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Journal articles on the topic 'Parity equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 16 February 2022

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1

Gertler, Janos, Xiaowen Fang, Qiang Luo, and Mark Costin. "Direct Identification of Structured Parity Equations." IFAC Proceedings Volumes 27, no. 8 (July 1994): 1057–62. http://dx.doi.org/10.1016/s1474-6670(17)47848-7.

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2

Gertler, J. J., and R. Monajemy. "Generating Directional Residuals with Dynamic Parity Equations *." IFAC Proceedings Volumes 26, no. 2 (July 1993): 507–12. http://dx.doi.org/10.1016/s1474-6670(17)48318-2.

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3

Noh, Taewan, Warren F. Miller, and Jim E. Morel. "The Even-Parity and Simplified Even-Parity Transport Equations in Two-Dimensionalx-yGeometry." Nuclear Science and Engineering 123, no. 1 (May 1996): 38–56. http://dx.doi.org/10.13182/nse96-a24211.

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4

Puig, Vicenç, and Joseba Quevedo. "Passive robust fault detection using fuzzy parity equations." Mathematics and Computers in Simulation 60, no. 3-5 (September 2002): 193–207. http://dx.doi.org/10.1016/s0378-4754(02)00014-9.

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5

Gertler, J., Q. Luo, K. Anderson, and Xiaowen Fang. "Diagnosis of Plant Failures Using Orthogonal Parity Equations." IFAC Proceedings Volumes 23, no. 8 (August 1990): 361–66. http://dx.doi.org/10.1016/s1474-6670(17)51850-9.

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6

Ballé, Peter. "Fuzzy-model-based parity equations for fault isolation." Control Engineering Practice 7, no. 2 (February 1999): 261–70. http://dx.doi.org/10.1016/s0967-0661(98)00152-x.

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7

NASRI, M. H. FATHI, J. FRANCE, N. E. ODONGO, S. LOPEZ, A. BANNINK, and E. KEBREAB. "Modelling the lactation curve of dairy cows using the differentials of growth functions." Journal of Agricultural Science 146, no. 6 (November 21, 2008): 633–41. http://dx.doi.org/10.1017/s0021859608008101.

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SUMMARYDescriptions of entire lactations were investigated using six mathematical equations, comprising the differentials of four growth functions (logistic, Gompertz, Schumacher and Morgan) and two other equations (Wood and Dijkstra). The data contained monthly milk yield records from 70 first, 70 second and 75 third parity Iranian Holstein cows. Indicators of fit were model behaviour, statistical evaluation and biologically meaningful parameter estimates and lactation features. Analysis of variance with equation, parity and their interaction as factors and with cows as replicates was performed to compare goodness of fit of the equations. The interaction of equation and parity was not significant for any statistics, which showed that there was no tendency for one equation to fit a given parity better than other equations. Although model behaviour analysis showed better performance of growth functions than the Wood and Dijkstra equations in fitting the individual lactation curves, statistical evaluation revealed that there was no significant difference between the goodness of fit of the different equations. Evaluation of lactation features showed that the Dijkstra equation was able to estimate the initial milk yield and peak yield more accurately than the other equations. Overall evaluation of the different equations demonstrated the potential of the differentials of simple empirical growth functions used in the current study as equations for fitting monthly milk records of Holstein dairy cattle.

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8

Wilkey, Andrew, Joseph Suelzer, Yogesh Joglekar, and Gautam Vemuri. "Parity–Time Symmetry in Bidirectionally Coupled Semiconductor Lasers." Photonics 6, no. 4 (November 27, 2019): 122. http://dx.doi.org/10.3390/photonics6040122.

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We report on the numerical analysis of intensity dynamics of a pair of mutually coupled, single-mode semiconductor lasers that are operated in a configuration that leads to features reminiscent of parity–time symmetry. Starting from the rate equations for the intracavity electric fields of the two lasers and the rate equations for carrier inversions, we show how these equations reduce to a simple 2 × 2 effective Hamiltonian that is identical to that of a typical parity–time (PT)-symmetric dimer. After establishing that a pair of coupled semiconductor lasers could be PT-symmetric, we solve the full set of rate equations and show that despite complicating factors like gain saturation and nonlinearities, the rate equation model predicts intensity dynamics that are akin to those in a PT-symmetric system. The article describes some of the advantages of using semiconductor lasers to realize a PT-symmetric system and concludes with some possible directions for future work on this system.

