Showing papers on "Antisymmetric relation published in 1995"
TL;DR: In this article, a new combinatorial description of the product of two Schur functions is proposed, which allows to discriminate in a very natural way between the symmetric and antisymmetric parts of the square.
Abstract: We propose a new combinatorial description of the product of two Schur functions. In the particular case of the square of a Schur function SI, it allows to discriminate in a very natural way between the symmetric and antisymmetric parts of the square. In other words, it describes at the same time the expansion on the basis of Schur functions of the plethysms S2(SI) and Λ2(SI). More generally our combinatorial interpretation of the multiplicities c_{IJ}^K \ = \ (S_IS_J, S_K) leads to interesting q-analogues c_{IJ}^K (q) of these multiplicities. The combinatorial objects that we use are domino tableaux, namely tableaux made up of 1 × 2 rectangular boxes filled with integers weakly increasing along the rows and strictly increasing along the columns. Standard domino tableaux have already been considered by many authors l33r, l6r, l34r, l8r, l1r, but, to the best of our knowledge, the expression of the Littlewood-Richardson coefficients in terms of Yamanouchi domino tableaux is new, as well as the bijection described in Section 7, and the notion of the diagonal class of a domino tableau, defined in Section 8. This construction leads to the definition of a new family of symmetric functions (H-functions), whose relevant properties are summarized in Section 9.
150 citations
TL;DR: In this article, a four-degree-of-freedom model able to capture the main phenomena which are likely to occur in the nonplanar finite dynamics of an elastic suspended cable subjected to external forcings and support motions is developed from the continuum equations.
147 citations
Journal Article•
TL;DR: In this article, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic.
Abstract: First, the dynamics of LC-circuits are formulated as a Hamiltonian system defined with respect to a Poisson bracket which may be degenerate, i.e., nonsymplectic. This Poisson bracket is deduced from the network graph of the circuit and captures the dynamic invariants due to Kirchhoff's laws. Second, the antisymmetric relations defining the Poisson bracket are realized as a physical network using the gyrator element and partially dualizing the network graph constraints. From the network realization of the Poisson bracket, the reduced standard Hamiltonian system as well as the realization of the embedding standard Hamiltonian system are deduced
123 citations
TL;DR: In this paper, a spontaneous breaking of the Munk problem with antisymmetric wind stress has been observed, where the amplitude of the cyclonic circulation exceeds that of the anticyclonic flow.
Abstract: The classical Munk problem of barotropic flow driven by an antisymmetric wind stress exhibits multiple steady solutions in the range of moderate to high forcing and moderate to low dissipation. Everywhere in the parameter space a perfectly antisymmetric solution exists in which the strength of the cyclonic gyre is equal and opposite to that of the anticyclonic gyre. This kind of solution has been well documented in the literature. In a subset of the parameter a pair of nonsymmetric stationary solutions coexists with the antisymmetric solution. For one member of the pair the amplitude of the cyclonic circulation exceeds that of the anticyclonic flow. The other member of the pair is obtained from the quasigeostrophic symmetry y→&minusy and ψ→−ψ. As a result, the point at which the western boundary current separates from the coast can be either south or north of the latitude at which the antisymmetric Ekman pumping changes sign. This is the first oceanogrphic example of spontaneous breaking of the q...
118 citations
TL;DR: In this paper, a lower bound of the size of the support for a given regularity exponent to achieve symmetry and antisymmetry is derived for compactly supported o.n. wavelets with scale factor a = 3.
101 citations
TL;DR: In this article, the axisymmetric static and dynamic deformations of laminated hollow cylinders composed of an arbitrary number of monoclinic layers are considered. But the main purpose of the paper is an exact, three-dimensional, free vibration analysis of such angle-ply laminated cylinders.
53 citations
TL;DR: In this article, the geometric phase arising from a conical intersection of the lowest potential energy surfaces of HO2 causes its bending vibrational wave functions to be double-valued, which enables them to be locally symmetric on one side of the intersection and locally antisymmetric on the other.
Abstract: We show that the geometric phase arising from a conical intersection of the lowest potential energy surfaces of HO2 causes its bending vibrational wave functions to be double‐valued, which enables them to be locally symmetric on one side of the intersection and locally antisymmetric on the other.
36 citations
TL;DR: The machinery of braided geometry introduced previously is used now to construct the e "totally antisymmetric tensor" on a general braided vector space determined by R • matrices.
Abstract: The machinery of braided geometry introduced previously is used now to construct the e ‘‘totally antisymmetric tensor’’ on a general braided vector space determined by R‐matrices. This includes natural q‐Euclidean and q‐Minkowski spaces. The formalism is completely covariant under the corresponding quantum group such as SOq(4) or SOq(1,3). The Hodge * operator and differentials are also constructed in this approach.
