Showing papers on "Antisymmetric relation published in 1979"
TL;DR: A finite element formulation of the equations governing the laminated anisotropic plate theory of Yang, Norris and Stavsky, is presented in this article, which is a generalization of Mindlin's theory for isotropic plates to laminated aisotropic plates and includes shear deformation and rotary inertia effects.
196 citations
TL;DR: In this paper, the dispersion curves of a sandwich plate with symmetric facings are computed and compared for plates with "thick, light, and soft" facings as well as for plates having thin, heavy, and stiff facings.
Abstract: Motions of a sandwich plate with symmetric facings are studied in the framework of the three-dimensional equations of elasticity. Both the core and facings are assumed to be isotropic and linearly elastic. Harmonic wave solutions, which satisfy traction-free face conditions and continuity conditions of tractions and displacements at the interfaces, are obtained for four cases: symmetric plane strain solutions for extensional motion, antisymmetric plane strain solutions for flexural motion, and solutions for the symmetric and antisymmetric SH-waves. The dispersion relation for each of these cases is obtained and computed. In order to exhibit the effect of the ratios of facing to core thicknesses, elastic stiffnesses and densities, on the dynamic behavior of sandwich plates, dispersion curves are computed and compared for plates with “thick, light, and soft” facings as well as for plates with “thin, heavy, and stiff” facings. Asymptotic expressions of dispersion relations for extensional, flexural, and symmetric SH-waves are obtained in explicit form, as the frequencies and wave numbers approach zero. The thickness vibrations in sandwich plates are studied in detail. The resonance frequencies and modal functions of the thickness-shear and thickness-stretch motions are obtained. Simple algebraic formulas for predicting the lowest thickness-shear and the lowest thickness-stretch frequencies are deduced. The orthogonality of the thickness modal functions is established.
46 citations
TL;DR: In this article, it was shown that the rate at which intrinsic angular velocity approaches its steady-state value (ω = 1/2▽ × u) is determined by the magnitude of the antisymmetric part of the pressure tensor.
Abstract: Nonequilibrium molecular dynamics calculations are used to show that polyatomic fluids can support antisymmetric stress. In a homogeneous system where the time dependence of vorticity is a step function, it is shown that the rate at which intrinsic angular velocity approaches its steady-state value (ω = 1/2▽ × u) is determined by the magnitude of the antisymmetric part of the pressure tensor.
40 citations
TL;DR: In this article, explicit expressions for the matrix elements of unitary group generators between geminally antisymmetric spin-adapted N-electron configurations in terms of the orbital occupancies and spin factors are derived by use of many-body time-independent diagrammatic techniques.
Abstract: The explicit expressions for the matrix elements of unitary group generators between geminally antisymmetric spin-adapted N-electron configurations in terms of the orbital occupancies and spin factors, given as spin function matrix elements of appropriate orbital permutations, are derived by use of the many-body time-independent diagrammatic techniques. It is also shown how this approach can be conveniently combined with graphical methods of spin algebras to obtain explicit expressions for the spin factors, once a definite coupling scheme is chosen. This method yields explicit expressions for the orbital permutations defining the spin factors. However, if desired, the explicit determination of line-up permutations can be avoided in this approach, since they are implicitly contained in the orbital diagrams. It also clearly indicates why the geminally antisymmetric spin functions have to be used when a simple formalism is desired. 5 figures.
40 citations
TL;DR: In this paper, an approximate solution of the title problem by use of very simple co-ordinate functions, which partially satisfy the boundary conditions, and the Ritz method is presented.
25 citations
TL;DR: In this paper, a generalization of Mobius inversion by constructing, on partially ordered sets, pairs of "contracted" matrices which are inverses of each other is presented.
Abstract: Summary
This work presents a generalization of Mobius inversion by constructing, on partially ordered sets, pairs of “contracted” matrices which are inverses of each other. We commence by defining some nonstandard matrix operations, for which a number of results are derived, culminating in a theorem that furnishes conditions under which matrix contraction will commute with matrix multiplication. One consequence of mapping these results into graph theoretical operations on partial ordering graphs (transitive, antisymmetric digraphs) is to suggest a novel class of functions defined thereon which generalize the Riemann and Mobius functions in a way that may lead to new algorithms for matrix inversion. The usefulness of these functions in physical science is illustrated with two examples which in recent publications made implicit use of graph contraction. The work suggests a number of tantalizing (as yet unsolved) problems; our paper concludes with a summary of these.
17 citations
01 Jan 1979
TL;DR: In this article, a general dynamic theory for antisymmetric responses that is not based on linearity is presented and is very difficult to formulate and is quite out of the realms of possibility at present.
