}_{\varvec{T}}\) against \(\left|\varvec{n}\right|\) Figure 8: Plot of log-log values of \({\varvec{B}}_{\varvec{L}\varvec{C}}\) against \(\left|\varvec{n}\right|\) Figure 8 is the plot of log-log values of \({B}_{LC}\) against \(\left|n\right|\) . The plot indicates that on the average, the subsample with \(n>0, G\ge 1\) appear to have higher values of \({B}_{LC}\) than other subsamples. This was also indicated in Table 2 3. Conclusion We carried out a comparative study of pulsars parameters with breaking index \(n0\) where \(n\) was evaluated from Eq. 2, the median results showed a difference in the timing and observed parameters. Further classification into glitching and non-glitching pulsars indicated that glitching pulsars appear older than non-glitching pulsars and on the average lower values of \(\left|n\right|\) . We also observed differences in the various subsamples. The values of correlation coefficients suggest that the studied parameters suggest that the all the subsamples showed similar relations between braking index and the derived parameters as shown in Table 4 . Though the values of the slope of the linear fit may suggest differences in pulsar derived parameters of the subsample with \(n> 0\) and \(n< 0\) , the errors associated with the slopes are large enough to cancel out any supposed significant difference. Similarly, we performed multiple linear regression to the timing parameters ( \(\nu , \dot{\nu }, \ddot{\nu }\) ) of various subsamples. The log-log model should be \(\text{log}\left|n\right|=\text{log}\nu +\text{log}\ddot{\nu }-2\text{log}\dot{\nu }\) (from Eq. 2), but the fit to the data for various subsamples are shown in Table 5 . For the log-log model fits of various subsamples, the values of the constants are suggestive of some quantities that yet to be properly modeled in the timing analysis solution of pulsars. Using the observed values, the coefficients of \(\nu , \dot{\nu }, \ddot{\nu }\) in the regression model fit, suggest there exist some difference between glitching pulsars and non-glitching pulsars and some differences between subsamples with \(n0\) , it also suggest that the contributions of the values of \(\ddot{\nu }\) to the estimation of \(n\) are of the order zero for the various subsamples Table 4 linear fit to log-log relation between \(\left|n\right|\) and derived pulsar parameters \(n0, G=0\) \(\varvec{n}/\varvec{\tau }\) \(\text{log}\tau =\left(0.5\pm 0.7\right)\text{log}n+5.4\) \(\text{log}\tau =\left(0.5\pm 0.7\right)\text{log}n+5.5\) \(\varvec{n}/\varvec{B}\) \(\text{log}B=-\left(0.5\pm 0.7\right)\text{log}n+13.3\) \(\text{log}B=-\left(0.4\pm 0.8\right)\text{log}n+12.9\) \(\varvec{n}/\dot{\varvec{E}}\) \(\text{log}\dot{E}=\left(0.1\pm 1.1\right)\text{log}n+32.6\) \(\text{log}\dot{E}=-\left(0.2\pm 1.2\right)\text{log}n+32.6\) \(\varvec{n}/\ddot{\varvec{E}}\) \(\text{log}\ddot{E}=-\left(0.1\pm 1.3\right)\text{log}n+31.9\) \(\text{log}\ddot{E}=-\left(0.3\pm 1.3\right)\text{log}n+32.5\) \(\varvec{n}/{\varvec{P}}_{\varvec{T}}\) \(\text{log}{P}_{T}=\left(0.1\pm 0.4\right)\text{log}n+1.5\) \(\text{log}{P}_{T}=\left(0.1\pm 0.4\right)\text{log}n+1.6\) \(\varvec{n}/{\varvec{V}}_{\varvec{T}}\) \(\text{log}{V}_{T}=\left(0.1\pm 0.4\right)\text{log}n+2.3\) \(\text{log}{V}_{T}=-\left(0.1\pm 0.4\right)\text{log}n+2.5\) \(\varvec{n}/{\varvec{B}}_{\varvec{L}\varvec{C}}\) \(\text{log}{B}_{LC}=\left(0.2\pm 1.1\right)\text{log}n+1.1\) \(\text{log}{B}_{LC}=\left(0.1\pm 1.2\right)\text{log}n+1.7\) \(n0, G\ge 1\) \(\varvec{n}/\varvec{\tau }\) \(\text{log}\tau =-\left(0.1\pm 0.8\right)\text{log}n+5.1\) \(\text{log}\tau =\left(0.2\pm 0.6\right)\text{log}n+4.8\) \(\varvec{n}/\varvec{B}\) \(\text{log}B=\left(0.3\pm 0.9\right)\text{log}n+12.3\) \(\text{log}B=\left(0.1\pm 0.5\right)\text{log}n+12.8\) \(\varvec{n}/\dot{\varvec{E}}\) \(\text{log}\dot{E}=-\left(0.4\pm 1.3\right)\text{log}n+35.2\) \(\text{log}\dot{E}=-\left(0.6\pm 1.1\right)\text{log}n+36.5\) \(\varvec{n}/\ddot{\varvec{E}}\) \(\text{log}\ddot{E}=-\left(0.1\pm 1.6\right)\text{log}n+33.6\) \(\text{log}\ddot{E}=-\left(0.4\pm 1.2\right)\text{log}n+35.1\) \(\varvec{n}/{\varvec{P}}_{\varvec{T}}\) \(\text{log}{P}_{T}=-\left(0.1\pm 0.3\right)\text{log}n+1.3\) \(\text{log}{P}_{T}=-\left(0.1\pm 0.5\right)\text{log}n+1.4\) \(\varvec{n}/{\varvec{V}}_{\varvec{T}}\) \(\text{log}{V}_{T}=-\left(0.1\pm 0.5\right)\text{log}n+2.5\) \(\text{log}{V}_{T}=-\left(0.1\pm 0.5\right)\text{log}n+2.5\) \(\varvec{n}/{\varvec{B}}_{\varvec{L}\varvec{C}}\) \(\text{log}{B}_{LC}=-\left(0.4\pm 1.3\right)\text{log}n+3.6\) \(\text{log}{B}_{LC}=-\left(0.5\pm 0.9\right)\text{log}n+4.4\) \(n0, G\ge 3\) \(\varvec{n}/\varvec{\tau }\) \(\text{log}\tau =\left(0.1\pm 0.1\right)\text{log}n+5.7\) \(\text{log}\tau =-\left(0.1\pm 0.1\right)\text{log}n+5.2\) \(\varvec{n}/\varvec{B}\) \(\text{log}B=-\left(0.4\pm 0.5\right)\text{log}n+12.9\) \(\text{log}B=-\left(0.1\pm 0.4\right)\text{log}n+12.5\) \(\varvec{n}/\dot{\varvec{E}}\) \(\text{log}\dot{E}=\left(0.8\pm 0.9\right)\text{log}n+32.8\) \(\text{log}\dot{E}=\left(0.3\pm 0.7\right)\text{log}n+34.8\) \(\varvec{n}/\ddot{\varvec{E}}\) \(\text{log}\ddot{E}=\left(1.2\pm 1.6\right)\text{log}n+31.1\) \(\text{log}\ddot{E}=\left(0.4\pm 0.9\right)\text{log}n+33.6\) \(\varvec{n}/{\varvec{P}}_{\varvec{T}}\) \(\text{log}{P}_{T}=\left(0.1\pm 0.3\right)\text{log}n+0.9\) \(\text{log}{P}_{T}=\left(0.4\pm 0.2\right)\text{log}n+1.2\) \(\varvec{n}/{\varvec{V}}_{\varvec{T}}\) \(\text{log}{V}_{T}=-\left(0.3\pm 0.5\right)\text{log}n+2.5\) \(\text{log}{V}_{T}=-\left(0.1\pm 0.5\right)\text{log}n+2.5\) \(\varvec{n}/{\varvec{B}}_{\varvec{L}\varvec{C}}\) \(\text{log}{B}_{LC}=\left(0.8\pm 0.9\right)\text{log}n+1.5\) \(\text{log}{B}_{LC}=\left(0.2\pm 0.7\right)\text{log}n+3.1\) . Table 5 Multiple Regression Using Log Values of \(\left|n\right|, \nu , \dot{\nu }, \ddot{\nu }\) \(n0\) \(G\ge 1\) \(\text{log}n={\left(1.18\pm 5.75\right)\times 10}^{-3}+\text{log}\ddot{\nu }-2\text{log}\dot{\nu }+\text{log}\nu\) \(n0\) \(G=0\) \(\text{log}n=-{\left(3.19\pm 3.18\right)\times 10}^{-3}+\text{log}\ddot{\nu }-2\text{log}\dot{\nu }+\text{log}\nu\) Multiple Regression Using Normal Values of \(n, \nu , \dot{\nu }, \ddot{\nu }\) \(n0\) \(G\ge 1\) \(n=\left(1503.3\pm 491.3\right)-\left(2.59\pm 1.03\right){10}^{13}\dot{\nu }-\left(73.97\pm 63.89\right)\nu +\mathcal{O}\left(\ddot{\nu }\right)\) \(n\) 0 \(G=0\) \(n=\left(6.46\pm 6.03\right)\times {10}^{7}+\left(1.93\pm 11.22\right){10}^{19}\dot{\nu }+\left(4.49\pm 5.5.\right){10}^{5}\nu +\mathcal{O}\left(\ddot{\nu }\right)\) Conclusively, we have analyzed some timing and derived parameters of pulsars with \(n0\) , analysis of the results shows that there are some significant differences in some of the derived and timing parameters of glitching and non-glitching pulsars and in the subsamples with \(n0\) . Declarations Author Contribution This work was carried out in collaboration among all the authors. All the author contributed in writing, analyses and reviewing the manuscript. All authors read and approved the final manuscript References Alpar M. A., Baykal A., (2006) MNRAS 372, 489–496 Basu, A., Shaw, B., Antonopoulou,D., Keith,M. J., Lyne, A. G., Mickaliger, M. B., Stappers, B. W., Weltevrede, P., Jordan, C. A., (2022) MNRAS, Vol 510, 3, 4049–4062, doi.org/10.1093/mnras/stab3336 Camilo, F., Kaspi, V. M., Lyne, A. G., Manchester, R. N., Bell, J. F., N. D'Amico, N., McKay, N. P. F. and Crawford, F.. (2000), ApJ, 541, 367 Chukwude A. E., Baiden, A. A., Onuchukwu, C. C., (2010), A&A 515, A21 (2010) DOI: 10.1051/0004-6361/200911634 Chukwude, A. E. (2003), A&A, 406, 667 Chukwude, A. E. (2007), Chin. J. Astron. Astrophys. 7, 521 Cordes, J. M., & Downs, G. S. (1985), ApJS, 59, 343 D’Alessandro, F., McCulloch, P. M., Hamilton, P. A., & Deshpande, A. A. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3961027","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":273541132,"identity":"5b9b3b12-1610-45e3-a932-1d70e8656d88","order_by":0,"name":"Chika 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8","display":"","copyAsset":false,"role":"figure","size":40394,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3961027/v1/970d0b21464e7a97d3c7af85.png"},{"id":51382135,"identity":"cdc20372-e0b3-4a1b-ad17-b3959f45eb1c","added_by":"auto","created_at":"2024-02-20 16:15:23","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1196346,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3961027/v1/43779c84-ebcf-4085-94eb-3176975a5426.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Comparative Analysis of Parameters of Pulsars With Breaking Indices n\u003e0 and n\u003c0","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe braking index of pulsar, \u003cem\u003en\u003c/em\u003e, is the parameter which describes how the pulsar spin-down rate varies with its rotation frequency and it is fundamental to a better understanding of the pulsar electrodynamics (Yue et al. \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2007\u003c/span\u003e, Chukwude et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). The current understanding of pulsars is that they are rapidly rotating, highly magnetized neutron stars powered by their rotational kinetic energy (Goldreich \u0026amp; Julian \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e1969\u003c/span\u003e; Manchester \u0026amp; Taylor \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1977\u003c/span\u003e; Shapiro \u0026amp; Teukolsky \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e1983\u003c/span\u003e, Chukwude et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Onuchukwu \u0026amp; Chukwude \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The standard model of pulsar theory assumes that pure magnetic dipole radiation is the dominant process responsible for energy losses by pulsars (Pacini \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1967\u003c/span\u003e; Manchester \u0026amp; Taylor \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1977\u003c/span\u003e). In the standard model, the spin-down of a pulsar should follow a simple power-law relation between the spin frequency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(\\nu \\right)\\)\u003c/span\u003e\u003c/span\u003eand its first time-derivative \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(\\dot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003e given as (e.g. Manchester \u0026amp; Taylor \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e1977\u003c/span\u003e, Chukwude et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\dot{\\nu }=-k{\\nu }^{n}\\)\u003c/span\u003e \u003c/span\u003e 1\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(k\\)\u003c/span\u003e \u003c/span\u003e is a positive constant, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=3\\)\u003c/span\u003e\u003c/span\u003e is the braking index for pure magnetic dipole energy loss process. Differentiating Eq.