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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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TL;DR: The theory of Schunck classes and projectors for soluble Leibniz algebras, parallel to that for Lie classes, has been studied in this article, where the authors set out the theory of projectors and Schuncks in the context of soluble leibnitz algesas.
Abstract: I set out the theory of Schunck classes and projectors for soluble Leibniz algebras, parallel to that for Lie algebras. Primitive Leibniz algebras come in pairs, one (Lie) symmetric, the other antisymmetric. A Schunck formation containing one member of a pair also contains the other. Projectors for a Schunck formation are intravariant.
31 citations
TL;DR: In this article, an analytical solution for the time evolution of decay of two identical noninteracting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states.
Abstract: An analytical solution for the time evolution of decay of two identical noninteracting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave function, and hence also the survival and nonescape probabilities, for factorized symmetric and entangled symmetric or antisymmetric initial states evolve in a distinctive form along the exponentially decaying and nonexponential regimes. Our findings show the influence of the Pauli exclusion principle on decay. We exemplify our results by solving exactly the $s$-wave $\ensuremath{\delta}$ shell potential model.
31 citations
TL;DR: In this paper, a finite element technique was introduced into an integro-differential equation formulation of a shallow arch to investigate two forms of instability when subjected to a symmetric dynamic load.
Abstract: When a shallow arch is subjected to a symmetric dynamic load, this load becomes “critical” if a slight increase in the load magnitude leads to a sudden snap-through. Another form of instability occurs when a slight antisymmetric component in the load produces a sharply increasing antisymmetric response. Both forms of instability are investigated by means of a numerical procedure which introduces a finite element technique into an integro-differential equation formulation. Where applicable the results generally confirm previous results obtained elsewhere, but cover a broader range of problems and are believed to be more accurate.
31 citations
TL;DR: This work provides a general, and yet simple, method to derive a new set of wavelets Ψ′ such that each wavelet inΨ′ is either symmetric or antisymmetric.
31 citations
TL;DR: In this paper, the authors consider a very generic family of teleparallel gravities, whose action depends on the torsion scalar $T$ and the boundary term $B$ as well as a scalar field with its kinetic term $X$ and find solutions corresponding to a generalization of the Taub-NUT metric.
Abstract: Axially symmetric spacetimes play an important role in the relativistic description of rotating astrophysical objects like black holes, stars, etc. In gravitational theories that venture beyond the usual Riemannian geometry by allowing independent connection components, the notion of symmetry concerns, not just the metric, but also the connection. As discovered recently, in teleparallel geometries, axial symmetry can be realized in two branches, while only one of these has a continuous spherically symmetric limit. In the current paper, we consider a very generic $f(T,B,\ensuremath{\phi},X)$ family of teleparallel gravities, whose action depends on the torsion scalar $T$ and the boundary term $B$, as well as a scalar field $\ensuremath{\phi}$ with its kinetic term $X$. As the field equations can be decomposed into symmetric and antisymmetric (spin connection) parts, we thoroughly analyze the antisymmetric equations and look for solutions of axial spacetimes which could be used as ans\"atze to tackle the symmetric part of the field equations. In particular, we find solutions corresponding to a generalization of the Taub-NUT metric, and the slowly rotating Kerr spacetime. Since this work also concerns a wider issue of how to determine the spin connection in teleparallel gravity, we also show that the method of ``turning off gravity'' proposed in the literature, does not always produce a solution to the antisymmetric equations.
31 citations