Abstract: In an earlier paper dealing with symmetric response to waves it was shown how transfer functions could be calculated for a ship responding in sinusoidal waves. The present paper deals with the problem of antisymmetric response. Possession of the techniques outline in the two papers permits the calculation of general response to sinusoidal waves and hence makes the study of random seas possible. As in previous work the treatment rests on the concept of linearity. While this is unlikely to be a serious drawback for anything but the most violent motions and distortions, it does admit a substantial simplification of the theory. Indeed a general dynamic theory for antisymmetric responses that is not based on linearity is certain to be very difficult to formulate and is quite out of the realms of possibility at present. Despite this simplification, however, one or two areas are exposed in the present paper in which even linear theory appears to be deficient. One object of this paper, then, is to focus attention on certain topics in which further research would be particularly useful. Order from BSRA as No. 52,631.
11 citations
TL;DR: In this article, the hamiltonian and three other operators are used to calculate the energy and some other properties of electronic systems without first having to form the antisymmetric projection of the functions.
9 citations
TL;DR: In this article, a theory concerning the excitation spectrum arising from the interaction between two-identical three-level atoms (molecules), one of which is excited in the presence of a strong resonant electromagnetic field (pump field).
Abstract: A theory is developed concerning the excitation spectrum arising from the interaction between two-identical three-level atoms (molecules), one of which is excited in the presence of a strong resonant electromagnetic field (pump field). General expressions for the Green's functions are derived in the limit of high photon densities, which describe the excitation spectrum of the symmetric and antisymmetric modes respectively. The theory is applied to the two-atom Hanle-type resonance spectra. Detailed expressions for the spectral functions have been derived which describe the excitation spectrum of the symmetric and antisymmetric modes when the two-atoms are close together as well as when they are far apart. It is found that the expressions for the spectral functions include two main specific processes which lead to the amplification of the signal field: (1) the probability amplitude for the central peak of the laser field becomes negative when the resonance condition ω 2 32 = Ω 2 2 + Ω 2 3 is satisfied, where ω32 = ω3 - ω2 is the energy separation between the two interacting excited states 2 and 3, and Ω2 and Ω3 are the corresponding energy shifts (Rabi frequencies) induced by the laser field. (2) Among the several sidebands, there are two pairs of sidebands which have positive and negative probability amplitudes respectively, and when certain conditions prevail, the sidebands with the negative amplitudes dominate. In this case, it seems that the amplification of the signal field is more pronounced for the antisymmetric rather than for the symmetric modes. The cooperative effects arising from the presence of the second atom are fully discussed.
8 citations
TL;DR: In this paper, a significant value for the cubic anharmonic force constant α33 = -1.80 (30) x 10-19 J A-3 of the one-particle potential was obtained, and is compared with other recent determinations.
Abstract: Recent elastic neutron scattering data [Merisalo & Larsen (1977). Acta Cryst. A33, 351-354] have been reconsidered. A significant value for the cubic anharmonic force constant α33 = -1.80 (30) x 10-19 J A-3 of the one-particle potential was obtained, and is compared with other recent determinations.
7 citations
TL;DR: In this article, Gierz showed that certain function spaces L ⊂ C (X;E) have the approximation property as soon as E has the approximate property, where E is a non-zero locally convex space and X is a Hausdorff space.
Abstract: Publisher Summary This chapter describes the approximation property for Nachbin spaces. In the chapter, X is a Hausdorff space that separates the points of X , and E is a non-zero locally convex space. The chapter proves that certain function spaces L ⊂ C (X;E) have the approximation property as soon as E has the approximation property. The chapter proves this for the class of all Nachbin spaces. Such spaces include C (X;E) with the compact-open topology; C b (X;E) with the strict topology; and C O (X;E) with the uniform topology. The techniques used in the chapter was suggested by Gierz, where he proved an analogue of a theorem for the case of X compact and bundles of Banach spaces. This technique of “localization” of the approximation property was used in the case of the partition by antisymmetric sets.
TL;DR: In this paper, the concepts of differentiability and codifferentiability in the Von Neumann algebra generated by the regular ω representation of Rn were defined for a C∞ multiplier ω, and analogs of the classical Schwartz space and its dual are formulated and the case where ω is fully antisymmetric is studied.
Abstract: For a C∞ multiplier ω, on Rn we define the concepts of differentiability and codifferentiability in the Von Neumann algebra generated by the regular ω representation of Rn. Analogs of the classical Schwartz space and its dual are formulated and the case where ω is fully antisymmetric is studied. Connections with the canonical Fourier transform of an earlier paper are investigated.
TL;DR: In this article, a semi-infinite crack extends nonuniformly against a body force that is antisymmetric about the fault plane but independent of the distance from the latter.
