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Journal articles on the topic 'Lorentz modeli'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

N.A., Razzoqov, Fayziyev Sh.Sh., and Sharipov M.Z. "MAGNETO-OPTIK EFFEKTLARNING MIKROSKOPIK MODELLARI." Zamonaviy dunyoda innovatsion tadqiqotlar: Nazariya va amaliyot, no. 11 (February 17, 2022): 72–79. https://doi.org/10.5281/zenodo.6126553.

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Fizikaning magnit maydon ta’sirida moddalarning optik xususiyatlari o‘zgarishini o‘rganuvchi bo‘limi magnitooptika deb ataladi. Magnitooptik effeektlarning xususiyligi muhitda elektr maydon yoki deformatsiya ta’sirida yuzaga keladigan chiziqli optik anizotropiyali magnit maydonda unga perpendikulyar bo‘lgan tekislikda ikkita yo‘nalishning noekvivalentligi bilan bog‘liq bo‘lgan sirkulyar anizotropiyaning yuzaga kelishidadir. Bu muhim xususiyat magnit maydonning aksialligi natijasidir.

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2

Vodinchar, Gleb, and Evgeny Kazakov. "The Lorenz system and its generalizations as dynamo models with memory." E3S Web of Conferences 62 (2018): 02011. http://dx.doi.org/10.1051/e3sconf/20186202011.

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The one of the known applications of the classical Lorenz system is an axisymmetric αω-dynamo with a dynamical quenching of the α-effect by the helicity. In this paper we consider generalizations of the Lorentz system, which are the models of α2 - and α2ω-dynamo. The cases of finite and infinite memory in the quenching functional are considered. The conditions for the existence of stationary dynamo regimes and regimes of regular and chaotic inversions are analytically and numerically studded.

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3

Ziehmann-Schlumbohm, Christine, Klaus Fraedrich, and Leonard A. Smith. "An internal predictability experiment in the Lorenz Model." Meteorologische Zeitschrift 4, no. 1 (1995): 16–21. http://dx.doi.org/10.1127/metz/4/1995/16.

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4

Meljanac, Stjepan, and Anna Pachoł. "Heisenberg Doubles for Snyder-Type Models." Symmetry 13, no. 6 (2021): 1055. http://dx.doi.org/10.3390/sym13061055.

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A Snyder model generated by the noncommutative coordinates and Lorentz generators closes a Lie algebra. The application of the Heisenberg double construction is investigated for the Snyder coordinates and momenta generators. This leads to the phase space of the Snyder model. Further, the extended Snyder algebra is constructed by using the Lorentz algebra, in one dimension higher. The dual pair of extended Snyder algebra and extended Snyder group is then formulated. Two Heisenberg doubles are considered, one with the conjugate tensorial momenta and another with the Lorentz matrices. Explicit fo

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5

Hoppe, Jens. "Matrix models and Lorentz invariance." Journal of Physics A: Mathematical and Theoretical 44, no. 5 (2011): 055402. http://dx.doi.org/10.1088/1751-8113/44/5/055402.

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6

Zhou, Lingli, and Bo-Qiang Ma. "Lorentz Violation of the Photon Sector in Field Theory Models." Advances in High Energy Physics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/374572.

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We compare the Lorentz violation terms of the pure photon sector between two field theory models, namely, the minimal standard model extension (SME) and the standard model supplement (SMS). From the requirement of the identity of the intersection for the two models, we find that the free photon sector of the SMS can be a subset of the photon sector of the minimal SME. We not only obtain some relations between the SME parameters but also get some constraints on the SMS parameters from the SME parameters. The CPT-odd coefficients(kAF)αof the SME are predicted to be zero. There are 15 degrees of

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7

Kundt, W. "Models for extragalactic radio sources." Symposium - International Astronomical Union 119 (1986): 415–16. http://dx.doi.org/10.1017/s0074180900153124.

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Doubt is cast on the reality of the following four assumptions commonly made in the treatment of extragalactic radio sources: (1) The central engine is a black hole; (2) Electrons can be accelerated in situ in the knots and heads of the jets, to large Lorentz factors γ ≥ 102, with an efficiency exceeding 30%; (3) The (non-thermal) radiation emitted by the beam fluid is isotropic in some (comoving) Lorentz frame; and (4) The flow velocity in the jets of SS 433 is v = 0.26 c.

