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arXivOrthogonalization of graded sets of vectors I. A. Shereshevskiĭ 20001231 I propose an orthogonalization procedure preserving the grading of the initial graded set of linearly independent vectors. In particular, this procedure is applicable for orthonormalization of any countable set of polynomials in several (finitely many) indeterminates.
Subject 수학 Source arXiv URL https://arxiv.org/abs/math/0101267view Article Title Orthogonalization of graded sets of vectorsAuthors I. A. ShereshevskiĭAbstract I propose an orthogonalization procedure preserving the grading of the initial graded set of linearly independent vectors. In particular, this procedure is applicable for orthonormalization of any countable set of polynomials in several (finitely many) indeterminates.Is Part Of J. Nonlinear Math. Phys. 8 (2001), no. 1, 5458 20001231 Identifier ISSN: DOI 10.2991/jnmp.2001.8.1.6Category math.CALicense 
arXivMesonexchange $\pi N$ Models in ThreeDimensional BetheSalpeter Formulation ChengTsung Hung, Shin Nan Yang, T. S. H. Lee... more(3) 20001231 The pionnucleon scattering is investigated by using several threedimensional reduction schemes of the BetheSalpeter equation for a model Lagrangian involving $\pi$, $N$, $\Delta$, $\rho$, and $\sigma$ fields. It is found that all of the resulting mesonexchange models can give similar good descriptions of the $\pi N$ scattering data up to 400 MeV. However they have significant differences in describing the $\pi NN$ and $\pi N\Delta$ form factors and the $\pi N$ offshell tmatrix elements. We point out that these differences can be best distinguished by investigating the near threshold pion production from nucleonnucleon collisions and pion photoproduction on the nucleon. The consequences of using these models to investigate various pionnucleus reactions are also discussed.
Subject Source arXiv URL https://arxiv.org/abs/nuclth/0101007view Article Title Mesonexchange $\pi N$ Models in ThreeDimensional BetheSalpeter FormulationAuthors ChengTsung Hung; Shin Nan Yang; T. S. H. LeeAbstract The pionnucleon scattering is investigated by using several threedimensional reduction schemes of the BetheSalpeter equation for a model Lagrangian involving $\pi$, $N$, $\Delta$, $\rho$, and $\sigma$ fields. It is found that all of the resulting mesonexchange models can give similar good descriptions of the $\pi N$ scattering data up to 400 MeV. However they have significant differences in describing the $\pi NN$ and $\pi N\Delta$ form factors and the $\pi N$ offshell tmatrix elements. We point out that these differences can be best distinguished by investigating the near threshold pion production from nucleonnucleon collisions and pion photoproduction on the nucleon. The consequences of using these models to investigate various pionnucleus reactions are also discussed.Is Part Of Phys.Rev. C64 (2001) 034309 20001231 Identifier ISSN: DOI 10.1103/PhysRevC.64.034309Category nuclthLicense 
arXivRegularization for effective field theory with two heavy particles J. L. Goity, D. Lehmann, G. Prezeau, ... more(4) 20001231 A regularization for effective field theory with two propagating heavy particles is constructed. This regularization preserves the lowenergy analytic structure, implements a lowenergy power counting for the oneloop diagrams, and preserves symmetries respected by dimensional regularization.
Subject Source arXiv URL https://arxiv.org/abs/hepph/0101011view Article Title Regularization for effective field theory with two heavy particlesAuthors J. L. Goity; D. Lehmann; G. Prezeau; J. SaezAbstract A regularization for effective field theory with two propagating heavy particles is constructed. This regularization preserves the lowenergy analytic structure, implements a lowenergy power counting for the oneloop diagrams, and preserves symmetries respected by dimensional regularization.Is Part Of Phys.Lett.B504:2127,2001 20001231 Identifier ISSN: DOI 10.1016/S03702693(01)002891Category hepph nuclthLicense 
arXivSemiclassical surface of section perturbation theory Oleg Zaitsev 20001231 We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the unperturbed states, which requires some sort of a resonant perturbation theory. We utilize the semiclassical surface of section method by Bogomolny that reduces the spatial dimensions of the problem by one. Among the systems considered are the circular billiard with a perturbed boundary, including the short stadium; the perturbed rectangular billiard, including the tilted square and the square in magnetic field; the bouncing ball states in the stadium and slanted stadium; and the whispering gallery modes. The surface of section perturbation theory is compared with the BornOppenheimer approximation, which is an alternative way to describe some classes of states in these systems. We discuss the derivation of the trace formulas from Bogomolny's transfer operator for the chaotic, integrable, and almost integrable systems.