\u0026nbsp;(1), and making \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e the subject, we have\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(n=\\frac{\\nu \\ddot{\\nu }}{{\\dot{\\nu }}^{2}}\\)\u003c/span\u003e \u003c/span\u003e 2\u003c/p\u003e \u003cp\u003eEquation (2) implies that once the second time derivative of a measured, pulsar\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e can be easily estimated. There are \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sim4170\\)\u003c/span\u003e\u003c/span\u003e known pulsars and only \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sim470\\)\u003c/span\u003e\u003c/span\u003e of the known pulsars have their values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e measured and are not given as zero (Manchester et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; ATNF pulsar catalogue, 2024). The values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e estimated for the pulsars with recorded values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e using Eq.\u0026nbsp;(2) ranges from \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(-2\\times {10}^{12}\\le n\\le 1.1\\times {10}^{11}\\)\u003c/span\u003e\u003c/span\u003e, with only \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\sim12\\)\u003c/span\u003e\u003c/span\u003ehaving\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(-3\\le n\\le 3.\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eJohnston and Galloway (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1999\u003c/span\u003e) suggested that it will take about hundreds of years of pulsar timing to get a better measurement of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e, since different effects tend to dominate the values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003eover that expected from spin-down alone. These effects include pulsars glitches and timing activities (Lyne et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e1988\u003c/span\u003e; Kaspi, et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e1994\u003c/span\u003e; Shemar \u0026amp; Lyne \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Lyne et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1996\u003c/span\u003e; Lyne \u0026amp; Graham-Smith \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1998\u003c/span\u003e; Camilo et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2000\u003c/span\u003e; Lorimer \u0026amp; Kramer, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Livingstone et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2006\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Hobbs, et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Chukwude et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) which lead to discontinuities in both frequency and first frequency time-derivative, making it very difficult to phase connect over the glitch and the recovery from a glitch in which the measurement of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e reflects the recovery rather than the intrinsic spin-down. Furthermore, the pulsar timing activities contaminate the deterministic spin parameters and the measurement of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e from pulsar timing seem most affected, perhaps due to its small values (Chukwude, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2007\u003c/span\u003e) and changes in the signs of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(+/-\\)\u003c/span\u003e\u003c/span\u003e), whereas \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e is always negative. Moreover, microglitches with all possible sign combination (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(+/+, +/-, -/-, -/+),\\)\u003c/span\u003e\u003c/span\u003e thus, are even difficult to understand (Cordes et al. 1988; D\u0026rsquo; Alessandro 1996, Chukwude et al. \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2010\u003c/span\u003e) and model, these add to the difficulties associated with estimating the true value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e. Melatos et al. (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2008\u003c/span\u003e) and Onuchukwu \u0026amp; Chukwude (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) assumed that glitches and microglicthes phenomena in pulsars may be interpreted in terms of self-organized critical state systems (SOCS), which show behaviors that are collective, scale invariant, discrete and randomly interaction dominated events. For such systems, like Johnston and Galloway (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1999\u003c/span\u003e), suggested, it may take hundreds of years for a reasonable value of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e to be measured.\u003c/p\u003e \u003cp\u003eConsequently, we want to statistically study pulsar parameters that have glitched at least once, whose \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e has been determined and breaking index using Eq.\u0026nbsp;(2) can be evaluated. This study we believe, will add to the general understanding of pulsars and whether the derived and timing parameters statistics of pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e are different from those with\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e"},{"header":"2. Data Analyses, Result and Discussion","content":"\u003cp\u003eThe data used for this study were obtained \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://www.jb.man.ac.uk/pulsar/glitches.html\u003c/span\u003e\u003cspan address=\"http://www.jb.man.ac.uk/pulsar/glitches.html\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e (Basu et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) and Manchester et al., (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2005\u003c/span\u003e - ATNF pulsar catalogue, 2024). There are 471 pulsars whose \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e were non-zero or given and thus, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e can be estimated from Eq.\u0026nbsp;(2), amongst 471 pulsars, 114 pulsars have record that it has glitched at least once, 56 pulsars have records that they have glitches at least 3 times or more. There were 275 pulsars that have \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, while 196 have \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e in our sample (both glitching and non-glitching pulsars). There are 36 pulsars that have glitched once in our sample \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e, among them only 15 have glitched at least 3 times; while there are 78 pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0,\\)\u003c/span\u003e\u003c/span\u003e among them, 29 pulsars have glitched at least 3 times. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e, shows the median and the mean with standard deviation of pulsar parameters (timing and some derived) we studied with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0 \\text{a}\\text{n}\\text{d} n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e for a sample of pulsars where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e can be estimated and for a subsample of pulsars that have glitched at least once. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e is the average values (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003ea \u0026ndash; median and 1b \u0026ndash; mean with standard error) of the timing and derived parameters of various subsamples of pulsars. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e suggest that glitching pulsars have lower values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e, and is it lower for subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e than for subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e. For pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e, the median value are - for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0, {n}_{med}={-2.7\\times 10}^{3}\\)\u003c/span\u003e\u003c/span\u003e, for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1, {n}_{med}={-1.8\\times 10}^{2},\\)\u003c/span\u003e\u003c/span\u003e for\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 3, {n}_{med}={-8.1\\times 10}^{1};\\)\u003c/span\u003e\u003c/span\u003eand for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, the median value is for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0, {n}_{med}={1.1\\times 10}^{3}\\)\u003c/span\u003e\u003c/span\u003e, for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1, {n}_{med}={4.6\\times 10}^{1},\\)\u003c/span\u003e\u003c/span\u003e for\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 3, {n}_{med}={4.1\\times 10}^{1}\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ea: The Median Values of Pulsar Parameters of Various Subsamples\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{P}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{P}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{400}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{1400}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eAll\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-4.6E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-1.4E-26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-1.4E\u0026thinsp;+\u0026thinsp;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.6E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e83.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e6.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e12.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e2.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-1.3E-14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e5.8E-26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.7E\u0026thinsp;+\u0026thinsp;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e5.0E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e102.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e10.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e13.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-4.0E-14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-3.3E-25\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-1.8E\u0026thinsp;+\u0026thinsp;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e6.1E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e184.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e7.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e20.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e2.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-6.6E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e4.5E-24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.6E\u0026thinsp;+\u0026thinsp;1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e4.4E-14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e142.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e10.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e16.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-6.0E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-1.0E-23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-8.1E\u0026thinsp;+\u0026thinsp;1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.7E-14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e205.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e23.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e27.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e2.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e6.