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8

Marakulin, Arthur, and Sergey Sibiryakov. "Supersymmetric models with broken Lorentz invariance." EPJ Web of Conferences 158 (2017): 02011. http://dx.doi.org/10.1051/epjconf/201715802011.

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9

Cordier, Stéphane, Brigitte Lucquin-Desreux, and Abdelhadi Sabry. "Numerical methods for Vlasov-Lorentz models." ESAIM: Proceedings 10 (2001): 201–10. http://dx.doi.org/10.1051/proc:2001011.

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10

Ben-David, Emanuel. "Maximal invariants for Lorentz–Wishart models." Journal of Geometry and Physics 69 (July 2013): 31–39. http://dx.doi.org/10.1016/j.geomphys.2013.02.009.

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11

Mukunda, N. "Mechanical models for Lorentz group representations." Foundations of Physics 23, no. 2 (1993): 245–60. http://dx.doi.org/10.1007/bf01883628.

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12

Li, De-Sheng. "Pati-Salam Model in Curved Space-Time from Square Root Lorentz Manifold." Physical Science & Biophysics Journal 5, no. 2 (2021): 1–10. http://dx.doi.org/10.23880/psbj-16000186.

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There is a ( ) ( ) 4' 4 UU × -bundle on four-dimensional square root Lorentz manifold. Then a Pati-Salam model in curved space-time (Lagrangian) and a gravity theory (Lagrangian) are constructed on square root Lorentz manifold based on self-parallel transportation principle. An explicit formulation of Sheaf quantization on this square root Lorentz manifold is shown. Sheaf quantization is based on superposition principle and construct a linear Sheaf space in curved space-time. The transition amplitude in path integral quantization is given which is consistent with Sheaf quantization. All partic

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13

HAAGENSEN, PETER E. "THE LORENTZ CHERN-SIMONS FORM IN HETEROTIC GREEN-SCHWARTZ SIGMA MODELS." Modern Physics Letters A 06, no. 05 (1991): 431–37. http://dx.doi.org/10.1142/s0217732391000439.

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By studying the 1-loop effective action of the heterotic Green-Schwartz sigma model, we identify the only source of anomaly in the target local Lorentz symmetry, and verify that it is canceled by the inclusion of a Lorentz Chern-Simons three-form in the definition of the supergravity field HABC.

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14

MARNELIUS, ROBERT, and ULF MÅRTENSSON. "NEW MANIFESTLY COVARIANT MODELS FOR RELATIVISTIC PARTICLES OF ARBITRARY SPIN." International Journal of Modern Physics A 06, no. 05 (1991): 807–44. http://dx.doi.org/10.1142/s0217751x91000459.

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By means of a previously developed procedure for the derivation of manifestly Lorentz covariant models of spinning particles, we derive new classes of models in which the internal variables transform as Lorentz spinors. Models for massless and massive particles of arbitrary spin are given in which the internal variables are fermionic or bosonic spinors. Lagrangians and their local invariances are explicitly written down for all models.

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15

Fedele, Francesco, Cristel Chandre, Martin Horvat, and Nedjeljka Žagar. "Hamiltonian Lorenz-like models." Physica D: Nonlinear Phenomena 472 (February 2025): 134494. https://doi.org/10.1016/j.physd.2024.134494.

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16

Kafi, Dina Ahmed. "Secure communications by chaotic carrier signal using Lorenz model." Iraqi Journal of Physics (IJP) 14, no. 30 (2019): 51–63. http://dx.doi.org/10.30723/ijp.v14i30.200.

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In this paper, the generation of a chaotic carrier by Lorenz modelis theoretically studied. The encoding techniques has been used ischaos masking of sinusoidal signal (massage), an optical chaoticcommunications system for different receiver configurations isevaluated. It is proved that chaotic carriers allow the successfulencoding and decoding of messages. Focusing on the effect ofchanging the initial conditions of the states of our dynamical systeme.i changing the values (x, y, z, x1, y1, and z1).

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17

Gautreau, Ronald. "Gravitational models of a Lorentz extended electron." Physical Review D 31, no. 8 (1985): 1860–63. http://dx.doi.org/10.1103/physrevd.31.1860.