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9

Höfling, T. "Detection of Parameter Variations by Continuous-Time Parity Equations." IFAC Proceedings Volumes 26, no. 2 (July 1993): 513–18. http://dx.doi.org/10.1016/s1474-6670(17)48319-4.

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10

Candau, José, Luís Javier de Miguel, and Javier García Ruiz. "Controller Reconfiguration System Using Parity Equations and Fuzzy Logic." IFAC Proceedings Volumes 30, no. 18 (August 1997): 1249–54. http://dx.doi.org/10.1016/s1474-6670(17)42568-7.

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11

Rappel, Wouter-Jan, and Hermann Riecke. "Parity breaking in directional solidification: Numerics versus amplitude equations." Physical Review A 45, no. 2 (January 1, 1992): 846–59. http://dx.doi.org/10.1103/physreva.45.846.

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12

Mimura, N., S. Isojima, M. Murata, and J. Satsuma. "Singularity confinement test for ultradiscrete equations with parity variables." Journal of Physics A: Mathematical and Theoretical 42, no. 31 (July 13, 2009): 315206. http://dx.doi.org/10.1088/1751-8113/42/31/315206.

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13

Poullet, Pascal, Edès Destyl, and Silvere Paul Nuiro. "Critical blowup in coupled Parity-Time-symmetric nonlinear Schrödinger equations." AIMS Mathematics 2, no. 1 (2017): 195–206. http://dx.doi.org/10.3934/math.2017.1.195.

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14

Dias, João-Paulo, Mário Figueira, Vladimir V. Konotop, and Dmitry A. Zezyulin. "Supercritical Blowup in Coupled Parity-Time-Symmetric Nonlinear Schrödinger Equations." Studies in Applied Mathematics 133, no. 4 (September 15, 2014): 422–40. http://dx.doi.org/10.1111/sapm.12063.

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15

Blesa, J., P. Jiménez, D. Rotondo, F. Nejjari, and V. Puig. "Fault Diagnosis of a Wind Farm using Interval Parity Equations." IFAC Proceedings Volumes 47, no. 3 (2014): 4322–27. http://dx.doi.org/10.3182/20140824-6-za-1003.00792.

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16

Miller, E. G., L. Huber, C. L. Levesque, and C. F. M. de Lange. "Accuracy of predicting chemical body composition of gilts and sows." Canadian Journal of Animal Science 98, no. 3 (September 1, 2018): 597–602. http://dx.doi.org/10.1139/cjas-2017-0061.

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Physical and chemical body composition of gilts and parity 3 sows were used to determine current prediction equation accuracy and propose alternative prediction equations that incorporate additional variables. Longissimus dorsi muscle depth and parity can be combined with body weight and backfat to improve gilt and sow body composition prediction.

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17

PÁLMAI, TAMÁS, MIKLÓS HORVÁTH, and BARNABÁS APAGYI. "SEMI-ANALYTIC EQUATIONS TO THE COX–THOMPSON INVERSE SCATTERING METHOD AT FIXED ENERGY FOR SPECIAL CASES." Modern Physics Letters B 22, no. 23 (September 10, 2008): 2191–99. http://dx.doi.org/10.1142/s0217984908016972.

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Solution of the Cox–Thompson inverse scattering problem at fixed energy1–3 is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered.

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18

GERASYUTA, S. M., and V. I. KOCHKIN. "NEGATIVE PARITY TETRAQUARKS WITH THE OPEN CHARM." International Journal of Modern Physics E 20, no. 10 (October 2011): 2153–66. http://dx.doi.org/10.1142/s0218301311020204.

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The relativistic four-quark equations are found in the framework of coupled-channel formalism. The dynamical mixing of the meson–meson states with the four-quark states is considered. The four-quark amplitudes of the negative parity tetraquarks including the quarks of three flavors (u, d, s) and the charmed quark are constructed. The poles of these amplitudes determine the masses of tetraquarks. The mass values of low-lying tetraquarks with the spin-parity JP = 0-, 1-, 2-, 3- are calculated.

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19

Schwarte, A., and R. Isermann. "NEURAL NETWORK APPLICATIONS FOR MODEL BASED FAULT DETECTION WITH PARITY EQUATIONS." IFAC Proceedings Volumes 35, no. 1 (2002): 205–10. http://dx.doi.org/10.3182/20020721-6-es-1901.01502.