30 citations
TL;DR: In this paper, the impact of the symmetry of the reaction coordinate dependence of the solvent friction on the thermally activated barrier crossing rate is examined and possible symmetry forms are defined for the reaction coordination dependence of solvent friction.
Abstract: The impact of the symmetry of the reaction‐coordinate dependence of the solvent friction on the thermally activated barrier crossing rate is examined. Possible symmetry forms are defined for the reaction‐coordinate dependence of the solvent friction. The implications in the effective Grote–Hynes theory of Voth [J. Chem. Phys. 97, 5908 (1992)] and the theory recently presented by Haynes, Voth, and Pollak [J. Chem. Phys. 101, 7811 (1994)] of a spatially antisymmetric solvent friction are illustrated. Surprisingly, no correction to the Kramers–Grote–Hynes theory for the transmission coefficient is predicted, although an antisymmetric spatial dependence of the solvent friction is a strong departure from the usual spatially independent friction‐based generalized Langevin equation. The results from the analytical theories are compared to numerically exact generalized Langevin equation simulation results for a simple model system and found to agree well for a wide range of damping strengths and friction time sca...
26 citations
TL;DR: In this article, an analytical type solution for resolving the problem of free vibration of cantilever plates with rectangular orthotropy is described, and verification checks performed to verify the mathematical procedure are described.
24 citations
TL;DR: In this paper, the tetrad-connection formulation of the Regge calculus is used: basic variables are connection matrices and antisymmetric area tensors with appropriate bilinear conditions imposed.
Abstract: (3+1) (continuous time) Regge calculus is reduced to the Hamiltonian form. For this purpose the tetrad-connection formulation of the Regge calculus is used: basic variables are connection matrices and antisymmetric area tensors with appropriate bilinear conditions imposed. In these variables the action can be made quasipolynomial (with arcsin as the only deviation from polynomiality). The constraints are classified, classical and quantum consequences are discussed.
TL;DR: An exact asymptotically flat four-parameter solution of the Einstein-Maxwell equations representing the exterior field of two identical Kerr-Newman sources with angular momenta oppositely orientated is constructed in a simple analytical form as discussed by the authors.
Abstract: An exact asymptotically flat four-parameter solution of the Einstein-Maxwell equations representing the exterior field of two identical Kerr-Newman sources with angular momenta oppositely orientated is constructed in a simple analytical form. We show that there are no equilibrium states in such compact systems except for the case when the masses of the sources are equal to their charges. The condition for the existence of two horizons in the `antisymmetric' binary system turns out to be more stringent than in the case of a single Kerr-Newman black hole.
TL;DR: In this article, the dynamic buckling global response of a nonlinear, 3-degree-of-freedom dissipative model under a step loading of infinite duration is thoroughly discussed and the reliability and efficiency of the proposed readily obtained estimates are illustrated via numerical simulation, the accuracy of which is checked using energy balance considerations.
Abstract: The dynamic buckling global response of a nonlinear, 3-degree-of-freedom dissipative model under a step loading of infinite duration is thoroughly discussed. Geometrically imperfect models with symmetric or antisymmetric imperfections losing their static stability through a limit point and an asymmetric bifurcation point, respectively, are considered. Emphasis is given to the combined effect of nonlinearities (geometric and/or material) and damping. Exact, approximate, and lower/upper bound estimates based on energy criteria for establishing the dynamic buckling response of such autonomous models without solving the highly nonlinear initial-value problem are assessed. The reliability and efficiency of the proposed readily obtained estimates is illustrated via numerical simulation, the accuracy of which is checked using energy balance considerations. Certain interesting byproducts associated with a postlimit point bifurcation and breakdown of the symmetry of deformation are also revealed.
Patent•
04 Oct 1995
TL;DR: In this article, a superconducting string is measured by two magnetic flux transformers, each comprising a signal coil and two pick-up coils (Lp1, Lp2), which lie in two perpendicular planes providing two independent channels of measurements.
Abstract: Apparatus for measuring gravitational fields comprising a superconducting string (1) fixed at both ends and forming part of a closed superconducting loop inductively coupled to two driving solenoids (Ld1, Ld2). Displacement of the string in response to a gravitational field is sensed by two magnetic flux transformers each comprising a signal coil and two pick-up coils (Lp1, Lp2). Pairs of pick-up coils lie in two perpendicular planes providing two independent channels of measurements. The two arms of each flux transformer are balanced to convert only the amplitudes of the string's antisymmetric natural modes into an output voltage. The output voltage of each channel is used to produce a feed-back current distribution (Iy1, Iy2) proximate and parallel to the string. By adjusting the feed-back current, the effective relaxation time and resonant frequency of the first antisymmetric mode of the string can be adjusted, while leaving the symmetric modes unchanged, thus increasing the apparatus' sensitivity to gravity gradients.