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18

García-Aguilar, J. D., and A. Pérez-Lorenzana. "Superfield formalism for 5D Lorentz violating models." Journal of Physics: Conference Series 378 (August 10, 2012): 012004. http://dx.doi.org/10.1088/1742-6596/378/1/012004.

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19

Escobar, C. A., and L. F. Urrutia. "Vector models with spontaneous Lorentz-symmetry breaking." Journal of Physics: Conference Series 952 (January 2018): 012013. http://dx.doi.org/10.1088/1742-6596/952/1/012013.

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20

Seifert, Michael. "Lorentz-Violating Gravity Models and the Linearized Limit." Symmetry 10, no. 10 (2018): 490. http://dx.doi.org/10.3390/sym10100490.

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Many models in which Lorentz symmetry is spontaneously broken in a curved spacetime do so via a “Lorentz-violating” (LV) vector or tensor field, which dynamically takes on a vacuum expectation value and provides additional local geometric structure beyond the metric. The kinetic terms of such a field will not necessarily be decoupled from the kinetic terms of the metric, and will generically lead to a set of coupled equations for the perturbations of the metric and the LV field. In some models, however, the imposition of certain additional conditions can decouple these equations, yielding an “

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21

Narges, Ansari, Moradi Maryam, and Ghorbani Farinaz. "Investigation of the Gauss model on improvement of permittivity and optical absorption of TMDC monolayers in the visible spectrum." Journal of Research on Many-body Systems 8, no. 16 (2018): 1–11. https://doi.org/10.22055/JRMBS.2018.13629.

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2-dimensional layers of transition metal dichalcogenids (TMDCs) with direct band gap in the visible and infrared range have shown open horizons in photonics and electro-optics. MoSe<sub>2</sub>, WSe<sub>2</sub>, MoS<sub>2</sub> and Ws<sub>2</sub> monolayers among TMDCs are better evaluated so far with special optical characterizations. In this paper, permittivity of these monolayers based on Lorentz, Lorentz- Gauss and Lorentz –Drude-Gauss model have been calculated with quite acceptable consistency with those experimental ones. Optical absorption responses of such monolayers are similar

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22

Alwan, Saba Mohammed. "Constrained Estimation, Chaos and Stability Study of Lorenz – Rössler Model." Journal of Advanced Research in Dynamical and Control Systems 12, SP8 (2020): 951–61. http://dx.doi.org/10.5373/jardcs/v12sp8/20202600.

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23

Zlatanovska, Biljana. "MODELS FOR THE LORENZ SYSTEM." Математички билтен/BULLETIN MATHÉMATIQUE DE LA SOCIÉTÉ DES MATHÉMATICIENS DE LA RÉPUBLIQUE MACÉDOINE, no. 2 (2018): 75–84. http://dx.doi.org/10.37560/matbil18200075z.

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24

Escobar, C. A., and L. F. Urrutia. "Extended Nambu models: Their relation to gauge theories." International Journal of Modern Physics A 32, no. 14 (2017): 1750077. http://dx.doi.org/10.1142/s0217751x17500774.

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Yang–Mills theories supplemented by an additional coordinate constraint, which is solved and substituted in the original Lagrangian, provide examples of the so-called Nambu models, in the case where such constraints arise from spontaneous Lorentz symmetry breaking. Some explicit calculations have shown that, after additional conditions are imposed, Nambu models are capable of reproducing the original gauge theories, thus making Lorentz violation unobservable and allowing the interpretation of the corresponding massless gauge bosons as the Goldstone bosons arising from the spontaneous symmetry

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25

Shen, Bo-Wen, Roger A. Pielke, Xubin Zeng, et al. "Three Kinds of Butterfly Effects within Lorenz Models." Encyclopedia 2, no. 3 (2022): 1250–59. http://dx.doi.org/10.3390/encyclopedia2030084.

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Within Lorenz models, the three major kinds of butterfly effects (BEs) are the sensitive dependence on initial conditions (SDIC), the ability of a tiny perturbation to create an organized circulation at large distances, and the hypothetical role of small-scale processes in contributing to finite predictability, referred to as the first, second, and third kinds of butterfly effects (BE1, BE2, and BE3), respectively. A well-accepted definition of the butterfly effect is the BE1 with SDIC, which was rediscovered by Lorenz in 1963. In fact, the use of the term “butterfly” appeared in a conference

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26

Weinfurtner, Silke, Stefano Liberati, and Matt Visser. "Modelling Planck-scale Lorentz violation via analogue models." Journal of Physics: Conference Series 33 (March 1, 2006): 373–85. http://dx.doi.org/10.1088/1742-6596/33/1/046.