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20

Höfling, T., and R. Isermann. "Fault detection based on adaptive parity equations and single-parameter tracking." Control Engineering Practice 4, no. 10 (October 1996): 1361–69. http://dx.doi.org/10.1016/0967-0661(96)00146-3.

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21

SZCZACHOR, MICHAŁ. "SUPERSYMMETRIC HOLST ACTION WITH MATTER COUPLING AND PARITY VIOLATION." International Journal of Geometric Methods in Modern Physics 09, no. 06 (August 3, 2012): 1261015. http://dx.doi.org/10.1142/s0219887812610154.

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A general construction of the Holst action is discussed. Based on this, the N = 1, 2, 4, 8 supergravities and N = 1 supergravities with matter coupling are presented. It is shown that in all these cases the Immirzi parameter does not influence the field equations. The construction ensures that the theory is invariant under supersymmetry as well as gauge transformations, but the Holst extension breaks parity.

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22

Poenaru, R., and A. A. Raduta. "Parity partner bands in 163Lu: A novel approach for describing the negative parity states from a triaxial super-deformed band." International Journal of Modern Physics E 30, no. 05 (May 2021): 2150033. http://dx.doi.org/10.1142/s0218301321500336.

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The wobbling spectrum of [Formula: see text]Lu is described through a novel approach, starting from a triaxial rotor model within a semi-classical picture, and obtaining a new set of equations for all four rotational bands that have wobbling character. Redefining the band structure in the present model is done by adopting the concepts of Signature Partner Bands and Parity Partner Bands. Indeed, describing a wobbling spectrum in an even–odd nucleus through signature and parity quantum numbers is an inedited interpretation of the triaxial super-deformed bands.

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23

Hötling, Thomas, and Rolf Isermann. "Adaptive Parity Equations and Advanced Parameter Estimation for Fault Detection and Diagnosis." IFAC Proceedings Volumes 29, no. 1 (June 1996): 6377–82. http://dx.doi.org/10.1016/s1474-6670(17)58704-2.

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24

Höfling, Thomas, Rüdiger Deibert, and Oliver Hecker. "Fault Detection of Flowrate and Temperature Control Loops using Estimated Parity Equations." IFAC Proceedings Volumes 28, no. 12 (June 1995): 193–98. http://dx.doi.org/10.1016/s1474-6670(17)45421-8.

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25

Seydou, Ramatou, Tarek Raïssi, Ali Zolghadri, Denis Efimov, and Christophe Combastel. "Robust Fault Diagnosis based on Constraint Satisfaction and Interval Continuous-time Parity Equations." IFAC Proceedings Volumes 45, no. 20 (January 2012): 1293–98. http://dx.doi.org/10.3182/20120829-3-mx-2028.00256.

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26

Sumisławska, Małgorzata, Tomasz Larkowski, and Keith J. Burnham. "Parity equations-based unknown input reconstruction for MIMO stochastic systems with an application." International Journal of Control 87, no. 2 (September 17, 2013): 410–21. http://dx.doi.org/10.1080/00207179.2013.838700.

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27

Sandberg, Richard D. "An axis treatment for flow equations in cylindrical coordinates based on parity conditions." Computers & Fluids 49, no. 1 (October 2011): 166–72. http://dx.doi.org/10.1016/j.compfluid.2011.05.009.

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28

Xie, Jiaquan, Xing Zhu, and Yingji He. "Vector solitons in nonlinear fractional Schrödinger equations with parity-time-symmetric optical lattices." Nonlinear Dynamics 97, no. 2 (June 19, 2019): 1287–94. http://dx.doi.org/10.1007/s11071-019-05048-9.

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29

Zhang, Hai-Qiang, and Min Gao. "Rational soliton solutions in the parity-time-symmetric nonlocal coupled nonlinear Schrödinger equations." Communications in Nonlinear Science and Numerical Simulation 63 (October 2018): 253–60. http://dx.doi.org/10.1016/j.cnsns.2018.02.029.

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30

ANDREOZZI, F., F. KNAPP, N. LO IUDICE, A. PORRINO, and J. KVASIL. "A NEW EQUATION OF MOTION METHOD FOR MULTIPHONON NUCLEAR SPECTRA." International Journal of Modern Physics E 18, no. 04 (April 2009): 944–50. http://dx.doi.org/10.1142/s0218301309013087.

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A method which generates a multiphonon basis through the construction and the iterative solution of a set of equations of motion is adopted to investigate the negative parity spectrum and the structure of the giant dipole resonance in 16 O .