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-4.8E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.5E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.1E\u0026thinsp;+\u0026thinsp;1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e9.6E-14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e194.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e5.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e25.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-2.4E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-1.1E-26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-2.7E\u0026thinsp;+\u0026thinsp;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.3E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e66.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e6.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e11.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e1.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-5.6E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.9E-26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1. 1E\u0026thinsp;+\u0026thinsp;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.6E-15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e86.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e9.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e13.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{R}}_{14}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\tau }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{s}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eAll\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e74.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e10.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e5.1E\u0026thinsp;+\u0026thinsp;6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.1E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e4.8E\u0026thinsp;+\u0026thinsp;32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e6.4E\u0026thinsp;+\u0026thinsp;31\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e14.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e167.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e53\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e90.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e15.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.0E\u0026thinsp;+\u0026thinsp;6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.7E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.4E\u0026thinsp;+\u0026thinsp;33\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e2.1E\u0026thinsp;+\u0026thinsp;32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e17.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e214.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e123\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e196.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e47.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e6.1E\u0026thinsp;+\u0026thinsp;5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.3E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e3.6E\u0026thinsp;+\u0026thinsp;33\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e1.9E\u0026thinsp;+\u0026thinsp;32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e22.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e365.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e306\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e93.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e17.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1.1E\u0026thinsp;+\u0026thinsp;5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e3.1E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e5.8E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e6.3E\u0026thinsp;+\u0026thinsp;33\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e17.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e233.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1115\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1184.0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e104.0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e6.3E\u0026thinsp;+\u0026thinsp;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e2.6E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.4E\u0026thinsp;+\u0026thinsp;35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e8.7E\u0026thinsp;+\u0026thinsp;33\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e34.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e715.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e3180\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e112.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e17.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.6E\u0026thinsp;+\u0026thinsp;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e3.6E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.0E\u0026thinsp;+\u0026thinsp;36\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e8.7E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e19.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e199.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e12000\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e66.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e8.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e8.7E\u0026thinsp;+\u0026thinsp;06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e9.5E\u0026thinsp;+\u0026thinsp;11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.5E\u0026thinsp;+\u0026thinsp;32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e4.3E\u0026thinsp;+\u0026thinsp;31\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e12.76\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e154.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e43.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e3.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e88.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e13.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.7E\u0026thinsp;+\u0026thinsp;06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.3E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e6.6E\u0026thinsp;+\u0026thinsp;32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e5.6E\u0026thinsp;+\u0026thinsp;31\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e17.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e211.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e57.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eNote\u003c/b\u003e: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the frequency in Hz;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the first time-derivative of frequency in\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{s}}^{-2}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the second time-derivative of frequency in\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{s}}^{-3}; \\varvec{n}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the breaking index;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{P}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the period in\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{s}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{P}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the first time-derivative of the period;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the dispersion measure in\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{c}\\varvec{m}}^{-3} \\varvec{p}\\varvec{c}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the rotation measure in\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{r}\\varvec{a}\\varvec{d} {\\varvec{m}}^{-2}\\)\u003c/span\u003e\u003c/span\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{400}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the mean flux density at 400 MHz in mJy;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{1400}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the mean flux density at 1400 MHz in mJy;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the distance in kpc;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the Radio luminosity at 400 MHz in mJy kpc\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{R}}_{14}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the Radio luminosity at 1400 MHz in mJy kpc\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\tau }=\\frac{\\varvec{P}}{2\\dot{\\varvec{P}}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the spin-down age in years;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{s}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the surface magnetic flux density in Gauss;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the spin down energy loss rate in ergs/s;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the energy flux at the Sun in ergs/kpc\u003c/b\u003e\u003csup\u003e\u003cb\u003e2\u003c/b\u003e\u003c/sup\u003e\u003cb\u003e/s;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the total proper motion in mas/yr;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the transverse velocity - based on\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003ein km/s;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the magnetic field at light cylinder in Gauss; G is number of glitches.\u003c/b\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eb: The Mean Values of Pulsar Parameters of Various Subsamples\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"12\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{P}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{P}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{400}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{1400}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eAll\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e31.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e50.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-4.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e8.3E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-7.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e15.5E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-1.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.4E\u0026thinsp;+\u0026thinsp;10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e0.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e3.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e6.3E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e158.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e138.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e-374.4\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e830.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e32.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e32.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e4.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e25.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e41.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-4.6\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e7.9E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e2.