Showing papers on "Space (mathematics) published in 1981"
TL;DR: In this article, a generalization of Kirchhoff's equations for the analysis of space-curved beams, in which account is taken of force-deformational effects in addition to the deformational effects of bending and twisting moments, is re-derived more simply, including a new description of rotational displacement states, and including an application to the problem of helical deformations of originally helical beams.
Abstract: A recent generalization of Kirchhoff's equations for the analysis of spacecurved beams, in which account is taken of force-deformational effects in addition to the deformational effects of bending and twisting moments (Studies Appl. Math.52, 87–95, 1973), is re-derived more simply, including a new description of rotational displacement states, and including an application to the problem of helical deformations of originally helical beams.
256 citations
TL;DR: In this article, the authors prove numerically that two dimensions are marginal for Anderson localisation and an associated transition is found, presenting close analogies with the Kosterlitz-Thouless transition of the XY model in two dimensions, while the behaviour in three dimensions is a standard one with a mobility edge.
Abstract: Using a new and powerful real space renormalisation method recently introduced for phase transitions, the authors prove numerically that two dimensions are marginal for Anderson localisation. An associated transition is found, presenting close analogies with the Kosterlitz-Thouless transition of the XY model in two dimensions, while the behaviour in three dimensions is shown to be a standard one with a mobility edge. The accuracy of the method is better than previous approaches in two dimensions and is not reduced when the number of dimensions is raised to three.
231 citations
01 Jan 1981
TL;DR: In this paper, the SEASAT Antenna Temperature Software System (SATSS) is used to simulate satellite observations from the multichannel Microwave Radiometer (SMMR).
Abstract: Wayne D. Mount Geo-Atmospherics Corporation P.O. Box 177 Lincoln, Mass., 01773, U.S.A. We have developed geophysical models and computer techniques to simulate satellite observation from the SEASAT Scanning Multichannel Microwave Radiometer (SMMR). We have combined our proprietary computer programs for incorporating antenna power response functions in the computation of antenna temperatures for millimeter and microwave satellite radiometers with National Oceanic and Atmospheric Administration (NOAA) developed models and computer programs applicable to the SEASAT satellite. Ocean surface effects were modelled to account for sea surface temperature and salinity, wind, friction velocity, foam and whitecaps scattering, sunglint, and galactic radiation. Our intervening atmospheric radiation absorption and emission models account for vertical profiles of air temperature, pressure, oxygen, water vapor, fog, cloud, and rain effects. Using the resulting SEASAT Antenna Temperature Software System (SATSS), it is now possible to study antenna pattern effects due to different antenna designs, configurations, and sizes as they impact spatial resolution in remotely measuring sea surface wind and temperature. Present plans call for studying 6.6 GHz microwave radiometric partial beam filling effects due to nonhomogenous precipitation, sunglint, and land-ocean features contained within the field of view.
215 citations
210 citations
TL;DR: In this paper, Bose and Fermi N-particle systems were recovered as unitarily inequivalent induced representations of the current group by lifting the action of K on an orbit Δ⊆S′ to its universal covering space δ.
Abstract: A recent paper established technical conditions for the construction of a class of induced representations of the nonrelativistic current group SΛK, where S is Schwartz’s space of rapidly decreasing C∞ functions, and K is a group of C∞ diffeomorphisms of Rs. Bose and Fermi N‐particle systems were recovered as unitarily inequivalent induced representations of the group by lifting the action of K on an orbit Δ⊆S′ to its universal covering space δ. For s⩾3, δ is the coordinate space for N particles, which is simply connected. In two‐dimensional space, however, the coordinate space is multiply connected, implying induced representations other than those describing the usual Bose or Fermi statistics; these are explored in the present paper. Likewise the Aharonov–Bohm effect is described by means of induced representations of the local observables, defined in a nonsimply connected region of Rs. The vector potential plays no role in this description of the Aharonov–Bohm effect.