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31

Matskevich, Elena. "Bottom (70,1-) baryon multiplet." E3S Web of Conferences 164 (2020): 01008. http://dx.doi.org/10.1051/e3sconf/202016401008.

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The aim of this paper is to derive systems of equations for the amplitudes for the case of negative parity (70,1-) bottom nonstrange baryons and to calculate the masses of these particles. In order to calculate masses of (70,1-) bottom baryons we use the relativistic quark model. The relativistic three-quark equations of the (70,1-) bottom baryon multiplet are derived in the framework of the dispersion relation technique. The relativistic three-quark equations of the (70,1-) bottom baryon multiplet are derived. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitude are obtained. The masses of 21 baryons are predicted.

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32

Hindes, Wade. "Rational points on certain families of symmetric equations." International Journal of Number Theory 11, no. 06 (August 26, 2015): 1821–38. http://dx.doi.org/10.1142/s1793042115500797.

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We generalize the work of Dem'janenko and Silverman for the Fermat quartics, effectively determining the rational points on the curves x2m + axm + aym + y2m = b whenever the ranks of some companion hyperelliptic Jacobians are at most one. As an application, we explicitly describe Xd(ℚ) for certain d ≥ 3, where Xd : Td(x) + Td(y) = 1 and Td is the monic Chebychev polynomial of degree d. Moreover, we show how this later problem relates to orbit intersection problems in dynamics. Finally, we construct a new family of genus 3 curves which break the Hasse principle, assuming the parity conjecture, by specifying our results to quadratic twists of x4 - 4x2 - 4y2 + y4 = -6.

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33

Myung, Yun Soo, and De-Cheng Zou. "Black holes in Gauss–Bonnet and Chern–Simons-scalar theory." International Journal of Modern Physics D 28, no. 09 (July 2019): 1950114. http://dx.doi.org/10.1142/s0218271819501141.

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We carry out the stability analysis of the Schwarzschild black hole in Gauss–Bonnet and Chern–Simons-scalar theory. Here, we introduce two quadratic scalar couplings ([Formula: see text]) to Gauss–Bonnet and Chern–Simons terms, where the former term is parity-even, while the latter one is parity-odd. The perturbation equation for the scalar [Formula: see text] is the Klein–Gordon equation with an effective mass, while the perturbation equation for [Formula: see text] is coupled to the parity-odd metric perturbation, providing a system of two coupled equations. It turns out that the Schwarzschild black hole is unstable against [Formula: see text] perturbation, leading to scalarized black holes, while the black hole is stable against [Formula: see text] and metric perturbations, implying no scalarized black holes.

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34

Fox, William P. "Discrete Combat Models." International Journal of Operations Research and Information Systems 1, no. 1 (January 2010): 16–34. http://dx.doi.org/10.4018/joris.2010101302.

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Lanchester’s equations and their solutions, as continuous differential equations, have been studied for years. This article introduces a new approach with the use of the discrete form of Lanchester’s equations, using dynamical systems or difference equations. It begins with Lanchester’s square law and develops a generalized analytical solution for the discrete model that can be built by knowing only the kill rates and the initial force sizes of the combatants. It then forms the condition of parity (a draw) to develop a simple relationship of these variables to determine who wins the engagement. This article illustrates these models and their solutions using historic combat examples. It also illustrates that current counter-insurgency combat models can be built and solved using various forms of difference equations.

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35

GERASYUTA, S. M., and E. E. MATSKEVICH. "CHARMED (70, 1-) BARYON MULTIPLET." International Journal of Modern Physics E 17, no. 04 (April 2008): 585–610. http://dx.doi.org/10.1142/s0218301308010027.

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The masses of negative parity (70, 1-) charmed nonstrange baryons are calculated in the relativistic quark model. The relativistic three-quark equations of the (70, 1-) charmed baryon multiplet are found in the framework of the dispersion relation technique. The approximate solutions of these equations using the method based on the extraction of leading singularities of the amplitude are obtained. The calculated mass values of the (70, 1-) charmed baryons are in good agreement with the experimental data.

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36

GUNARATNE, GEMUNU H., MOHAMED EL-HAMDI, MICHAEL GORMAN, and KAY A. ROBBINS. "ASYMMETRIC CELLS AND ROTATING RINGS IN CELLULAR FLAMES." Modern Physics Letters B 10, no. 28 (December 10, 1996): 1379–87. http://dx.doi.org/10.1142/s0217984996001553.