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.6E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.6\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.1E\u0026thinsp;+\u0026thinsp;7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.7\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.4\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.3E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e172.3\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e136.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e21.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e161.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e81.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e109.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e12.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e17.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e5.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-2.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.0E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-8.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.5E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-8.5\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e10.1E\u0026thinsp;+\u0026thinsp;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.2E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e228.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e150.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e47.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e216.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e46.1\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e44.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e4.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e6.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e4.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-1.4\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.2E-11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e5.5\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.0E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.7E\u0026thinsp;+\u0026thinsp;3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e0.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.5\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.4E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e216.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e158.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e28.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e184.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e161.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e246.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e22.3\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e35.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-2.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.4E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-2.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.9E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-6.5\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.5E\u0026thinsp;+\u0026thinsp;2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e2.3\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e5.6\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.0E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e281.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e193.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e-134.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e283.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e115.0\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e120.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e5.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e9.6\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e7.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-2.8\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.9E-11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e1.1\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.4E-21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e9.9\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e11.1E\u0026thinsp;+\u0026thinsp;1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.3\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e0.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.5\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.8E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e249.6\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e163.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e-5.2\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e263.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e421.3\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e627.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e51.3\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e86.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e37.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e59.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-1.3\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.2E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-8.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e17.1E-21\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-1.5E\u0026thinsp;+\u0026thinsp;10\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.9E\u0026thinsp;+\u0026thinsp;10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.8\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e0.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e3.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e7.1E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e144.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e131.0\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e-475.1\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1014.\u0026plusmn;4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e30.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e30.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e5.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e6.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e33.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e55.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-7.8\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e13.1E-12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e6.3E-23\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.2E-22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e6.5E\u0026thinsp;+\u0026thinsp;7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.3E\u0026thinsp;+\u0026thinsp;8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e0.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e9.9\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e17.1E-13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e154.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e124.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e19.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e151.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e53.8\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e64.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e7.3\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{D}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{R}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{R}}_{14}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\tau }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{s}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cb\u003eAll\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e426.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e565.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e60.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e73.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e9.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e19.1E\u0026thinsp;+\u0026thinsp;10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e2.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.9E\u0026thinsp;+\u0026thinsp;13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.5\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.6E\u0026thinsp;+\u0026thinsp;35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e3.2\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.6E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e25.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e20.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e263.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e183.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e7.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e12.1E3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e539.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e689.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e115.9\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e163.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e7.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e12.2E\u0026thinsp;+\u0026thinsp;8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e4.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.3E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e4.7\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e8.6E\u0026thinsp;+\u0026thinsp;36\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e8.3\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e15.2E\u0026thinsp;+\u0026thinsp;36\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e29.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e22.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e323.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e227.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e2.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e4.2E3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e5.3\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e1027.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1233.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e84.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e76.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e4.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.8E\u0026thinsp;+\u0026thinsp;6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e3.8\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e6.4E\u0026thinsp;+\u0026thinsp;13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e6.6\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.9E\u0026thinsp;+\u0026thinsp;35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e4.1\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e6.1E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e36.3\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e24.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e487.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e279.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e6.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e9.4E3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.9\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e671.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e889.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e142.0\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e205.