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Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.


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Journal ArticleDOI
Xicheng Li1, Wen Chen1
TL;DR: In this article, anomalous diffusion in a half-plane with a constant source and a perfect sink at each half of the boundary is considered, and the discontinuity of boundary condition is erased by decomposing the solution into two parts, a symmetric part and an antisymmetric part.
Abstract: In this study, anomalous diffusion in a half-plane with a constant source and a perfect sink at each half of the boundary is considered. The discontinuity of the boundary condition is erased by decomposing the solution into two parts—a symmetric part and an antisymmetric part. The symmetric part which has been studied extensively can be solved by an integral transform method, Green's function method or others. To obtain the solution of the antisymmetric part, a separable similarity solution is assumed and the Erdelyi–Kober-type fractional derivative is used. By doing so, the partial differential equation reduces to an ordinary one. Using the Mellin transform method, the solution of the antisymmetric part in terms of a Fox-H function is obtained. Some figures are given to show the characters of the diffusion process and the influences of different orders of fractional derivatives.

20 citations

Journal ArticleDOI
TL;DR: This work finds the Hamiltonian generator of this symmetry and the corresponding conserved momentum by interpreting the simple translational symmetries of the sine-Gordon chain in terms of the embedded coordinates.
Abstract: A connection between the dynamics of a sine-Gordon chain and a certain static membrane folding problem was recently found. The one-dimensional membrane profile is a cross section of the position-time sine-Gordon amplitude profile. Here we show that when one system is embedded in a higher-dimensional system in this way, obvious symmetries in the larger system can lead to nontrivial symmetries in the embedded system. In particular, a thin buckled membrane on a fluid substrate has a continuous degeneracy that interpolates between a symmetric and an antisymmetric fold. We find the Hamiltonian generator of this symmetry and the corresponding conserved momentum by interpreting the simple translational symmetries of the sine-Gordon chain in terms of the embedded coordinates. We discuss possible extensions to other embedded dynamical systems.

20 citations

Journal ArticleDOI
01 Oct 1986
TL;DR: In this article, sufficient conditions for the invariants of the maximal isotropic subgroups (Lagrangians) and asymptotic values for a lower bound of a group which contains Lagrangians of all symplectic modules of a fixed order were derived.
Abstract: A symplectic module is a finite group with a regular antisymmetric form. The paper determines sufficient conditions for the invariants of the maximal isotropic subgroups (Lagrangians), and asymptotic values for a lower bound of a group which contains Lagrangians of all symplectic modules of a fixed orderpn. These results have application to the splitting fields of universal division algebras.

20 citations

Journal ArticleDOI
TL;DR: In this article, the BRST cohomologies of a class of constraint (super) Lie algebras are presented as detour complexes, which correspond to gauge invariant spinning particle models.
Abstract: We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric and K\"ahler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form K\"ahler electromagnetism. We also discuss how our results generalize to other special geometries.

20 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider an array of waveguides with identical widths but alternating spacings using the discrete nonlinear Schrodinger model (tight-binding approximation) and identify the two fundamental, antisymmetric and symmetric, discrete gap solitons, which can be numerically continued to a continuum limit gap soliton at one band edge.
Abstract: We consider an array of waveguides with identical widths but alternating spacings using the discrete nonlinear Schr\"odinger model (tight-binding approximation). In the highly discrete (anticontinuous) limit when one of the spacings is infinite, the model reduces to an integrable chain of uncoupled dimers. From this limit, we identify the two fundamental, antisymmetric and symmetric, discrete gap solitons, which can be numerically continued to a continuum limit gap soliton at one band edge. Other composite solutions at the uncoupled limit disappear in bifurcations. Similarly to the case of waveguides with alternating widths and constant spacings, oscillatory instabilities appear for the fundamental solutions only for frequencies in the upper half of the gap. In contrast to the alternating-width case, there is no stability exchange between the two fundamental solutions: the symmetric solution is always unstable while the antisymmetric solution is always stable in the lower half of the gap. Thus, the Peierls-Nabarro barrier can vanish only in the continuum limit.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023145
2022286
2021109
2020112
2019118
2018122