Abstract: A semiinfinite crack extends nonuniformly against a body force that is antisymmetric about the fault plane but independent of the distance from the latter. Conversion of the inhomogeneous wave equation for SH motion into a radiation equation incorporates fault plane distributed mechanisms. An integral equation is then formulated for fault plane observations preceding the crack. Both the body force and the stress drop are assumed to be bounded over finite histories. Multiple inversion yields a formal exterior solution which behaves singularly near the crack edge. An analogy with a Barenblatt postulate cancels the singularity through a nonlinear integral equation governing the edge coordinate. The resultant non-singular displacement gradient turns out to be continuous at the crack edge; here, the force-induced contribution vanishes. The interior problem is also solved for the displacement along either crack face. An application is illustrated for an impulsive body force; this leads to an interesting corollary with totally uniform results. Finally, if the body force exists within a half-space away from which extension occurs, it contributes nothing to the exterior solution; furthermore, the interior solution can be evaluated in terms of only the stress drop and the edge locus, i.e. without explicit prescription of such a body force.
TL;DR: In contrast to the previously measured differential cross sections, which show symmetry about 90° for both the S = 1 and S = 0 channels, Ay is consistent with being antisymmetric about 90 degrees for the S 0 channel and is approximately symmetric for the s = 1 channel as discussed by the authors.
TL;DR: The analysis of the K± 12C scattering leads to the conclusion that the corresponding effective coupling constant is significantly larger than the coherent sum of the elementary coupling constants as mentioned in this paper. But this is not the case for the K−12C scattering.
Abstract: Possibilities are examined of obtaining information on kaon nuclear coupling constants, without referring to any specific models. The basis for such a type of analyses is the use of analytic properties of the scattering amplitudes. Particularly useful is the forward dispersion relation for the antisymmetric amplitude. The analysis of the K± 12C scattering leads to the conclusion that the corresponding effective coupling constant is significantly larger than the coherent sum of the elementary coupling constants.
TL;DR: In this paper, the effect of phase error on the difference Fourier map was investigated and it was shown that the peak heights due to antisymmetric density distribution are reduced considerably and parasitic peaks appear on the map.
Abstract: In the Fourier and the difference Fourier syntheses, the contribution of antisymmetric components of the density distribution to the phases of structure factors are usually ignored. From an analysis of the asymmetric thermal vibration of the Cu atom in a CuCl crystal by neutron diffraction, the effects of phase error are shown to appear in the following two forms on the difference Fourier map: (i) the peak heights due to antisymmetric density distribution are reduced considerably, and (ii) parasitic peaks appear on the map and modulate the difference density distribution.
TL;DR: A complete set of relations between geminals, which generate the N-particle antisymmetric function, is given in this paper, where the authors also describe the relations between the geminals.
Abstract: A complete set of relations between geminals, which generate the N-particle antisymmetric function, is given.
01 Sep 1979
TL;DR: In this paper, the authors considered a fin-tailplane configuration with two flat half-tailplanes and a flat fin joined together so as to be symmetric about the plane of the fin.
Abstract: : The fin-tailplane configuration consists of two flat half-tailplanes and a flat fin joined together so as to be symmetric about the plane of the fin. The half-tailplanes may be set at a non-zero dihedral angle to each other. The chords of all the surfaces at their junction are of the same length and are coincident. The fin-tailplane configuration is assumed to be isolated and to be oscillating harmonically about its mean position in a subsonic flow whose main stream is parallel to the junction chord. The oscillatory motion is taken to be antisymmetric about the plane of the fin. Linearized equations of potential flow are assumed to be valid so that the normal velocities on the fin and tailplane surfaces may be related to the loadings on these surfaces by means of linear integral equations. These integral equations are solved numerically for the loadings for oscillation at general frequency in any antisymmetric modes, and the generalised airforce coefficients are then obtained. Approximations to the loadings are taken as linear combinations of basis functions.
TL;DR: In this article, a method of separating the intensities of bands which are highly overlapping was proposed to solve the uncertainty in the intensity analysis in the infrared spectra of molecules with more than one C-H bond.
Abstract: In the infrared spectra of molecules with more than one C-H bond the symmetric and antisymmetric stretching bonds often overlap, causing uncertainty in the intensity analysis. For CH2Cl2 and CD2Cl2 in the vapour state, the two bands overlap to such an extent that Straley who takes it as one band attributes it to antisymmetric stretching while Saekiet al assign it to the symmetric stretching. Following the method of analysis initiated in this laboratory, we have solved this problem by ultimately obtaining intensities separately forA
1 andB
2 species. The band is mostly due to the symmetric stretching, 0.06 out of the total of 0.31 contributing toB
2. Thus, this gives a method of separating the intensities of bands which are highly overlapping.
TL;DR: In this paper, an analytical method is presented for predicting the behavior of an emitter-coupled single-ended differential pair of transistors adjusted for the generation of symmetric pulse waveform.