208 citations
TL;DR: In this article, an algorithm for calculating atomic properties based on the topological theory of molecular structure is described and applied for any given molecular system atoms are rigorously defined in terms of the topology properties of the system's charge distribution rho (x) in three-dimensional space.
Abstract: An algorithm for calculating atomic properties, based on the topological theory of molecular structure, is described and applied For any given molecular system atoms are rigorously defined in terms of the topological properties of the system's charge distribution rho (x) in three-dimensional space The essential feature of this distribution is that its only local maxima, the attractors of the associated gradient vector field grad rho (x), occur at the positions of the nuclei The region of space occupied by an atom, the atomic basin, is the space traversed by all gradient paths of grad rho (x) which terminate at its nucleus This property is used to construct a coordinate transformation which maps each atomic basin onto three-dimensional space The Jacobian J, of this transformation depends solely on the second derivatives of rho (x) The determinant of J is obtained by solving a first-order differential equation governed by grad2 rho (x) Any atomic property may then be calculated by an integration of an associated single-particle density over the basin of the atom Numerical integrations of some atomic properties of diatomic and polyatomic molecules are reported
163 citations
TL;DR: In this paper, it was shown that the unique solution of Vlasow hierarchy is induced by the flow on the space of probability measures on R6 which is obtained from the solution of the Vlasov equation.
Abstract: Motivated by a recent paper of H. Narnhofer and G. Sewell, we investigate the problem of existence and uniqueness of solutions of the Vlasov hierarchy. It is shown that the unique solution of the Vlasow hierarchy is induced by the flow on the space of probability measures on R6 which is obtained from the solution of the Vlasov equation.
149 citations
TL;DR: The theory of H -space, the four-dimensional manifold of complex null hypersurfaces of an asymptotically flat space-time which are asymmptotic shear-free, is reviewed in this paper, and two independent formalisms for the derivation of the basic properties of H-space are presented.
131 citations
TL;DR: In this article, the radiative degrees of freedom of the gravitational field are isolated by analyzing the structure available at null infinity, and all information about gravitational radiation can be extracted from the curvature tensors of these connections directly on J without any reference to the interior of space-time.
Abstract: The radiative degrees of freedom of the gravitational field are isolated by analyzing the structure available at null infinity, JIt is shown thay they are coded in certain equivalence classes {D} of connections; all information about gravitational radiation can be extracted from the curvature tensors of these connections directly on J without any reference to the interior of space–time. The space of classical vacua—i.e., of {D} with trivial curvature—is analyzed. It is shown that the quotient ST/T of the BMS supertranslation group by its translation subgroup acts simply and transitively on this space. The available structure is compared with that of gauge theories. Since the entire discussion can be carried out onJ without any reference to the interior, it suggests a new approach to quantum gravity. This approach will be presented in detail in a subsequent paper.
120 citations
TL;DR: In this paper, the authors define a family of nonempty and bounded subsectors of a metrically constrained space with nonnegative values and define a measure of noncompactness to be equal to zero.
Abstract: 1. In t roduc t ion Up to now a l o t of var ious d e f i n i t i o n s of the not ion of a measure of noncompactness have been proposed (see e . g . b i bliography in [ 8 ] ) . Almost in a l l d e f i n i t i o n s a measure of noncompactness i s a f u n c t i o n which i s def ined on,the family of a l l nonempty and bounded subse t s of a metr ic space with r e a l nonnegative values and ye t s a t i s f i e s some other condi t i o n s ( c f . [ 8 ] ) . Among those condi t ions the most c h a r a c t e r i s t i c i s t ha t which r e q u i r e s the measure of noncompactness to be equal to zero on the whole family of a l l r e l a t i v e l y compact, s e t s . The most important measures of noncompactness are the Kura towski measure a and the Hausdorff measure 2 [ 8 ] . The l a s t one i s def ined hy the formula
86 citations
TL;DR: In this article, a review of the recent techniques investigated by the authors for numerical, asymptotic and approximate evaluations of the Somraerfeld integrals is given and their numerical characteristics are illustrated using representative numerical data.
