scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: It is proved that an interpolatory mask whose center of symmetry is different from the origin cannot generate wavelets with vanishing moments of order n > 0, and an explicit method is given for construction of masks (non-interpolatory) m0 symmetric with respect to a semi-integer point and providing vanishing moments up to arbitrary order n.
Abstract: For arbitrary matrix dilation M whose determinant is odd or equal to ±2, we describe all symmetric interpolatory masks generating dual compactly supported wavelet systems with vanishing moments up to arbitrary order n. For each such mask, we give explicit formulas for a dual refinable mask and for wavelet masks such that the corresponding wavelet functions are real and symmetric/antisymmetric. We proved that an interpolatory mask whose center of symmetry is different from the origin cannot generate wavelets with vanishing moments of order n > 0. For matrix dilations M with |det M| = 2, we also give an explicit method for construction of masks (non-interpolatory) m0 symmetric with respect to a semi-integer point and providing vanishing moments up to arbitrary order n. It is proved that for some matrix dilations (in particular, for the quincunx matrix) such a mask does not have a dual mask. Some of the constructed masks were successfully applied for signal processes.

18 citations

Journal ArticleDOI
TL;DR: In this article, the theory of flexural wave propagation in an elastic beam with periodic structure is developed in terms of Floquet waves, and two lemmas about the properties of the fundamental solutions are proved.
Abstract: The theory of flexural waves in an elastic beam with periodic structure is developed in terms of Floquet waves. Special relationships have been determined among the fundamental solutions of the governing equation. Two lemmas about the properties of the fundamental solutions are proved. With the help of these relations and lemmas, the analysis and classification of the dynamic nature of the problem is greatly simplified. We show that the flexural wave propagation in a periodic beam can be interpreted as the superposition of two pairs of waves propagating in opposite directions, of which one pair behaves as an attenuated wave. The dispersion spectrum of the second pair of waves shows the band structure, consisting of stopping bands and passing bands. Exploiting the symmetry of the structure, the dispersion equation at the end points of Brillouin zones is uncoupled into two simpler equations. These uncoupled equations represent the dispersion spectrum of waves which are either symmetric, or antisymmetric.

18 citations

Journal ArticleDOI
TL;DR: In this paper, a microscopic derivation of the symmetric spin interaction (SSI) and antisymmetric spin interactions (ASI) is given for a metal which has no inversion center, and the obtained ASI energy is concluded to be not always small compared with the SSI energy.
Abstract: The bilinear term of the spin-polarization density in the spin-dependent energy of metals is separated into the terms of the symmetric spin interaction (SSI) and of the antisymmetric spin interaction (ASI), whose properties are first investigated phenomenologically. A microscopic derivation of the SSI and ASI is given for a metal which has no inversion center. It is shown that the spin-orbit coupling which splits electronic bands in the absence of inversion center produces an antisymmetric component of the wave-vector-dependent susceptibility and the ASI is proportional to the antisymmetric component to the first order of the latter quantity. The obtained ASI energy is concluded to be not always small compared with the SSI energy.

18 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the reciprocal theorem requires unexpected relations between the newly found singularities and ones found previously, and that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets.
Abstract: If two spheres are nearly touching, and the flow around them is governed by the Stokes equations, the integral moments of the surface stress are singular functions of the gap width. The method used previously to calculate the singular terms in the zeroth moment (the force) and the antisymmetric first moment (the couple) is extended here to calculate the singular terms in the symmetric first moment (the stresslet) for motions perpendicular to the line of centres. It is shown that the reciprocal theorem requires unexpected relations between the newly found singularities and ones found previously. It is also shown that the singular terms can be used to improve the rate of convergence of series expressions for the stresslets. The series expressions then become valid for all separations of the spheres.

18 citations

Journal ArticleDOI
05 Oct 2010
TL;DR: In this paper, the authors analyzed the influence of symmetric, antisymmetric and asymmetric signals on directed transport and revealed the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal.
Abstract: We study transport properties of an inertial Brownian particle moving in viscous symmetric periodic structures and driven by an oscillating signal of two harmonic components. We analyze the influence of symmetric, antisymmetric and asymmetric signals on directed transport and reveal the shift symmetry of the stationary averaged velocity of the Brownian particle with respect to the relative phase of two components of the signal. The shift symmetry holds true in all regimes.

18 citations


Network Information
Related Topics (5)
Scattering
152.3K papers, 3M citations
86% related
Matrix (mathematics)
105.5K papers, 1.9M citations
86% related
Boundary value problem
145.3K papers, 2.7M citations
86% related
Excited state
102.2K papers, 2.2M citations
84% related
Ground state
70K papers, 1.5M citations
83% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023145
2022286
2021109
2020112
2019118
2018122