TL;DR: In this paper, it was shown that trapped modes do not exist below the cut-off frequency for a large class of sound-soft guides containing both soundsoft and sound-hard bodies.
Abstract: It is well known that trapped modes exist in certain types of acoustic waveguides. These modes correspond to localized fluid oscillations and occur at frequencies at which propagating modes down the guide are not able to exist, below a so-called ‘cut-off frequency’. For example, antisymmetric trapped-mode motions are known to occur in two-dimensional, parallel-plate waveguides containing bodies, at wavenumbers which are less than π/2d, where 2d is the width of the guide. So far, however, these modes have only been found in waveguides that have acoustically hard walls and either contain acoustically hard bodies or have variable cross-section. The purpose of this work is to investigate the existence or otherwise of trapped modes when one or more of the boundaries is replaced by an acoustically soft boundary.
We prove here that trapped modes do not exist below the cut-off frequency for a large class of sound-soft guides containing both sound-soft and sound-hard bodies. In addition, we show that antisymmetric trapped modes do not exist below the cut-off frequency in many two-dimensional, sound-hard guides containing sound-soft bodies. This second result is also generalized to certain types of trapped-mode motion in axisymmetric waveguides. The method of proof relies on finding a strictly positive function w which satisfies a certain field inequality within the guide and boundary inequalities on the guide walls and body surfaces. A vector identity is established which relates w to the possible trapped-mode potential φ in such a way that it may be deduced that φ must be identically equal to zero throughout the guide.
TL;DR: Travelling wave solutions for equations that model two parallel coupled nerve fibres are found and it is shown that the introduction of weak coupling between the fibres induces either symmetry or antisymmetry of the action potentials.
Abstract: Travelling wave solutions for equations that model two parallel coupled nerve fibres are found. The travelling wave here represents the action potential. It is shown that the introduction of weak coupling between the fibres induces either symmetry or antisymmetry of the action potentials. A symmetric pulse is a solution where both fibres fire simultaneously and the action potentials propagate locked in phase at the same wave speed along the length of each fibre; an antisymmetric pulse is a solution where one fibre fires, resulting in an action potential propagating along it, while the other remains at rest. Geometric singular perturbation theory and the exchange lemma are used to prove the existence of solutions. In addition, a technique which involves the use of differential forms for detecting transversalities of small order is introduced.
TL;DR: This work calculates analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix and suggests that the analytic calculation yields the correct value for the typical number ofFixed points.
Abstract: We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.
TL;DR: In this article, the spline strip method based on the first-order shear deformation shell theory was applied to analyze vibration of antisymmetric angle-ply laminated cylindrical panels with two opposite circumferential edges simply supported and varying boundary conditions on the remaining two straight edges.
TL;DR: In this article, an approximate method based on the wave function expansion procedure has been used to solve the problem of reflection of time harmonic plane strain waves normally incident upon the fixed edge of a semi-infinite, uniaxially fiber-reinforced, composite plate of linearly elastic materials.
Abstract: An approximate method based on the wave‐function expansion procedure has been used to solve the problem of reflection of time harmonic plane strain waves normally incident upon the fixed edge of a semi‐infinite, uniaxially fiber‐reinforced, composite plate of linearly elastic materials. Both symmetric and antisymmetric incident waves have been considered. The dispersion relation of the infinite plate has been solved through an approximate technique to obtain wave functions. The amplitudes of reflected waves have been determined by satisfying the fixed edge condition through the application of a variational principle. It is shown that the results agree well with known solutions for homogeneous isotropic plates. Numerical results are presented for a graphite/epoxy composite plate. The accuracy of the results is demonstrated through satisfaction of the principle of energy conservation and the reciprocity relations. The influence of fiber‐direction elastic stiffness on reflection coefficients has also been st...
TL;DR: In this paper, a non-standard way, the coupling of a bosonic string theory with a dilaton and antisymmetric fields is investigated, and an interpretation of the static potential as a type of non-local Casimir effect is given.
Abstract: The coupling, in a non-standard way, of a bosonic string theory with a dilaton and antisymmetric fields is investigated. By integrating over the antisymmetric fields, a Coulomb-like interaction term is generated. The static potential of a theory of this kind is obtained from the corresponding non-local zeta function, in some approximation. An interpretation of the static potential as a type of non-local Casimir effect is given.
TL;DR: In this paper, the authors compare order $R^4$ terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories.
