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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: In this paper, an efficient procedure for the evaluation of the coefficients of fractional parentage (cfp's) for L-S coupled wave functions is presented, which involves the construction and diagonalization of the matrices representing the quadratic Casimir operators for the appropriate special unitary and orthogonal groups.
Abstract: An efficient procedure for the evaluation of the coefficients of fractional parentage (cfp’s) for L–S coupled wave functions is presented. The cfp’s are calculated separately for N particles, each with angular momentum l (s), coupled into a total angular momentum L (S). The N‐particle states formed can belong to any permutational symmetry. The procedure for the evaluation of the L and the S cfp’s for arbitrary permutational symmetry is a generalization of the procedure proposed by Bayman and Lande [Nucl. Phys. 77, 1 (1966)] for symmetric and antisymmetric states. It involves the construction and diagonalization of the matrices representing the quadratic Casimir operators for the appropriate special unitary and symplectic (or orthogonal) groups. The cfp’s of the antisymmetric L–S coupled states are obtained in terms of products of cfp’s for L and S corresponding to conjugate representations of the symmetric group. This method is demonstrated to provide cfp’s for L–S states for systems with a considerably l...

25 citations

Journal ArticleDOI
TL;DR: The integrals which are common to the application of the method of antisymmetric molecular orbitals to unsaturated as well as to aromatic molecules are tabulated in this paper.
Abstract: The integrals which are common to the application of the method of antisymmetric molecular orbitals to unsaturated as well as to aromatic molecules are tabulated. Accordingly, all integrals are evaluated with 2pπ hydrogen‐like functions. Tables are given for the Coulomb (aa; bb), exchange (ab; ab), and hybrid Coulomb exchange (ab; bb) repulsions of two electrons, and for the Coulomb and exchange attraction of a carbon ion for an electron.

25 citations

Journal ArticleDOI
TL;DR: In this article, the authors established an energy quantization (or energy identity) result for solutions to scaling invariant variational problems in dimension 4 which includes biharmonic maps (extrinsic and intrinsic).
Abstract: In the present work we establish an energy quantization (or energy identity) result for solutions to scaling invariant variational problems in dimension 4 which includes biharmonic maps (extrinsic and intrinsic) To that aim we first establish an angular energy quantization for solutions to critical linear 4th order elliptic systems with antisymmetric potentials The method is inspired by the one introduced by the authors previously in [LaR] for 2nd order problems

25 citations

Journal ArticleDOI
TL;DR: In this paper, the degeneracy of stable temporal Orr-Sommerfeld eigenmodes for plane Poiseuille flow was studied and the responses of the degeneracies were investigated through the initial value problem.
Abstract: Degenerating stable temporal Orr-Sommerfeld eigenmodes are studied for plane Poiseuille flow. The discrete spectrum of the eigenmodes is shown to possess infinitely many degeneracies, each appearing at a certain combination of k (the modulus of resultant wavenumber) and α R (the streamwise wavenumber time the Reynolds number). The eigenmodes are found to degenerate in a specific manner which confines the streamwise phase velocities of the degeneracies to be around $\frac{2}{3}$ of the centreline velocity. The responses of the degeneracies are investigated through the initial-value problem. The responses of the first four symmetric and the first two antisymmetric degeneracies are evaluated numerically for arbitrary initial disturbances expanded in terms of Chebyshev polynomials. The first symmetric and the first antisymmetric degeneracies exhibit temporal growth of the amplitudes in the wavenumber space. The maximum amplitudes are at most 7 times larger than the corresponding initial amplitudes. The amplitudes of the responses of the other four degeneracies decay rapidly owing to their higher damping rates. The time for which the degeneracy-response is in the growing phase is shown to be stretched with increasing Reynolds number. The degeneracies can therefore be active for longer periods of time at larger Reynolds numbers.

25 citations

Journal ArticleDOI
TL;DR: In this paper, a finite-difference analysis was used to study the free axially symmetric vibrations of solid, isotropic, elastic cylinders and the results indicated an accuracy within 1% for the first longitudinally symmetric mode and within 4% for second symmetric and first and second antisymmetric modes over a height-to-radius ratio range of 0.8-3.5 and for Poisson's ratio up to 0.34.
Abstract: A finite‐difference analysis has been used to study the free axially symmetric vibrations of solid, isotropic, elastic cylinders. A grid having up to 36 independent lattice points was used with simple central‐difference formulas to set up a system of homogeneous equations, whose determinant was solved to yield the resonance frequencies. The results have been compared with Rayleigh‐type thickness corrections to the frequency equations for thin disks and slender rods and with experimental observations on solid steel and aluminum cylinders. The results indicate an accuracy within 1% for the first longitudinally symmetric mode and within 4% for the second symmetric and first and second antisymmetric modes over a height‐to‐radius ratio range of 0.8–3.5 and for Poisson's ratio up to 0.34.

25 citations


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