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27

Bunimovich, L. A., and S. E. Troubetzkoy. "Topological dynamics of flipping Lorentz lattice gas models." Journal of Statistical Physics 72, no. 1-2 (1993): 297–307. http://dx.doi.org/10.1007/bf01048051.

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28

Gallerati, Antonio, Matteo Luca Ruggiero, and Lorenzo Iorio. "Impact of Lorentz Violation Models on Exoplanets’ Dynamics." Universe 8, no. 11 (2022): 608. http://dx.doi.org/10.3390/universe8110608.

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Many exoplanets have been detected by the radial velocity method, according to which the motion of a binary system around its center of mass can produce a periodical variation of the Doppler effect of the light emitted by the host star. These variations are influenced by both Newtonian and non-Newtonian perturbations to the dominant inverse-square acceleration; accordingly, exoplanetary systems lend themselves to testing theories of gravity alternative to general relativity. In this paper, we consider the impact of the Standard Model Extension (a model that can be used to test all possible Lor

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29

Sadatian, S. Davood. "Considering Late-Time Acceleration in Some Cosmological Models." Advances in High Energy Physics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/802685.

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We study two cosmological models: a nonminimally coupled scalar field on brane world model and a minimally coupled scalar field on Lorentz invariance violation model. We compare some cosmological results in these scenarios. Also, we consider some types of Rip singularity solution in both models.

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30

Odegov, Nikolay Anatoliyovich, Iryna Oleksandrivna Hlushchenko, and Vitaliy Olehovich Duridivka. "Phenomenological models of the main characteristics of a step optical fiber." Problemi telekomunìkacìj, no. 1(26) (December 11, 2020): 33–47. http://dx.doi.org/10.30837/pt.2020.1.03.

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The paper considers a group of polynomial models of various characteristics of an optical fiber (OF) depending on the wavelength and chemical composition of the fiber. A method for structural identification of such models is proposed. The following characteristics are considered: the refractive index of the fiber core and cladding, group refractive index, group velocity, dispersion coefficients, numerical aperture, cutoff wavelength of the fundamental mode, etc. An analysis of the well-known Cauchy, Lorentz-Lorenz equations, Sellmeier’s formulas, etc. is given in relation to the problem being

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31

SON, EDWIN J., and WONTAE KIM. "NOTE ON TWO-DIMENSIONAL GAUGED LIFSHITZ MODELS." Modern Physics Letters A 26, no. 37 (2011): 2755–60. http://dx.doi.org/10.1142/s0217732311037157.

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We fermionize the two-dimensional free Lifshitz scalar field in order to identify what the gauge-covariant couplings are, and then they are bosonized back to get the gauged Lifshitz scalar field theories. We show that they give the same physical modes with those of the corresponding Lorentz invariant gauged scalar theories, although the dispersion relations are different.

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32

Zbăganu, Gheorghiță. "Asymptotic Results in Broken Stick Models: The Approach via Lorenz Curves." Mathematics 8, no. 4 (2020): 625. http://dx.doi.org/10.3390/math8040625.

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A stick of length 1 is broken at random into n smaller sticks. How much inequality does this procedure produce? What happens if, instead of breaking a stick, we break a square? What happens asymptotically? Which is the most egalitarian distribution of the smaller sticks (or rectangles)? Usually, when studying inequality, one uses a Lorenz curve. The more egalitarian a distribution, the closer the Lorenz curve is to the first diagonal of [ 0 , 1 ] 2 . This is why in the first section we study the space of Lorenz curves. What is the limit of a convergent sequence of Lorenz curves? We try to answ

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33

Bauer, Silke, Zoltan Barta, Bruno J. Ens, Graeme C. Hays, John M. McNamara, and Marcel Klaassen. "Animal migration: linking models and data beyond taxonomic limits." Biology Letters 5, no. 4 (2009): 433–35. http://dx.doi.org/10.1098/rsbl.2009.0324.

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An international workshop on animal migration was held at the Lorentz Center in Leiden, The Netherlands, 2–6 March 2009, bringing together leading theoreticians and empiricists from the major migratory taxa, aiming at the identification of cutting-edge questions in migration research that cross taxonomic borders.