Subject Source arXiv URL https://arxiv.org/abs/nlin/0101002view Article Title Semiclassical surface of section perturbation theoryAuthors Oleg ZaitsevAbstract We derive analytic expressions for the wavefunctions and energy levels in the semiclassical approximation for perturbed integrable systems. We find that some eigenstates of such systems are substantially different from any of the unperturbed states, which requires some sort of a resonant perturbation theory. We utilize the semiclassical surface of section method by Bogomolny that reduces the spatial dimensions of the problem by one. Among the systems considered are the circular billiard with a perturbed boundary, including the short stadium; the perturbed rectangular billiard, including the tilted square and the square in magnetic field; the bouncing ball states in the stadium and slanted stadium; and the whispering gallery modes. The surface of section perturbation theory is compared with the BornOppenheimer approximation, which is an alternative way to describe some classes of states in these systems. We discuss the derivation of the trace formulas from Bogomolny's transfer operator for the chaotic, integrable, and almost integrable systems.Is Part Of 20001231 Identifier ISSN: Category nlin.CDLicense 
arXivReflectionless analytic difference operators I. algebraic framework Simon N. M. Ruijsenaars 20001231 We introduce and study a class of analytic difference operators admitting reflectionless eigenfunctions. Our construction of the class is patterned after the Inverse Scattering Transform for the reflectionless selfadjoint Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice solitons.
Subject Source arXiv URL https://arxiv.org/abs/nlin/0101058view Article Title Reflectionless analytic difference operators I. algebraic frameworkAuthors Simon N. M. RuijsenaarsAbstract We introduce and study a class of analytic difference operators admitting reflectionless eigenfunctions. Our construction of the class is patterned after the Inverse Scattering Transform for the reflectionless selfadjoint Schr\"odinger and Jacobi operators corresponding to KdV and Toda lattice solitons.Is Part Of J. Nonlinear Math. Phys. 8 (2001), no. 1, 106138 20001231 Identifier ISSN: DOI 10.2991/jnmp.2001.8.1.10Category nlin.SILicense 
arXivQuasiclassical Calculations for Wigner Functions via Multiresolution Antonina N. Fedorova, Michael G. Zeitlin 20001231 We present the application of variationalwavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations are the key points.
Subject 수학 Source arXiv URL https://arxiv.org/abs/physics/0101006view Article Title Quasiclassical Calculations for Wigner Functions via MultiresolutionAuthors Antonina N. Fedorova; Michael G. ZeitlinAbstract We present the application of variationalwavelet analysis to numerical/analytical calculations of Wigner functions in (nonlinear) quasiclassical beam dynamics problems. (Naive) deformation quantization and multiresolution representations are the key points.Is Part Of 20001231 Identifier ISSN: Category physics.accph mathph math.MP nlin.PS physics.compph quantphLicense 
arXivHard loss of stability in Painlev\'e2 equation Oleg M. Kiselev 20001231 A special asymptotic solution of the Painlev\'e2 equation with small parameter is studied. This solution has a critical point $t_*$ corresponding to a bifurcation phenomenon. When $t
t_*$ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and matching procedures. Subject 수학 Source arXiv URL https://arxiv.org/abs/mathph/0101037view Article Title Hard loss of stability in Painlev\'e2 equationAuthors Oleg M. KiselevAbstract A special asymptotic solution of the Painlev\'e2 equation with small parameter is studied. This solution has a critical point $t_*$ corresponding to a bifurcation phenomenon. When $tt_*$ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and matching procedures. Is Part Of J. Nonlinear Math. Phys. 8 (2001), no. 1, 6595 20001231 Identifier ISSN: DOI 10.2991/jnmp.2001.8.1.8Category mathph math.MPLicense 
arXivOn algebraic integrability of the deformed elliptic CalogeroMoser problem Larisa A. Khodarinova, I. A. Prikhodsky 20001231 Algebraic integrability of the elliptic CalogeroMoser quantum problem related to the deformed root systems $\pbf{A_{2}(2)}$ is proved. Explicit formulae for integrals are found.