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e4.1E\u0026thinsp;+\u0026thinsp;6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e5.5\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e4.6E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e1.6\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.8E\u0026thinsp;+\u0026thinsp;37\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e2.7\u003c/b\u003e\u0026plusmn;\u003c/p\u003e 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colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e5.9\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e2277.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2235.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e106.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e81.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e6.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e8.2E\u0026thinsp;+\u0026thinsp;5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.1\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.7E\u0026thinsp;+\u0026thinsp;14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e5.9\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e6.8E\u0026thinsp;+\u0026thinsp;35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e5.6\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e7.1E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e85.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e72.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e607.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e219.7\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e6.9\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e7.5E3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e5.3\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e4.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e827.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1098.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e248.6\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e401.8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e2.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.3E\u0026thinsp;+\u0026thinsp;5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e5.6\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.8E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e3.6\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e6.1E\u0026thinsp;+\u0026thinsp;37\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e7.1\u003c/b\u003e\u0026plusmn;\u003c/p\u003e \u003cp\u003e\u003cb\u003e13.1E\u0026thinsp;+\u0026thinsp;37\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e36.7\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e29.5\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e264.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e179.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e12.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e19.2E4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.0\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e341.8\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e451.2\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e54.5\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e70.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1.2\u0026thinsp;\u0026plusmn;\u0026thinsp;2.3E\u0026thinsp;+\u0026thinsp;10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e1.8\u0026thinsp;\u0026plusmn;\u0026thinsp;3.2E\u0026thinsp;+\u0026thinsp;13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.7\u0026thinsp;\u0026plusmn;\u0026thinsp;4.6E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e3.1\u0026thinsp;\u0026plusmn;\u0026thinsp;5.5E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e23.9\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e19.6\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e223.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e146.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e7.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e12.7E3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e4.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e494.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e617.9\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e104.0\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e145.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e1.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e1.6E\u0026thinsp;+\u0026thinsp;8\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e4.4\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.4E\u0026thinsp;+\u0026thinsp;12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e2.\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e3.7E\u0026thinsp;+\u0026thinsp;35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e3.1\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e5.3E\u0026thinsp;+\u0026thinsp;34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e\u003cb\u003e27.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e21.3\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c11\"\u003e \u003cp\u003e\u003cb\u003e319.2\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e223.1\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c12\"\u003e \u003cp\u003e\u003cb\u003e1.4\u0026plusmn;\u003c/b\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003e2.3E4\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e also suggests that the average value of pulsar rotational frequency seems higher for pulsars that have glitched once \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }=3.1 Hz \\left(for n\u0026lt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }=3.3 Hz\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(for n\u0026gt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e, and gets larger for more glitching pulsars (for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 3\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }=4.1 Hz \\left(for n\u0026lt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(6.9 Hz\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(for n\u0026gt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e as against when all the glitching pulsars in our sample were considered \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }=1.9 Hz \\left(for n\u0026lt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }=2.3 Hz\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(for n\u0026gt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\nu }=1.9 Hz \\left(for n\u0026lt;0 and n\u0026gt;0\\right)\\)\u003c/span\u003e\u003c/span\u003e \u0026ndash; for completeness \u0026ndash; for pulsars that have no record of glitching. It can be inferred from this analysis, that glitching increases the rotational frequency of pulsars, and pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e appear to rotate faster than those with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e. This trend is similar if the period derivative \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{P},\\)\u003c/span\u003e\u003c/span\u003e the absolute values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\dot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e are considered\u003c/p\u003e \u003cp\u003eThus, one can infer the glitching in pulsars increases the values of the timing activity parameters and perhaps the magnitude of the timing noise associated with these parameters. Chukwude (2003) reported an exceptionally strong correlation between the magnitude of the observed second derivative of the pulse rotation frequency and phase residuals from 2nd-and 3rd-order polynomial models and conclude that standard timing technique, is reasonably contaminated by effects attributable to pulsar timing irregularity, implying that effective measurement of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e is on how deterministic spin-down effects are decoupled from dominant timing activities.\u003c/p\u003e \u003cp\u003eCarrying similar analysis for the derived parameters, the median values of the dispersion measure and rotation measure showed that pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e or \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003eare located in similar environment, though if we consider only glitching pulsars, the median value \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DM = 184.7 {\\varvec{c}\\varvec{m}}^{-3} \\varvec{p}\\varvec{c} and 205.5 {\\varvec{c}\\varvec{m}}^{-3} \\varvec{p}\\varvec{c}\\)\u003c/span\u003e\u003c/span\u003e for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003efor \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=1and G=3\\)\u003c/span\u003e\u003c/span\u003e respectively; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(DM = 142.1 {\\varvec{c}\\varvec{m}}^{-3} \\varvec{p}\\varvec{c} and 194.2 {\\varvec{c}\\varvec{m}}^{-3} \\varvec{p}\\varvec{c}\\)\u003c/span\u003e\u003c/span\u003e for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=1\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=3\\)\u003c/span\u003e\u003c/span\u003e respectively; a marginal difference. The median values of the mean flux density at 400 MHz (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{400}\\)\u003c/span\u003e\u003c/span\u003e) and 1400 MHz (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{S}}_{1400}\\)\u003c/span\u003e\u003c/span\u003e) seems to suggest higher fluxes from pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e than pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e. This is also seen is the radio luminosity at measure 400 MHz and at 1400 MHz, while the reverse is the case for non-glitching pulsars. The median values of the characteristic age of pulsars indicate that non-glitching pulsars are older, and as G increases, the characteristic age of pulsars decreases, also for also the subsamples, the median characteristic age of pulsars indicates that pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e are older than pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, while it appears that the surface magnetic field of pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e are greater that those with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;\\)\u003c/span\u003e\u003c/span\u003e 0, also, the median values of the magnetic field of glitching pulsars surface are greater than the median values of non-glitching pulsars in our sample. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e1\u003c/span\u003e indicates that the spin down energy loss rate, the energy flux at the Sun and the magnetic field at light cylinder are greater in glitching pulsars than non-glitching pulsars and are higher for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e than pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e for all the subsamples. Furthermore, the median values of the total proper motion and the transverse velocity - based on \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D\\)\u003c/span\u003e\u003c/span\u003e indicated that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({P}_{T}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({V}_{T}\\)\u003c/span\u003e\u003c/span\u003e follow similar trend in our subsamples, higher for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e than pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e and increases as the number of glitches increases for each subsample.