Abstract: We compare order $R^4$ terms in the 10-dimensional effective actions of SO(32) heterotic and type I superstrings from the point of view of duality between the two theories. Some of these terms do not receive higher-loop corrections being related by supersymmetry to `anomaly-cancelling' terms which depend on the antisymmetric 2-tensor. At the same time, the consistency of duality relation implies that the `tree-level' $R^4$ super-invariant (the one which has $\zeta(3)$-coefficient in the sphere part of the action) should appear also at higher orders of loop expansion, i.e. should be multiplied by a non-trivial function of the dilaton.
TL;DR: A general formula is reported which, condensing all the reduction steps, leads to the direct evaluation of those traces of p-order replacement operators calculated in finite-dimensional, antisymmetric, and spin-adapted N-electron spaces.
Abstract: In our previous studies with the evaluation of traces of p-order replacement operators calculated in finite-dimensional, antisymmetric, and spin-adapted N-electron spaces (p\ensuremath{\le}N), we described a technique for the calculation of those expressions based on the reduction of the opertor order [A. Torre, L. Lain, and J. Millan, Phys. Rev. A 47, 923 (1993)]. Now, we report a general formula which, condensing all the reduction steps, leads to the direct evaluation of those traces. Some examples for illuminating the usefulness of that formula are reported.
TL;DR: In this article, the authors derived a class of finite elements from wavelets generated using affine, fractal interpolation functions (AFIF), which are similar to conventional finite elements in that they are compactly supported, and are interpolatory at dyadic points which define the nodes.
Abstract: This paper derives a class of finite elements from wavelets generated using affine, fractal interpolation functions (AFIF). The finite elements derived from wavelets generated from an AFIF differ from recent elements derived by the authors in that multivalued scaling functions are employed. These elements are similar to conventional finite elements in that they are compactly supported, and are interpolatory at dyadic points which define the nodes. Specifically, two scaling functions and two wavelets that are Lipschitz continuous are employed. Each scaling function has support of length one or two, and is either symmetric or antisymmetric. These properties enables the incorporation of both Dirichlet or Neumann boundary conditions in a straightforward manner. For either class of boundary conditions, the multiresolution Vk+1≡Vk⊕Wk restricted to the compact interval of interest is fully orthogonal. This fact is advantageous in that it facilitates both the analysis of the convergence of the multigrid methods.
TL;DR: In this paper, the generalized modal approach in conjunction with the biorthogonality conditions of the principal modes with respect to the eigenfunctions of the original and adjoint equations are used to decouple the equations of motion.
TL;DR: In this paper, a free-vibration analysis of orthotropic cantilever plates resting on point supports is presented, where support points are assumed to be symmetrically distributed about the plate centerline running normal to the clamped edge.
Abstract: The method of superposition is used to achieve a free-vibration analysis of orthotropic cantilever plates resting on point supports. In the initial development of the analysis it is assumed that the supports are symmetrically distributed about the plate centerline running normal to the clamped edge. Delineation is then made between modes that are symmetric, or antisymmetric, with respect to this centerline. It is shown how a small modification to the theory permits the obtaining of solutions for the case where supports are located at the plate outer corners. Modifications required to handle the case where support points do not have a symmetric distribution are also described. Free-vibration eigenvalues are provided for square plates with a pair of symmetrically distributed support points and various combinations of orthotropic property ratios. The problem under study is one that may occur, for example, in cantilevered mezzanine floors in buildings. It is expected that the tabulated eigenvalues will also provide useful reference points for other researchers. This appears to be the first analytical-type solution developed for this realistic industrial problem.
TL;DR: In this article, the nonabelian generalization of a recently proposed abelian axial gauge model for tensor matter fields is obtained from a ϕ4-type theory for antisymmetric fields obeying a complex self-dual condition.
TL;DR: In this paper, the mean square response of a single-degree-of-freedom thin composite plate model was analyzed using five different time domain simulation methods and two equivalent linearization solutions, and the results showed that the solution is highly dependent on step size, numerically simulated loading, damping, simulation time and the numerical integration method.
TL;DR: Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function.
Abstract: Predictions of Akkermans et al. are essentially changed when the Krein spectral displacement operator is regularized by means of zeta function. Instead of piecewise constant persistent current of free electrons on the plane one has a current which varies linearly with the flux and is antisymmetric with regard to all time preserving values of $\alpha$ including $1/2$. Different self-adjoint extensions of the problem and role of the resonance are discussed.
TL;DR: In this article, a finite element code employing radial discretization is formulated for the calculations of linear bifurcation stability of laminated anisotropic circular cylinders using Biot's incremental deformation theory.