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.

Natural Frequencies and Mode Shapes of Composite Conoids with Complicated Boundary Conditions

Abstract: A finite element code is developed using an eight-noded curved quadratic isoparametric element and the formulation is validated through solution of a benchmark problem which was earlier solved by other researchers. Numerical problems are solved for ten different practical boundary conditions and for different symmetric and antisymmetric laminations of conoidal shells on square planform to study the performances of different shell options in terms of fundamental frequencies. Effects of number of boundary constraints and arrangement of boundary conditions along the four edges on fundamental frequencies are studied meticulously and also performance of symmetric and antisymmetric laminations are compared in detail. A comparative performance study of cross ply and angle ply laminations is also made. Specific conclusions are drawn at the end, to summarize the outcome of the present investigation that are expected to serve as important guidelines to engineers engaged in analysis, design, and construction of comp...

Quantum coherence of the Heisenberg spin models with Dzyaloshinsky-Moriya interactions

Abstract: We study quantum coherence in a spin chain with both symmetric exchange and antisymmetric Dzyaloshinsky-Moriya couplings. Quantum coherence is quantified using the recently introduced quantum Jensen-Shannon divergence, which has the property that it is easily calculable and has several desirable mathematical properties. We calculate exactly the coherence for arbitrary number of spins at zero temperature in various limiting cases. The $\sigma^{z} \sigma^{z}$ interaction tunes the amount of coherence in the system, and the antisymmetric coupling changes the nature of the coherence. We also investigate the effect of non-zero temperature by looking at a two-spin system and and similar behavior, with temperature dampening the coherence. The characteristic behavior of coherence resembles that of entanglement and is opposite to that of discord. The distribution of the coherence on the spins is investigated and found that it arises entirely due to the correlations between the spins.

Theory and lattice structure of complex paraunitary filterbanks with filters of (Hermitian-)symmetry/antisymmetry properties

Abstract: The theory of the real-coefficient linear-phase filterbank (LPFB) is extended to the complex case in two ways, leading to two generalized classes of M-channel filterbanks. One is the symmetric/antisymmetric filterbank (SAFB), where all filters are symmetric or antisymmetric. The other is the complex linear phase filterbank (CLPFB), where all filters are Hermitian symmetric or Hermitian antisymmetric and, hence, have the linear-phase property. Necessary conditions on the filter symmetry polarity and lengths for the existence of permissible solutions are investigated. Complete and minimal lattice structures are developed for the paraunitary SAFB and paraunitary CLPFB, where the channel number M is arbitrary (even or odd), and the subband filters could have different lengths. With the elementary unitary matrices in the structure of the paraunitary SAFB constrained to be real and orthogonal, the structure covers the most general real-coefficient paraunitary LPFBs. Compared with the existing results, the number of parameters is reduced significantly.