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34

Ogwang, Tomson, and U. L. Gouranga Rao. "Hybrid models of the Lorenz curve." Economics Letters 69, no. 1 (2000): 39–44. http://dx.doi.org/10.1016/s0165-1765(00)00274-3.

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35

Sordo, Miguel A., Jorge Navarro, and José María Sarabia. "Distorted Lorenz curves: models and comparisons." Social Choice and Welfare 42, no. 4 (2013): 761–80. http://dx.doi.org/10.1007/s00355-013-0754-y.

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36

BODOOR, K., H. J. WEBER, T. FREDERICO, and M. BEYER. "VIOLATIONS OF LORENTZ COVARIANCE IN LIGHT FRONT QUARK MODELS." Modern Physics Letters A 15, no. 36 (2000): 2191–204. http://dx.doi.org/10.1142/s0217732300002814.

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Electromagnetic form factors of the nucleon from relativistic quark models are analyzed: Results from null-plane projection of the Feynman triangle diagram are compared with a Bakamjian–Thomas model. The magnetic form factors of the models differ by about 15% at spacelike momentum transfer 0.5 GeV2, while the charge form factors are much closer. Spurious contributions to electromagnetic form factors due to violations of rotational symmetry are eliminated for both models. One method changes magnetic form factors by about 10%, whereas the charge form factors remain nearly the same. Another one c

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37

Gonzalez-Mestres, Luis. "AUGER-HiRes results and models of Lorentz symmetry violation." Nuclear Physics B - Proceedings Supplements 190 (May 2009): 191–97. http://dx.doi.org/10.1016/j.nuclphysbps.2009.03.088.

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38

Kr�mli, Andr�s, N�ndor Sim�nyi, and Domokos Sz�sz. "Heat conduction in caricature models of the Lorentz gas." Journal of Statistical Physics 46, no. 1-2 (1987): 303–18. http://dx.doi.org/10.1007/bf01010348.

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39

Farakos, K., N. E. Mavromatos, and P. Pasipoularides. "Asymmetrically warped brane models, bulk photons and Lorentz invariance." Journal of Physics: Conference Series 189 (October 1, 2009): 012029. http://dx.doi.org/10.1088/1742-6596/189/1/012029.

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40

MIGNEMI, S. "HAMILTONIAN FORMALISM AND SPACE–TIME SYMMETRIES IN GENERIC DSR MODELS." International Journal of Modern Physics D 15, no. 06 (2006): 925–35. http://dx.doi.org/10.1142/s0218271806008516.

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We study the structure of the classical phase space of generic models of deformed special relativity, which gives rise to a definition of velocity consistent with the deformed Lorentz symmetry. In this way we can also determine the laws of transformation of space–time coordinates.

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41

LIU, YU-XIAO, YI-SHI DUAN, and LI-JIE ZHANG. "ANGULAR MOMENTUM CONSERVATION LAW FOR RANDALL–SUNDRUM MODELS." Modern Physics Letters A 22, no. 37 (2007): 2855–64. http://dx.doi.org/10.1142/s0217732307023365.

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In Randall–Sundrum models, by the use of general Noether theorem, the covariant angular momentum conservation law is obtained with respect to the local Lorentz transformations. The angular momentum current also has superpotential and is therefore identically conserved. The space-like components Jij of the angular momentum for Randall–Sundrum models are zero. But the component J04 is infinite.

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42

Pène, Françoise. "Random walks in random sceneries and related models." ESAIM: Proceedings and Surveys 68 (2020): 35–51. http://dx.doi.org/10.1051/proc/202068003.

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We present random walks in random sceneries as well as three related models: U-statistics indexed by random walks, a model of stratified media with inhomogeneous layers (random one-way streets) and the one-dimensional Lévy-Lorentz gas (random roundabouts on a line). We present in particular results obtained in collaboration with Castell, Guillotin-Plantard, Br. Schapira, Franke, Wendler, Aurzada, Bianchi and Lenci.

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43

MACÍAS, ALFREDO, ECKEHARD W. MIELKE, and JOSÉ SOCORRO. "SUPERSYMMETRIC QUANTUM COSMOLOGY FOR BIANCHI CLASS A MODELS." International Journal of Modern Physics D 07, no. 05 (1998): 701–12. http://dx.doi.org/10.1142/s0218271898000462.

