Showing papers on "Space (mathematics) published in 1984"
TL;DR: The determinant, characteristic polynomial and adjoint over an arbitrary commutative ring with unity can be computed by a circuit with size O(n3.496) and depth O(log2n).
395 citations
TL;DR: In this article, a probability distribution has been proposed as an order parameter for spin-glasses, and this probability depends on the particular realization of the couplings even in the thermodynamic limit.
Abstract: A probability distribution has been proposed recently by one of us as an order parameter for spin-glasses We show that this probability depends on the particular realization of the couplings even in the thermodynamic limit, and we study its distribution We also show that the space of states has an ultrametric topology
383 citations
TL;DR: In this article, a priori inequalities are defined which must be satisfied by the force-free equations, and upper bounds for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of a region can be shown to decay sufficiently fast at infinity.
Abstract: Techniques for solving boundary value problems (BVP) for a force free magnetic field (FFF) in infinite space are presented. A priori inequalities are defined which must be satisfied by the force-free equations. It is shown that upper bounds may be calculated for the magnetic energy of the region provided the value of the magnetic normal component at the boundary of the region can be shown to decay sufficiently fast at infinity. The results are employed to prove a nonexistence theorem for the BVP for the FFF in the spatial region. The implications of the theory for modeling the origins of solar flares are discussed.
333 citations
TL;DR: Polyakov's quantization is extended to strings embedded in a curved space, and the critical dimension calculated as mentioned in this paper, however the no-ghost theorem fails there unless the space is supersymmetric and Ricci-flat.
307 citations
01 Jan 1984
293 citations
TL;DR: On considere l'existence a t grand de solutions de petite amplitude for des equations d'onde d'ordre 2 non lineaires a 4 dimensions d'espace-temps.
Abstract: On considere l'existence a t grand de solutions de petite amplitude pour des equations d'onde d'ordre 2 non lineaires a 4 dimensions d'espace-temps
227 citations
TL;DR: In this paper, the authors explore the analysis of the geometrically nonlinear behavior of space structures, using the modified arc length method of Riks and Crisfield, which is robust and able to handle problems that exhibit several negative eigenvalues simultaneously.
175 citations
TL;DR: In this paper, exact orders for the Kolmogorov and linear widths of the unit ball of the space in the metric of a unit ball were given for the first time, and the determination of the upper estimates is based on approximation by random objects.
Abstract: Precise orders are given for the Kolmogorov and linear widths of the unit ball of the space in the metric of for The determination of the upper estimates is based on approximation by random objects This method goes back to Kashin (Math USSR Izv 11 (1977), 317-333) The corresponding lower estimates were obtained in a previous article of the author (Vestnik Leningrad Univ Math 14 (1982), 163-170)Bibliography: 12 titles
107 citations
30 Apr 1984
TL;DR: This paper argues that the "absurd subspace" (all but the first billion modes) is not a strength of continuum modeling, but, in fact, a weakness, and contends that the partial differential equation model and the finite-element model are not real structures, only mathematical models.
101 citations
TL;DR: In this paper, the nonlinear Bolzmann equation is discussed without cutoff approximations on potentials of infinite range, and the Cauchy problem is solved locally in time, for both the spatially homogeneous and inhomogeneous cases.
Abstract: The nonlinear Bolzmann equation is discussed without cutoff approximations on potentials of infinite range. The Cauchy problem is solved locally in time, for both the spatially homogeneous and inhomogeneous cases. For the former case, this is done in function spaces of Gevrey classes in the velocity variables, and for the latter, in spaces of functions which are analytic in the space variables and of Gevrey classes in the velocity variables. The obtained existence theorem is of Cauchy-Kowalewski type. Also, the convergence of Grad’s angular cutoff approximations is established.
97 citations
TL;DR: In this article, a space-time least-square finite element scheme is presented for the advection-diffusion problems at moderate to high Peclet numbers, which can be used to define the steady-state solution as the asymptotic transient solution for large time.
TL;DR: In this article, a notion of uniform convexity is defined for quasi-normed (complex) spaces by replacing norms of midpoints of segments in the space by norms of centers of complex discs.
TL;DR: In this paper, a theory of ℒp-spaces for 0 < p < 1 was developed, based on the concept of a locally complemented subspace of a quasi-BANACH space.