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Theoretical analysis and experimental results are presented to demonstrate the universal characteristics of parity-breaking bifurcations for pattern-forming systems in a circular domain. Ordered patterns of concentric rings of cells which form in a premixed flame on a circular burner at low pressure are used to demonstrate these ideas. Cells belonging to stationary rings are symmetric, while those of rotating rings are not. The important characteristics of the experimental results are reproduced in a theoretical model which can be numerically integrated in polar coordinates. Normal form equations for the Fourier–Bessel coefficients of this model lead to parity breaking.

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37

HOSSEIN-ZADEH, N. GHAVI. "Comparison of non-linear models to describe the lactation curves of milk yield and composition in Iranian Holsteins." Journal of Agricultural Science 152, no. 2 (July 29, 2013): 309–24. http://dx.doi.org/10.1017/s0021859613000415.

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SUMMARYIn order to describe the lactation curves of milk yield (MY) and composition, six non-linear mathematical equations (Wood, Dhanoa, Sikka, Nelder, Hayashi and Dijkstra) were used. Data were 5 535 995 test-day records for MY, fat (FC) and protein (PC) contents and somatic cell score (SCS) from the first three lactations of Iranian Holstein cows that were collected on 2547 dairy herds in the period from 2000 to 2011 by the Animal Breeding Center of Iran. Each model was fitted to monthly production records of dairy cows using the NLIN and MODEL procedures in SAS and the parameters were estimated. The models were tested for goodness of fit using root-mean-square error (RMSE), Durbin–Watson statistic (DW) and Akaike's information criterion (AIC). The Wood and Dhanoa models provided the best fit of the lactation curve for MY in the first and second parities due to the lower values of RMSE and AIC than other models; but the Dijkstra model showed the best fit of milk lactation curve for third-parity dairy cows, FC, PC and SCS in the first three parities because of the lowest values of RMSE and AIC. Also, In general, the Sikka model did not fit the production data as well as the other equations. The results showed that the Dijkstra equation was able to estimate the time to the peak and peak MY more accurately than the other equations. However, the Wood equation provided more accurate predictions of peak MY at second- and third parities than the other equations. For first lactation FC, the Dijkstra equation was able to estimate the minimum FC and for second- and third-parity FC, the Wood equation provided more accurate predictions of minimum FC. For first- and second-lactation PC, the Dijkstra equation was able to estimate the minimum PC but for third parity, the minimum value of PC was predicted more accurately by the Wood model. The Dhanoa and Dijkstra equations for first lactation SCS and the Dhanoa equation for second- and third- lactation SCS were able to estimate the minimum SCS more accurately than the other equations. Overall, evaluation of different equations used in the current study indicated the potential of the non-linear functions for fitting monthly productive records of Holstein cows.

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38

FERREIRA, P. LEAL, and A. P. GALEÃO. "SOLUTIONS FOR THE TWO-BODY DIRAC EQUATION WITH PHENOMENOLOGICAL INTERACTIONS." Modern Physics Letters A 05, no. 30 (December 10, 1990): 2523–30. http://dx.doi.org/10.1142/s0217732390002936.

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Solutions for the relativistic two-body Dirac equation with an enlarged class of phenomenological potentials including several Breit-type terms are investigated for the general case of unequal masses. The solutions corresponding to definite total angular momentum and parity are shown to fall into two classes, each being obtained by solving a system of four coupled first order differential equations. The reduction of this system to a pair of coupled Schrödinger-type equations and the particular case of equal masses are also discussed.

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39

Guerra, Pedro, and Vicenç Puig. "Passive Robust Fault Detection using Interval MA Parity Equations: Inverse vs Direct Image Tests." IFAC Proceedings Volumes 41, no. 2 (2008): 4523–28. http://dx.doi.org/10.3182/20080706-5-kr-1001.00761.

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40

Beckerle, Philipp, Hendrik Schaede, Norman Butzek, and Stephan Rinderknecht. "Balancing filters: An approach to improve model-based fault diagnosis based on parity equations." Mechanical Systems and Signal Processing 29 (May 2012): 137–47. http://dx.doi.org/10.1016/j.ymssp.2011.12.004.