\u003c/p\u003e \u003cp\u003eThe estimated median value of the distance parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D\\)\u003c/span\u003e\u003c/span\u003e (kpc), seems to suggest that in glitching pulsars, pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e are located in greater distances than pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0,\\)\u003c/span\u003e\u003c/span\u003e (for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0, D=4.2 kpc, n\u0026gt;0, D=3.2 kpc; \\text{f}\\text{o}\\text{r} G\\ge 3, n\u0026lt;0, D=4.5 kpc, n\u0026gt;0, D=3.6 kpc,\\)\u003c/span\u003e\u003c/span\u003e while for non-glitching pulsars, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0, D=3.2 kpc kpc, n\u0026gt;0, D=3.5\\)\u003c/span\u003e\u003c/span\u003e. We also investigated the seemingly trend observed in the distance\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(D\\)\u003c/span\u003e\u003c/span\u003e of pulsars using other distance measure e.g. the parallax (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(PX\\)\u003c/span\u003e\u003c/span\u003e), the distance from the Galactic plane (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(ZZ\\)\u003c/span\u003e\u003c/span\u003e), the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X\\)\u003c/span\u003e\u003c/span\u003e-distance in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X-Y-Z\\)\u003c/span\u003e\u003c/span\u003e Galactic coordinate system and the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(Y\\)\u003c/span\u003e\u003c/span\u003e-distance in the \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(X-Y-Z\\)\u003c/span\u003e\u003c/span\u003e Galactic coordinate system. The calculated median (we used absolute values, because we are interested in distances away from the galactic plane) values were shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e seems to suggest that glitching pulsars exhibit more parallax than non-glitching pulsars (higher values of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(PX\\)\u003c/span\u003e\u003c/span\u003e as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\)\u003c/span\u003e\u003c/span\u003e increases for both \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e subsamples), while non-glitching pulsars and are at larger distances above or below the Galactic plane than the glitching pulsars (lower values of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(ZZ\\)\u003c/span\u003e\u003c/span\u003e as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\)\u003c/span\u003e\u003c/span\u003e increases for both \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e subsamples). The XX values indicate increasing values as G increases for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e, but decreases as G increases for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, while YY values showed decreasing values as G increases for both pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e. The median values of YY and ZZ are similar for both pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, XX values of subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e are higher than those of the subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, while PX values are higher for subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e (similar trend was observed in the D parameter).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAverage values of Distance parameters of various subsamples of pulsars in our sample\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePX\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eabs ZZ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eabs XX\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eabs YY\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePX\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eabs ZZ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eabs XX\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eabs YY\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emas\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003ekpc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ekpc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ekpc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003emas\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003ekpc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003ekpc\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003ekpc\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c9\" namest=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eALL\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.28\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.55\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e6.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e6.62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e4.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e5.07\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eUsing the mean values, similar trends observed for the various subsamples with the median values were difficult to observe because of large standard errors associated with the mean values due to extreme large values measured or derived in pulsar parameters. We believe that the trends observed in the subsamples using the median values may be significant to pulsar research.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e is the distribution plot of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|.\\)\u003c/span\u003e\u003c/span\u003e The plot indicates that the distribution of all the subsamples are lognormal with the peak values of the subsamples with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e generally less than the peak values of the subsamples with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the correlation coefficient results between the braking index and the timing/derived parameters of pulsars. It seems the values of braking indices of pulsars do not depend on any of the measured values of the timing parameters nor the derived parameters. Though the correlation coefficient result between the characteristic age of pulsars and the braking index of pulsars suggests an inverse relationship for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and a direct relation for pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, this is simply due to the opposite signs in the values of breaking index. Using the absolute values, the correlation between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\tau\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e follow the similar trends for \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e. Also, Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows that there is no correlation between braking index and pulsar\u0026rsquo;s glitch parameters for all the subsamples. This null correlation between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003eand pulsar parameters indicates that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e values obtained by Eq.\u0026nbsp;2, may be affected by different factors (for instance, the difficulty in measuring \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e used in Eq.\u0026nbsp;2 to estimate \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e (Johnston and Galloway, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Alpar and Baykal \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2006\u003c/span\u003e); pulsar timing activities and timing effects \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\)\u003c/span\u003e\u003c/span\u003e(Chukwude, 2003; Chukwude, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2007\u003c/span\u003e; Zou et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Hobbs et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2006\u003c/span\u003e); pulsars as SOCS (Melatos et al. \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2008\u003c/span\u003e; Onuchukwu \u0026amp; Chukwude \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) are expected to have random values of glitch parameters and randomness in timing noises parameters). We also plotted the scatter diagram of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{log}}_{10}\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e and logarithm of the derived parameters. the log-log plots are shown in Figs.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;8.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCorrelation Coefficient\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eAll\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003eAll\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{G}\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{G}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003en/a\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.12\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.18\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003en/a\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{P}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.07\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.07\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.27\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.34\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\dot{\\varvec{P}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.07\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{\\nu }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e-0.11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.19\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\dot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\ddot{\\varvec{\\nu }}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{D}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.17\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{R}\\varvec{M}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.30\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.25\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.32\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.23\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{S}}_{400}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.25\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.49\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{S}}_{1400}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.22\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.19\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{D}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e-0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.07\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.75\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.64\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{R}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.86\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.98\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.83\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{R}}_{14}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.55\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.87\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{\\tau }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e-0.99\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e-0.99\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.43\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.88\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.65\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.94\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{B}}_{\\varvec{s}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.10\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.15\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.26\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.07\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.17\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.08\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.37\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.47\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.20\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.74\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.04\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.13\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.35\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.24\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.07\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.14\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{\\varDelta }\\varvec{T}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.16\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.09\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\left|\\varvec{\\varDelta }\\varvec{\\nu }/\\varvec{\\nu }\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.11\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\left|\\varvec{\\varDelta }\\dot{\\varvec{\\nu }}/\\dot{\\varvec{\\nu }}\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\varDelta }\\varvec{T}/\\left|\\varvec{\\varDelta }\\varvec{\\nu }/\\varvec{\\nu }\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e0.05\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e0.00\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e0.01\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\varDelta }\\varvec{T}/\\left|\\varvec{\\varDelta }\\dot{\\varvec{\\nu }}/\\dot{\\varvec{\\nu }}\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cb\u003e-0.06\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e\u003cb\u003e-0.02\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e\u003cb\u003e-0.03\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003e\u003cb\u003eNote\u003c/b\u003e: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{\\varDelta }\\varvec{T}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the waiting time estimated for sources that have glitched for more than once;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|\\varvec{\\varDelta }\\varvec{\\nu }/\\varvec{\\nu }\\right|\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the magnitude of the glitch size in frequency;\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|\\varvec{\\varDelta }\\dot{\\varvec{\\nu }}/\\dot{\\varvec{\\nu }}\\right|\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|\\varvec{\\varDelta }\\varvec{\\nu }/\\varvec{\\nu }\\right|\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eis the magnitude of the glitch size in first-time derivative of frequency.\u003c/b\u003e\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e6\u003c/span\u003e: \u003cb\u003ePlot of log-log values of\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eagainst\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|\\varvec{n}\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure\u0026nbsp;8: Plot of log-log values of\u003c/b\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e \u003cb\u003eagainst\u003c/b\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|\\varvec{n}\\right|\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003cp\u003eFigure 8 is the plot of log-log values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{LC}\\)\u003c/span\u003e\u003c/span\u003e against \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e. The plot indicates that on the average, the subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0, G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e appear to have higher values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({B}_{LC}\\)\u003c/span\u003e\u003c/span\u003e than other subsamples. This was also indicated in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u003c/p\u003e"},{"header":"3. Conclusion","content":"\u003cp\u003eWe carried out a comparative study of pulsars parameters with breaking index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003e was evaluated from Eq.\u0026nbsp;2, the median results showed a difference in the timing and observed parameters. Further classification into glitching and non-glitching pulsars indicated that glitching pulsars appear older than non-glitching pulsars and on the average lower values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e. We also observed differences in the various subsamples. The values of correlation coefficients suggest that the studied parameters suggest that the all the subsamples showed similar relations between braking index and the derived parameters as shown in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Though the values of the slope of the linear fit may suggest differences in pulsar derived parameters of the subsample with\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt; 0\\)\u003c/span\u003e\u003c/span\u003eand \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt; 0\\)\u003c/span\u003e\u003c/span\u003e, the errors associated with the slopes are large enough to cancel out any supposed significant difference.\u003c/p\u003e \u003cp\u003eSimilarly, we performed multiple linear regression to the timing parameters (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\nu , \\dot{\\nu }, \\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e) of various subsamples. The log-log model should be \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\left|n\\right|=\\text{log}\\nu +\\text{log}\\ddot{\\nu }-2\\text{log}\\dot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e (from Eq.\u0026nbsp;2), but the fit to the data for various subsamples are shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e5\u003c/span\u003e. For the log-log model fits of various subsamples, the values of the constants are suggestive of some quantities that yet to be properly modeled in the timing analysis solution of pulsars. Using the observed values, the coefficients of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\nu , \\dot{\\nu }, \\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e in the regression model fit, suggest there exist some difference between glitching pulsars and non-glitching pulsars and some differences between subsamples with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, it also suggest that the contributions of the values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e to the estimation of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\\)\u003c/span\u003e\u003c/span\u003eare of the order zero for the various subsamples\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003elinear fit to log-log relation between \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e and derived pulsar parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0, G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0, G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{\\tau }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\tau =\\left(0.5\\pm 0.7\\right)\\text{log}n+5.4\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\tau =\\left(0.5\\pm 0.7\\right)\\text{log}n+5.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{B}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}B=-\\left(0.5\\pm 0.7\\right)\\text{log}n+13.3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}B=-\\left(0.4\\pm 0.8\\right)\\text{log}n+12.9\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\dot{E}=\\left(0.1\\pm 1.1\\right)\\text{log}n+32.6\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\dot{E}=-\\left(0.2\\pm 1.2\\right)\\text{log}n+32.6\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\ddot{E}=-\\left(0.1\\pm 1.3\\right)\\text{log}n+31.9\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\ddot{E}=-\\left(0.3\\pm 1.3\\right)\\text{log}n+32.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{P}_{T}=\\left(0.1\\pm 0.4\\right)\\text{log}n+1.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{P}_{T}=\\left(0.1\\pm 0.4\\right)\\text{log}n+1.6\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{V}_{T}=\\left(0.1\\pm 0.4\\right)\\text{log}n+2.3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{V}_{T}=-\\left(0.1\\pm 0.4\\right)\\text{log}n+2.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{B}_{LC}=\\left(0.2\\pm 1.1\\right)\\text{log}n+1.1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{B}_{LC}=\\left(0.1\\pm 1.2\\right)\\text{log}n+1.7\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0, G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0, G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{\\tau }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\tau =-\\left(0.1\\pm 0.8\\right)\\text{log}n+5.1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\tau =\\left(0.2\\pm 0.6\\right)\\text{log}n+4.8\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{B}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}B=\\left(0.3\\pm 0.9\\right)\\text{log}n+12.3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}B=\\left(0.1\\pm 0.5\\right)\\text{log}n+12.8\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\dot{E}=-\\left(0.4\\pm 1.3\\right)\\text{log}n+35.2\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\dot{E}=-\\left(0.6\\pm 1.1\\right)\\text{log}n+36.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\ddot{E}=-\\left(0.1\\pm 1.6\\right)\\text{log}n+33.6\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\ddot{E}=-\\left(0.4\\pm 1.2\\right)\\text{log}n+35.1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{P}_{T}=-\\left(0.1\\pm 0.3\\right)\\text{log}n+1.3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{P}_{T}=-\\left(0.1\\pm 0.5\\right)\\text{log}n+1.4\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{V}_{T}=-\\left(0.1\\pm 0.5\\right)\\text{log}n+2.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{V}_{T}=-\\left(0.1\\pm 0.5\\right)\\text{log}n+2.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{B}_{LC}=-\\left(0.4\\pm 1.3\\right)\\text{log}n+3.6\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{B}_{LC}=-\\left(0.5\\pm 0.9\\right)\\text{log}n+4.4\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0, G\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0, G\\ge 3\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{\\tau }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\tau =\\left(0.1\\pm 0.1\\right)\\text{log}n+5.7\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\tau =-\\left(0.1\\pm 0.1\\right)\\text{log}n+5.2\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\varvec{B}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}B=-\\left(0.4\\pm 0.5\\right)\\text{log}n+12.9\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}B=-\\left(0.1\\pm 0.4\\right)\\text{log}n+12.