Topic
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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TL;DR: In this paper, a boundary continuous displacement-based generalized Navier solution technique is used to solve the five highly coupled linear second-order partial differential equations with constant coefficients, and the associated geometric boundary conditions.
19 citations
TL;DR: In this paper, an unambiguous method for calculating branching rules for the classical subgroups of the even-dimensional rotation group SO2k was developed for the subgroups SUk*U1, SUk+1*SO2q, SO2p+1+1*, SO2q+1.
Abstract: Unambiguous methods are developed for calculating branching rules for the classical subgroups of the even-dimensional rotation group SO2k. Complete results are given for the subgroups SUk*U1, SO2k-2*U1, SO2p*SO2q and SO2p+1*SO2q+1. A number of examples relevant to problems in supergravity and unification theories are given. A complete resolution of the antisymmetric powers of the basic spinor irrep of SO10 is given and the results extended to SO11.
19 citations
TL;DR: This work puts forward existence of surface breathers, which represent two-frequency modes localized about the array edges, and provides classification of the modes based on the anti-continuum limit, and discusses relation between surface and bulk modes.
Abstract: We present the complete set of symmetric and antisymmetric (edge and corner) surface modes in finite one- and two-dimensional arrays of waveguides. We provide classification of the modes based on the anti-continuum limit, study their stability and bifurcations, and discuss relation between surface and bulk modes. We put forward existence of surface breathers, which represent two-frequency modes localized about the array edges.
19 citations
TL;DR: In this article, the Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antismmetric tridiagonal matrix with all independent elements, where the random variables permit the introduction of a positive parameter β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly.
Abstract: The Householder reduction of a member of the antisymmetric Gaussian unitary ensemble gives an antisymmetric tridiagonal matrix with all independent elements. The random variables permit the introduction of a positive parameter β, and the eigenvalue probability density function of the corresponding random matrices can be computed explicitly, as can the distribution of {qi}, the first components of the eigenvectors. Three proofs are given. One involves an inductive construction based on bordering of a family of random matrices which are shown to have the same distributions as the antisymmetric tridiagonal matrices. This proof uses the Dixon–Anderson integral from Selberg integral theory. A second proof involves the explicit computation of the Jacobian for the change of variables between real antisymmetric tridiagonal matrices, its eigenvalues, and {qi}. The third proof maps matrices from the antisymmetric Gaussian β-ensemble to those realizing particular examples of the Laguerre β-ensemble. In addition to t...
19 citations
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TL;DR: In this article, a global approach to the study of duality transformations between antisymmetric fields with transitions is described. But the approach needs the introduction of an auxiliary form satisfying a global constraint which in the case of 1-form potentials coincides with the quantization of the magnetic flux.
Abstract: We describe a global approach to the study of duality transformations between antisymmetric fields with transitions and argue that the natural geometrical setting for the approach is that of gerbes, these objects are mathematical constructions generalizing U(1) bundles and are similarly classified by quantized charges. We address the duality maps in terms of the potentials rather than on their field strengths and show the quantum equivalence between dual theories which in turn allows a rigorous proof of a generalized Dirac quantization condition on the couplings. Our approach needs the introduction of an auxiliary form satisfying a global constraint which in the case of 1-form potentials coincides with the quantization of the magnetic flux. We apply our global approach to refine the proof of the duality equivalence between d=11 supermembrane and d=10 IIA Dirichlet supermembrane.
19 citations