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The canonical theory of [Formula: see text] supergravity, with a matrix representation for the gravitino covector–spinor, is applied to the Bianchi class A spatially homogeneous cosmologies. The full Lorentz constraint and its implications for the wave function of the universe are analyzed in detail. We found that in this model no physical states other than the trivial "rest frame" type occur.

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44

Schulz, Sönke E. "Subsidiarität im Wandel." Verwaltung & Management 30, no. 6 (2024): 243–50. http://dx.doi.org/10.5771/0947-9856-2024-6-243.

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Das Subsidiaritätsprinzip ist ein wesentlicher Pfeiler des Sozialstaats. Es ist für zahlreiche Bereiche der Sozialverwaltung gesetzlich normiert. Das kooperative Miteinander von Verwaltung und gemeinnützigen Anbietern hat sich grundsätzlich bewährt. Sowohl seitens der Anbieter, insbesondere der freien Wohlfahrtspflege, als auch von den kommunalen Aufgabenträgern wird jedoch auch Kritik geäußert: Das System sei insgesamt schwerfällig, es gebe zu hohe Transaktionsaufwände, eine zu kleinteilige Steuerung sowie zu viel Bürokratie. Dabei hat Lorenz von Stein ein Modell der „freien Verwaltung“ entwo

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45

Fadhel, Kadhom F., and A. A. Al-Rubaiee. "Simulation and Parameterization of Longitudinal Development Using Different Hadronic Interaction Models." Al-Mustansiriyah Journal of Science 32, no. 4 (2021): 97–103. http://dx.doi.org/10.23851/mjs.v32i4.1035.

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The importance of investigating ultra-high energy cosmic ray particles interactions was investigated in this work. Different hadronic interaction models such as (SIBYLL, EPOS, and QGSJET) were used air showers simulation AIRES program (version 19.04.00). Also, the shower size of Extensive Air Showers (EAS) was calculated by estimating the longitudinal development. Moreover, the longitudinal development simulation of the two primary particles (iron nuclei and proton) was performed, taking into account their primary energies effect as well the zenith angle for charged particles that produced in

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46

Smolec, Radosław, and Paweł Moskalik. "Order and chaos in hydrodynamic BL Her models." Proceedings of the International Astronomical Union 9, S301 (2013): 489–90. http://dx.doi.org/10.1017/s1743921313015196.

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AbstractMany dynamical systems of different complexity, e.g. 1D logistic map, the Lorentz equations, or real phenomena, like turbulent convection, show chaotic behaviour. Despite huge differences, the dynamical scenarios for these systems are strikingly similar: chaotic bands are born through the series of period doubling bifurcations and merge through interior crises. Within chaotic bands periodic windows are born through the tangent bifurcations, preceded by the intermittent behaviour. We demonstrate such behaviour in models of pulsating stars.

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47

Kuryzhov, E., E. Karatetskaia, and D. Mints. "Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps." Nelineinaya Dinamika 17, no. 2 (2021): 165–74. http://dx.doi.org/10.20537/nd210203.

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We consider the system of two coupled one-dimensional parabola maps. It is well known that the parabola map is the simplest map that can exhibit chaotic dynamics, chaos in this map appears through an infinite cascade of period-doubling bifurcations. For two coupled parabola maps we focus on studying attractors of two types: those which resemble the well-known discrete Lorenz-like attractors and those which are similar to the discrete Shilnikov attractors. We describe and illustrate the scenarios of occurrence of chaotic attractors of both types.

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48

Appert, C., H. van Beijeren, M. H. Ernst, and J. R. Dorfman. "Thermodynamic formalism and localization in Lorentz gases and hopping models." Journal of Statistical Physics 87, no. 5-6 (1997): 1253–71. http://dx.doi.org/10.1007/bf02181283.

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49

Bradfield, Terry. "Weyl gauging and spontaneously broken Lorentz symmetry: Some alternative models." General Relativity and Gravitation 22, no. 2 (1990): 217–31. http://dx.doi.org/10.1007/bf00756210.

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50

Narita, Kazuaki. "New Lorentz Invariant Partial Differential Equations and Their Discrete Models." Journal of the Physical Society of Japan 73, no. 10 (2004): 2655–61. http://dx.doi.org/10.1143/jpsj.73.2655.

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