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\dot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\dot{E}=\\left(0.8\\pm 0.9\\right)\\text{log}n+32.8\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\dot{E}=\\left(0.3\\pm 0.7\\right)\\text{log}n+34.8\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/\\ddot{\\varvec{E}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\ddot{E}=\\left(1.2\\pm 1.6\\right)\\text{log}n+31.1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}\\ddot{E}=\\left(0.4\\pm 0.9\\right)\\text{log}n+33.6\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{P}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{P}_{T}=\\left(0.1\\pm 0.3\\right)\\text{log}n+0.9\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{P}_{T}=\\left(0.4\\pm 0.2\\right)\\text{log}n+1.2\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{V}}_{\\varvec{T}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{V}_{T}=-\\left(0.3\\pm 0.5\\right)\\text{log}n+2.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{V}_{T}=-\\left(0.1\\pm 0.5\\right)\\text{log}n+2.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\varvec{n}/{\\varvec{B}}_{\\varvec{L}\\varvec{C}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{B}_{LC}=\\left(0.8\\pm 0.9\\right)\\text{log}n+1.5\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}{B}_{LC}=\\left(0.2\\pm 0.7\\right)\\text{log}n+3.1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eMultiple Regression Using Log Values of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|, \\nu , \\dot{\\nu }, \\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}n={\\left(4.11\\pm 77.71\\right)\\times 10}^{-3}+\\text{log}\\ddot{\\nu }-2\\text{log}\\dot{\\nu }+\\text{log}\\nu\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}n={\\left(1.18\\pm 5.75\\right)\\times 10}^{-3}+\\text{log}\\ddot{\\nu }-2\\text{log}\\dot{\\nu }+\\text{log}\\nu\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}n={\\left(2.59\\pm 3.76\\right)\\times 10}^{-3}+\\text{log}\\ddot{\\nu }-2\\text{log}\\dot{\\nu }+\\text{log}\\nu\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\text{log}n=-{\\left(3.19\\pm 3.18\\right)\\times 10}^{-3}+\\text{log}\\ddot{\\nu }-2\\text{log}\\dot{\\nu }+\\text{log}\\nu\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colspan=\"3\" nameend=\"c3\" namest=\"c1\"\u003e \u003cp\u003eMultiple Regression Using Normal Values of\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n, \\nu , \\dot{\\nu }, \\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=-\\left(1172.11\\pm 393.15\\right)-\\left(2.82\\pm 4.39\\right){10}^{13}\\dot{\\nu }-\\left(53.14\\pm 51.55\\right)\\nu +\\mathcal{O}\\left(\\ddot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G\\ge 1\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=\\left(1503.3\\pm 491.3\\right)-\\left(2.59\\pm 1.03\\right){10}^{13}\\dot{\\nu }-\\left(73.97\\pm 63.89\\right)\\nu +\\mathcal{O}\\left(\\ddot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=-\\left(8.91\\pm 13.41\\right)\\times {10}^{9}-\\left(1.60\\pm 1.26\\right){10}^{8}\\nu +\\mathcal{O}\\left(\\dot{\\nu }\\right)+\\mathcal{O}\\left(\\ddot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;\\)\u003c/span\u003e\u003c/span\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(G=0\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n=\\left(6.46\\pm 6.03\\right)\\times {10}^{7}+\\left(1.93\\pm 11.22\\right){10}^{19}\\dot{\\nu }+\\left(4.49\\pm 5.5.\\right){10}^{5}\\nu +\\mathcal{O}\\left(\\ddot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eConclusively, we have analyzed some timing and derived parameters of pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, analysis of the results shows that there are some significant differences in some of the derived and timing parameters of glitching and non-glitching pulsars and in the subsamples with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eThis work was carried out in collaboration among all the authors. All the author contributed in writing, analyses and reviewing the manuscript. All authors read and approved the final manuscript\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAlpar M. A., Baykal A., (2006) MNRAS 372, 489\u0026ndash;496 \u003c/li\u003e\n\u003cli\u003eBasu, A., Shaw, B., Antonopoulou,D., Keith,M. J., Lyne, A. G., Mickaliger, M. B., Stappers, B. W., Weltevrede, P., Jordan, C. A., (2022) MNRAS, Vol 510, 3, 4049\u0026ndash;4062, doi.org/10.1093/mnras/stab3336\u003c/li\u003e\n\u003cli\u003eCamilo, F., Kaspi, V. M., Lyne, A. G., Manchester, R. N., Bell, J. F., N. D\u0026apos;Amico, N., McKay, N. P. F. and Crawford, F.. (2000), ApJ, 541, 367\u003c/li\u003e\n\u003cli\u003eChukwude A. E., Baiden, A. A., Onuchukwu, C. C., (2010), A\u0026amp;A 515, A21 (2010) DOI: 10.1051/0004-6361/200911634\u003c/li\u003e\n\u003cli\u003eChukwude, A. E. (2003), A\u0026amp;A, 406, 667\u003c/li\u003e\n\u003cli\u003eChukwude, A. E. (2007), Chin. J. Astron. Astrophys. 7, 521\u003c/li\u003e\n\u003cli\u003eCordes, J. M., \u0026amp; Downs, G. S. (1985), ApJS, 59, 343\u003c/li\u003e\n\u003cli\u003eD\u0026rsquo;Alessandro, F., McCulloch, P. M., Hamilton, P. A., \u0026amp; Deshpande, A. A. (1995), MNRAS, 277, 1033\u003c/li\u003e\n\u003cli\u003eGoldreich, P., \u0026amp; Julian, W. H. (1969), ApJ, 157, 869\u003c/li\u003e\n\u003cli\u003eHobbs, G., Lyne, A. G., \u0026amp; Kramer, M. (2006), Chin. J. Astron. Astrophys. 6, 169\u003c/li\u003e\n\u003cli\u003eJohnston, S., \u0026amp; Galloway, D. (1999), MNRAS, 306, L50\u003c/li\u003e\n\u003cli\u003eKaspi, V. M., Manchester, R. N., Siegman, B., Johnston. S., Lyne, A. G., (1994), ApJ, 422, L83\u003c/li\u003e\n\u003cli\u003eLivingstone, M. A., Kaspi, V. M., Gavriil, F. P., Kaspi, V. M. Livingstone, M. A., Wood, P. M. (2007), Ap\u0026amp;SS, 308, 317\u003c/li\u003e\n\u003cli\u003eLivingstone, M. A., Kaspi, V. M., Gotthelf, E. V., \u0026amp; Kuiper, L. (2006), ApJ, 647, 1286\u003c/li\u003e\n\u003cli\u003eLorimer, D., \u0026amp; Kramer, M. (2005), Handbook of Pulsar Astronomy (Cambridge University Press)\u003c/li\u003e\n\u003cli\u003eLyne, A. G., \u0026amp; Graham-Smith, F. (1998), Pulsar Astronomy (Cambridge University Press)\u003c/li\u003e\n\u003cli\u003eLyne, A. G., Pritchard, R. S., \u0026amp; Smith, F. G. (1988), MNRAS, 233, 667\u003c/li\u003e\n\u003cli\u003eLyne, A. G., Pritchard, R. S., Graham-Smith, F., \u0026amp; Camilo, F. (1996), Nature, 381, 497\u003c/li\u003e\n\u003cli\u003eManchester, R. N., \u0026amp; Taylor, J. H. (1977), Pulsars (San Francisco: Freeman)\u003c/li\u003e\n\u003cli\u003eManchester, R. N., Hobbs, G.B., Teoh, A. \u0026amp; Hobbs, M., (2005) AJ, 129, 1993-2006 \u003c/li\u003e\n\u003cli\u003eMelatos, A., Peralta, C., \u0026amp; Wyithe, J. S. B. (2008), ApJ, 672, 1103 \u003c/li\u003e\n\u003cli\u003eOnuchukwu, C. C. \u0026amp; Chukwude, A. 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Y., 2008, MNRAS, 384, 106 doi.org/10.1111/j.1365-2966.2010.16272.x \u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"astrophysics-and-space-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"astr","sideBox":"Learn more about [Astrophysics and Space Science](https://www.springer.com/journal/10509)","snPcode":"10509","submissionUrl":"https://submission.nature.com/new-submission/10509/3","title":"Astrophysics and Space Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"pulsar: general, Method: Data Analysis - Statistical, Glitches","lastPublishedDoi":"10.21203/rs.3.rs-3961027/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3961027/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe analyzed the timing parameters (the rotational frequency \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\nu\\)\u003c/span\u003e\u003c/span\u003e, the first \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(\\dot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003eand second \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left(\\ddot{\\nu }\\right)\\)\u003c/span\u003e\u003c/span\u003e time-derivative of frequency) and the derived parameters of a sample of pulsars that have their values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\ddot{\\nu }\\)\u003c/span\u003e\u003c/span\u003e (470 pulsars) recorded in the Australian Telescope National Facility (ATNF) pulsar catalogue. We formed various subsamples, those with breaking index \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e, glitching and non-glitching pulsars. Our statistical analyses of the timing and derived parameters indicated some level of differences and similarities in the parameters analyzed. Glitching pulsars appear to have higher rotational frequency of pulsars than non-glitching pulsars, and pulsars with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e appear to rotate faster than those with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e. Our results also suggest that glitching pulsars have lower values of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e (where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\left|n\\right|\\)\u003c/span\u003e\u003c/span\u003e is the absolute value of breaking index), and is it lower for subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026gt;0\\)\u003c/span\u003e\u003c/span\u003e than for subsample with \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(n\u0026lt;0\\)\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e","manuscriptTitle":"Comparative Analysis of Parameters of Pulsars With Breaking Indices n\u0026gt;0 and n\u0026lt;0","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-02-20 16:07:14","doi":"10.21203/rs.3.rs-3961027/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-03-15T09:15:31+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-03-13T04:24:08+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"79357ddb-0549-480f-b2c2-5545ed1a622f","date":"2024-02-20T08:55:31+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-02-20T04:04:12+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-02-18T18:41:11+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-02-17T07:03:44+00:00","index":"","fulltext":""},{"type":"submitted","content":"Astrophysics and Space Science","date":"2024-02-16T11:09:20+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"astrophysics-and-space-science","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"astr","sideBox":"Learn more about [Astrophysics and Space Science](https://www.springer.com/journal/10509)","snPcode":"10509","submissionUrl":"https://submission.nature.com/new-submission/10509/3","title":"Astrophysics and Space Science","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"97190f48-19c5-4d60-ae1e-d3a934b77639","owner":[],"postedDate":"February 20th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-05-13T17:02:57+00:00","versionOfRecord":[],"versionCreatedAt":"2024-02-20 16:07:14","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-3961027","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3961027","identity":"rs-3961027","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}