Abstract: An analytical method is presented here for correctly predicting the behaviour of an emitter-coupled single-ended differential pair of transistors adjusted for the generation of symmetric pulse waveform. Here the antisymmetric self-saturating transfer characteristics of the differential pair has been approximated by a transcendental function of hyperbolic tangent type and the frequency relation ia obtained by jump behaviour. Conditions for minimum sensitivity have been obtained and the scope for obtaining the cancellation of the effect of temperature on tuning elements is indicated. More comprehensive design criteria arc thus made available for such circuits in general and experimental verifications through the circuit implementation of the derived conditions have been made to show the close corroboration of the theoretical expectations with the practical results.
01 Jan 1979
TL;DR: In this article, the duality properties of the electromagnetic field completed by the "Clebsch" decomposition of the "matter current" permits to formulate the Maxwell equations in a simple way in complex vectorial space.
Abstract: The duality properties of the electromagnetic field completed by the “Clebsch” decomposition of the “matter current” permits to formulate the Maxwell equations in a simple way in complex vectorial space. It is then discussed what sort of materials relations permit to obtain orthonormal solutions of the total field as extensions of the usual T.M. and T.E. modes. A way to “linearise” the plasma transport equations is pointed out where symmetric and antisymmetric properties of field and matter are outlined without direct use of Fourier-transformed spaces.
TL;DR: In this paper, the influence of various components of the Preedom-wildenthal interaction on properties of A = 20,21 nuclei was investigated and the effects of the LS and ALS components on the one hand and of the central and tensor components were found to be very similar.
TL;DR: In this article, it was shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantismmetric wave function, which leads to the coexistence of cluster models including the single particle model as a special case of the cluster model.
Abstract: It is shown that each Yakubovski component of the totally antisymmetric four-body wave function satisfies the same equation as the unantisymmetric wave function. In the antisymmetric total wave function, the wave functions belonging to the same kind of partition are totally antisymmetric among themselves. This leads to the coexistence of cluster models, including the single particle model as a special case of the cluster model, as a sum.
TL;DR: In this article, a nonlinear integral equation consistent with a nonsingular crack-preceding reception is converted to a series equation and results inside and outside the crack domain are represented by, principally, infinite series of hypergeometric functions.
Abstract: Multiple series solutions are extracted from certain recently established integral convolutions (Chee-Seng [5]) pertaining to crack extension against an antisymmetric quasiuniform body force. Analyticity of the source mechanism plays the crucial role. The nonlinear integral equation consistent with a nonsingular crack-preceding reception is likewise converted to a series equation. Results inside and outside the crack domain are represented by, principally, infinite series of hypergeometric functions. The source mechanism contributes to their coefficients which generally depend on reception coordinates. An application is illustrated for a linear source distribution with analytic coefficients. If these are uniform, the infinite series solutions degenerate to finite combinations involving inverse trigonometric functions; moreover, under compatible conditions, the crack edge describes a hyperbolic locus. Another application concerns a body force with an exponentially diminishing intensity; it leads to a logarithmic locus for the crack edge. Finally, general criteria are determined for a zero initial edge-velocity.
TL;DR: The antisymmetric kernel of the quasi-order is determined by the symmetry classes with only one element as discussed by the authors, and all matrices suited for lower bounds are contained in the antisymmetric kernel.
15 Jul 1979
TL;DR: The analysis of the K±12C scattering leads to the conclusion that the corresponding effective coupling constant is significantly larger than the coherent sum of the elementary coupling constants as discussed by the authors, without referring to any specific models.
Abstract: Possibilities are examined of obtaining information on kaon nuclear coupling constants, without referring to any specific models. The basis for such a type of analyses is the use of analytic properties of the scattering amplitudes. Particularly useful is the forward dispersion relation for the antisymmetric amplitude. The analysis of the K±12C scattering leads to the conclusion that the corresponding effective coupling constant is significantly larger than the coherent sum of the elementary coupling constants.
TL;DR: In this article, an equation for frequencies caused by local distortions in stereo-regularity of polymers was derived and analyzed using a simple model of coupled oscillators, and it was shown that these distortions produce localized oscillations, of which the frequencies are near the upper and lower boundaries of each frequency branch.
Abstract: An equation was derived for frequencies caused by local distortions in stereo-regularity of polymers. Using a simple model of coupled oscillators the solutions obtained were analysed. It was shown that these distortions produce localized oscillations, of which the frequencies are near the upper and lower boundaries of each frequency branch and correspond to symmetric and antisymmetric local oscillation.