Abstract: We develop a theory of ℒp-spaces for 0 < p < 1, basing our definition on the concept of a locally complemented subspace of a quasi-BANACH space. Among the topics we consider are the existence of basis in ℒp-spaces, and lifting and extension properties for operators. We also give a simple construction of uncountably many separable ℒp-spaces of the form ℒp(X) where X is not a ℒp-space. We also give some applications of our theory to the spaces Hp, 0 < p < 1.
TL;DR: In this paper, a general expression for the Riemann and Ricci tensors in terms of rescaled vielbeins and the group structure constants is derived, and a simple criterion to find which rescalings preserve the isometry group is given.
01 Jan 1984
TL;DR: In this paper, the AP Calderon theorem for interpolation spaces between two quasi-normed Lorentz spaces ∧p(φ) and, in the case of Banach spaces, between two Sobolev spaces is deduced and trace theorems are given for these spaces.
Abstract: In this paper we show that interpolation with a function parameter is perfectly suited to identify interpolation spaces between two quasi-normed Lorentz spaces ∧p(φ) and, in the case of Banach spaces, between two Sobolev spaces \(W_{\Lambda ^p (\phi )}^m\) We deduce the AP Calderon theorem for these spaces We prove the identity \((H_p^{\phi _0 } ,H_p^{\phi _1 } )_{f,q;K} = B_{p,q}^\psi\) where ψ is classically connected with φ0, φ1 and f, and in which the Sobolev space H p φ and the Besov space B p,q φ are constructed in the same way as in the classical case Imbedding and trace theorems are given for these spaces, as well as equivalent norms on space H p,q φ in connection with semi-groups and approximation theory
TL;DR: By starting with a reaction-diffusion equation, a mapping model for the continuous system is proposed in this article, where the transition from the uniform state to the non-uniform one occurs at the same value of the diffusion constant for the mapping model as for the original reactiondiffusion equations if the transition exists.
Abstract: By starting with a reaction-diffusion equation a mapping model for the continuous system is proposed The transition from the uniform state to the non-uniform one occurs at the same value of the diffusion constant for the mapping model as for the original reaction-diffusion equation if the transition exists The mapping model is further studied by adopting the logistic model in one-dimensional space with a periodic boundary condition Equal time spectra in wave number space and power spectra for several values of wave numbers are numerically obtained A comparison of the numerical results of the equal time spectra with a simple theory is made to give a satisfactory agreement for large wave numbers
TL;DR: In this article, a characterization of Lipschitzchitz spaces with positive coefficients is presented, which enables the authors to describe an isomorphism of a Hardy space onto a solid sequence space and establish new connections between some classical inequalities concerning Hardy spaces.
Abstract: Various results on LP·behaviour of power series with positive coeffi dents are extended to Lipschitz spaces. For example, we have a characterization (decomposition) of these spaces, which enables us to describe an isomorphism of a Lipschitz space onto a solid sequence space and to establish new connections between some classical inequalities concerning Hardy spaces. 1. Introduction. In (15) we have considered some theorems on LP-be haviour of power series with positive coefficients and their applications to HP spaces. In this paper we continue the investigation in this direction. First we introduce some notations and then we list some known results from this area. ex> Throughout the paper let fez) = .2 anz n be an analytic function n=O' . in the open unit disc. Unless specified otherwise, the letters p, q, r, a denote numbers satisfying 0 < p, s« 00, 0 < r < 1, 0 < a < 00. The letter ~ al ways denotes a non-negative increasing function defined on (0,1) for which
TL;DR: An overview of cross validated spline methods for smoothing noisy data in the plane, in Euclidean space, and on the sphere is given in this article, where the use of generalized cross-validation to estimate both the smoothing parameter as well as the relative energy to be assigned to the divergent and nondivergent part of the smoothed vector field is described.
Abstract: An overview of cross validated spline methods for smoothing noisy data in the plane, in Euclidean espace, and on the sphere is given. Cross-validated thin plate smoothing splines are reviewed and an efficient numerical algorithm for computing them for problems with up to several hundred data points is described. Some numerical results for a two-dimensional example are given. A theory of vector splines for smoothing noisy vector data on the sphere is given. The use of generalized cross-validation to estimate both the smoothing parameter as well as the relative energy to be assigned to the divergent and nondivergent part of the smoothed vector field is described and tested numerically on simulated upper air horizontal wind fields.