Subject Source arXiv URL https://arxiv.org/abs/nlin/0101060view Article Title On algebraic integrability of the deformed elliptic CalogeroMoser problemAuthors Larisa A. Khodarinova; I. A. PrikhodskyAbstract Algebraic integrability of the elliptic CalogeroMoser quantum problem related to the deformed root systems $\pbf{A_{2}(2)}$ is proved. Explicit formulae for integrals are found.Is Part Of J. Nonlinear Math. Phys. 8 (2001), no. 1, 5053 20001231 Identifier ISSN: DOI 10.2991/jnmp.2001.8.1.5Category nlin.SILicense 
arXivUltra Efficient Internal Shocks Shiho Kobayashi, Re'em Sari 20001231 Gammaray bursts are believed to originate from internal shocks which arise in an irregular relativistic wind. The process has been thought to be inefficient, converting only a few percent of the kinetic energy into gammarays. We define ultra efficient internal shocks as those in which the fraction of emitted energy is larger than the fraction of energy given to the radiating electrons at each collision. We show that such a scenario is possible and even plausible. In our model, colliding shells which do not emit all their internal energy are reflected from each other and it causes subsequent collisions, allowing more energy to be emitted. As an example, we obtain about 60% overall efficiency even if the fraction of energy that goes to electrons is $\epsilon_e=0.1$ provided that the shells' Lorentz factor varies between 10 and $10^4$. The numerical temporal profile reflects well the activity of the source which ejects the shells, though numerous collisions take place in this model.
Subject Source arXiv URL https://arxiv.org/abs/astroph/0101006view Article Title Ultra Efficient Internal ShocksAuthors Shiho Kobayashi; Re'em SariAbstract Gammaray bursts are believed to originate from internal shocks which arise in an irregular relativistic wind. The process has been thought to be inefficient, converting only a few percent of the kinetic energy into gammarays. We define ultra efficient internal shocks as those in which the fraction of emitted energy is larger than the fraction of energy given to the radiating electrons at each collision. We show that such a scenario is possible and even plausible. In our model, colliding shells which do not emit all their internal energy are reflected from each other and it causes subsequent collisions, allowing more energy to be emitted. As an example, we obtain about 60% overall efficiency even if the fraction of energy that goes to electrons is $\epsilon_e=0.1$ provided that the shells' Lorentz factor varies between 10 and $10^4$. The numerical temporal profile reflects well the activity of the source which ejects the shells, though numerous collisions take place in this model.Is Part Of 20001231 Identifier ISSN: DOI 10.1086/320249Category astrophLicense 
arXivDynamical turbulent flow on the Galton board with friction A. D. Chepelianskii, D. L. Shepelyansky 20001231 We study numerically and analytically the dynamics of particles on the Galton board, a regular lattice of disc scatters, in the presence of a constant external force and friction. It is shown that under certain conditions friction leads to the appearance of a strange chaotic attractor in an initially conservative Hamiltonian system. In this regime the particle flow becomes turbulent and its average velocity depends in nontrivial manner on friction and other system parameters. We discuss the applications of these results to the transport properties of suspended particles in a laminar viscous flow streaming through scatters.
Subject Source arXiv URL https://arxiv.org/abs/condmat/0101006view Article Title Dynamical turbulent flow on the Galton board with frictionAuthors A. D. Chepelianskii; D. L. ShepelyanskyAbstract We study numerically and analytically the dynamics of particles on the Galton board, a regular lattice of disc scatters, in the presence of a constant external force and friction. It is shown that under certain conditions friction leads to the appearance of a strange chaotic attractor in an initially conservative Hamiltonian system. In this regime the particle flow becomes turbulent and its average velocity depends in nontrivial manner on friction and other system parameters. We discuss the applications of these results to the transport properties of suspended particles in a laminar viscous flow streaming through scatters.Is Part Of Phys. Rev. Lett. 87, 034101 (2001) 20001231 Identifier ISSN: DOI 10.1103/PhysRevLett.87.034101Category condmat nlin.CDLicense