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41

des Noes, Mathieu, Valentin Savin, Laurent Ros, and Jean-Marc Brossier. "Selection of Parity Check Equations For the Iterative Message-Passing Detection of M-Sequences." IEEE Transactions on Communications 65, no. 8 (August 2017): 3214–25. http://dx.doi.org/10.1109/tcomm.2017.2706724.

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42

Shilkov, A. V. "Evenand odd-parity kinetic equations of particle transport. 3: Finite analytic scheme on tetrahedra." Mathematical Models and Computer Simulations 7, no. 5 (September 2015): 409–29. http://dx.doi.org/10.1134/s2070048215050117.

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43

Miller, Warren F. "An Analysis of the Finite Differenced, Even-Parity, Discrete Ordinates Equations in Slab Geometry." Nuclear Science and Engineering 108, no. 3 (July 1991): 247–66. http://dx.doi.org/10.13182/nse91-a23823.

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44

Chung, Won Sang, and Hassan Hassanabadi. "Dunkl–Maxwell equation and Dunkl-electrostatics in a spherical coordinate." Modern Physics Letters A 36, no. 18 (June 14, 2021): 2150127. http://dx.doi.org/10.1142/s0217732321501273.

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This paper deals with Maxwell equations with Dunkl derivatives. Dunkl-deformed gauge transform is investigated. Dunkl-electrostatics in spherical coordinates is also studied. The multi-pole expansion of potential is obtained for even and odd potential for parity in z-direction. The conducting sphere in a uniform electric field in Dunkl-electrostatics is also discussed.

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45

Obukhov, Yuri N. "Exact Solutions in Poincaré Gauge Gravity Theory." Universe 5, no. 5 (May 24, 2019): 127. http://dx.doi.org/10.3390/universe5050127.

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In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion.

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46

HO, FEI-HUNG, and JAMES M. NESTER. "POINCARÉ GAUGE THEORY WITH COUPLED EVEN AND ODD PARITY DYNAMIC SPIN-0 MODES: DYNAMICAL EQUATIONS FOR ISOTROPIC BIANCHI COSMOLOGIES." International Journal of Modern Physics D 20, no. 11 (October 19, 2011): 2125–38. http://dx.doi.org/10.1142/s0218271811020391.

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We are investigating the dynamics of a new Poincaré gauge theory of gravity model, which has cross coupling between the spin-0+ and spin-0- modes. To this end we here consider a very appropriate situation — homogeneous-isotropic cosmologies — which is relatively simple, and yet all the modes have nontrivial dynamics which reveals physically interesting and possibly observable results. More specifically we consider manifestly isotropic Bianchi class A cosmologies; for this case we find an effective Lagrangian and Hamiltonian for the dynamical system. The Lagrange equations for these models lead to a set of first-order equations that are compatible with those found for the FLRW models and provide a foundation for further investigations. Typical numerical evolution of these equations shows the expected effects of the cross parity coupling.

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47

BERGMANN, OTTO, and P. N. RAYCHOWDHURY. "SYMMETRICAL TREATMENT OF ELECTRON AND NUCLEAR MOTIONS IN M. BORN’S THEORY OF IDEAL CRYSTALS." Reviews in Mathematical Physics 01, no. 04 (January 1989): 497–504. http://dx.doi.org/10.1142/s0129055x89000183.

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The equilibrium positions of the nuclei in an ideal crystal can be determined by thermal averages, as suggested by Max Born many years ago. We derive these equations without appealing to Born’s second condition which relates the proper frequencies to the statistical operator. We obtain these frequencies directly from the action principle and develop a perturbation theory including all the parity-violating terms (under reflection of generalized, proper coordinates). The equation which determines the equilibrium positions allows us to derive a system of differential equations for the derivatives of these positions with respect to the temperature.

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López-Pouso, Óscar, and Rafael Muñoz-Sola. "About the solution of the even parity formulation of the transient radiative heat transfer equations." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 104, no. 1 (March 2010): 129–52. http://dx.doi.org/10.5052/racsam.2010.12.

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Yang, Jianke, and Sean Nixon. "Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials." Physics Letters A 380, no. 45 (November 2016): 3803–9. http://dx.doi.org/10.1016/j.physleta.2016.09.023.

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Berton, Antoine, and Daniel Hodouin. "Fault Detection and Diagnosis in the Parity Space Generated by Mass and Energy Conservation Equations." IFAC Proceedings Volumes 34, no. 18 (September 2001): 71–76. http://dx.doi.org/10.1016/s1474-6670(17)33184-1.

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