01 Apr 1984-Graphical Models \/graphical Models and Image Processing \/computer Vision, Graphics, and Image Processing
TL;DR: It is shown that the so-called Euler operators completely describe the family of objects bounded by 2-manifold surfaces.
Abstract: Alternative modeling spaces for physical solid objects are discussed and it is shown that the so-called Euler operators completely describe the family of objects bounded by 2-manifold surfaces.
TL;DR: The large-scale properties of non-interacting random surfaces embedded in an arbitrary dimensional continuum space are related to the infrared behavior of two-dimensional massless free fields as mentioned in this paper.
01 Jan 1984
TL;DR: In this paper, the authors focus on the preservation of separation and covering properties under the product operation and show that the Lindelof property is not preserved by products, unlike all of the weaker separation properties.
Abstract: Publisher Summary
This chapter focuses on the preservation of separation and covering properties under the product operation. Unlike all of the weaker separation properties, normality, paracompactness, and the Lindelof property are not preserved by products. A space is said to be κ-paracompact if its every open covering of cardinality has a locally finite open refinement, and a space is κ-collectionwise normal if for every discrete family {Fα}α < x of its closed subsets there is a family{Uα}α < x of mutually disjoint open sets such that Fα ⊂ Uα. A space is perfect if all of its open subsets are Fα sets and a space is perfectly normal if it is perfect and normal.
TL;DR: In this paper, the eigenvalues of the Laplacian and the Lichnerowicz operator acting on arbitrary tensor harmonics are given in terms of the quadratic Casimir operators of G and H. Explicit examples for Sn, CPn, and real (complex) Grassmann manifolds are analyzed.
Abstract: On a symmetric coset space G/H the eigenvalues of the Laplacian and the Lichnerowicz operator acting on arbitrary tensor harmonics are given in terms of the eigenvalues of the quadratic Casimir operators of G and H. Explicit examples for Sn, CPn, and real (complex) Grassmann manifolds are analyzed.
01 Jan 1984
TL;DR: In this paper, the authors discuss initial κ-compact and related spaces, and show that the notion of initially κ is a special case of countable compactness and the Lindelof property.
Abstract: Publisher Summary This chapter discusses initially κ-compact and related spaces. A main reason for studying initial κ and, more generally, interval compactness is that compactness, countable compactness, and the Lindelof property are special cases of one or both of these concepts. Another reason is that the theory of initially κ-compact and related spaces provides a means for answering fundamental questions that arise in other areas of topology. A third reason is that results in this area illustrate the usefulness of the close relationship that exists between the set theory of uncountable cardinals and properties of topological spaces. A space is countably compact if and only if it is initially ω-compact, and it is Lindelof if and only if it is finally ω1-compact. Like compactness, initial κ-compactness is preserved by continuous mappings, perfect pre-images, and closed subsets.
TL;DR: The York mapping from the space of freely chosen conformal data to the constraint-satisfying physical data is shown to be a canonical transformation for both the vacuum Einstein theory and the Einstein-Maxwell theory as mentioned in this paper.
TL;DR: In this article, the authors compare the behavior of hard hyperspheres in four and five-dimensional space with the behaviour of the three-dimensional system and find that the fluid-solid phase transition occurs at lower densities, relative to the close-packed density, for a higher dimensionality.
TL;DR: The recent demise of certain global unbroken symmetry generators in the presence of a grand unified magnetic monopole leads us to consider more carefully the notion of charges associated with gauge symmetries.
TL;DR: In this paper, a coordinate transformation which regularizes the classical Kepler problem was used to solve the hydrogen-atom case via the phase-space formulation of nonrelativistic quantum mechanics.
Abstract: Using a coordinate transformation which regularizes the classical Kepler problem, we show that the hydrogen-atom case may be analytically solved via the phase-space formulation of nonrelativistic quantum mechanics. The problem is essentially reduced to that of a four-dimensional oscillator whose treatment in the phase-space formulation is developed. Furthermore, the method allows us to calculate the Green's function for the H atom in a surprisingly simple way.