Abstract: This paper reviews some of the recent techniques investigated by the authors for numerical, asymptotic and approximate evaluations of the Somraerfeld integrals. Only the summaries of the final formulations are given and their numerical characteristics are illustrated using representative numerical data. Due to space limitations, the discussion in this paper is limited to the cases where both the source and the observation points are above the lossy half-space.
TL;DR: The main result of the present paper is the following theorem which was conjectured by Thurs ton ([6], section 6.1] as mentioned in this paper : there is, up to isometry, only one ideal regular n-simplex in H n with vertices v0,..., v, 6 Hn U ~H ~.
Abstract: An n-simplex in H n with vertices v0, ..., v , 6 Hn U ~H ~ is the dosed subset of Hn bounded by the n + I spheres which contain all the vertices except one and which are orthogonal to S \"-1. k simplex is called ideal if all the vertices arc on the sphere at infinity. I t is easy to see tha t the volume of a hyperbolic n-simplex is finite also ff some of the vertices are on the sphere at infinity. A simplex is called regular if any permuta t ion of its vertices can be induced by an isometry of H n. This makes sense also for ideal simplices since any i sometry of H n can be extended continuously to HnU OH n. There is, up to isometry, only one ideal regular n-simplex in H ~. The main result of the present paper is the following theorem which was conjectured by Thurs ton ([6], section 6.1).
TL;DR: In this article, the disorder in amorphous materials is described in terms of defects occurring during the mapping of curved spaces on the euclidian space, similar to the crystallographic laws used to describe crystals.
Abstract: The local order is well defined in amorphous material, but filling all the space with a unit cluster involves distortions. This is due to an incompatibility between the local order symmetry and the properties of euclidian space. Nevertheless curved spaces can be tessellated with a given cell; in this paper we discuss the case of tetrahedral packing. It is well known that tetrahedra cannot fill euclidean space, but they can be packed together to build a regular structure (called a polytope) in a space of uniform positive curvature. The disorder in amorphous materials is then described in terms of defects occurring during the mapping of curved spaces on the euclidian space. This method of describing an amorphous structure provides a mathematical tool, similar to the crystallographic laws used to describe crystals.
TL;DR: In this paper, the authors proved a theorem on the existence of a classical solution of the Stefan problem for the equation on a small time interval, where the solution is obtained as a limit as of solutions of auxiliary regularized problems.
Abstract: In this paper the author proves a theorem on the existence of a classical solution of the Stefan problem for the equation on a small time interval.The solution is obtained as a limit as of solutions of auxiliary regularized problems. Estimates for solutions of the auxiliary problems are established that do not depend on . These estimates permit one to say something about the compactness of the family of solutions in the space .Bibliography: 13 titles.
TL;DR: In this paper, the authors define the notion of the Galois lattice of a discrete arithmetic group generated by reflections in a Lobachevsky space and prove finiteness of the set of such lattices.
Abstract: Using E. B. Vinberg's arithmeticity criterion, the author defines the notion of the Galois lattice of a discrete arithmetic group generated by reflections in a Lobachevsky space. The author proves finiteness of the set of such lattices and, as a corollary, finiteness of the set of maximal discrete arithmetic groups generated by reflections for fixed dimension of the Lobachevsky space and fixed degree of the ground field over Q. Figures: 6. Tables: 1. Bibliography: 19 titles.
TL;DR: In this paper, a mapping from a prescribed subspace of a shell model space to an associated boson space is described, and a new dynamical procedure for selecting the collective variables within the cosy space is presented.
TL;DR: In this paper, a weak canonical form for vector spaces of m x n matrices all of rank at most r is derived, and it is shown that m and n are bounded by functions of r and these bounds are tight.
Abstract: A weak canonical form is derived for vector spaces of m x n matrices all of rank at most r. This shows that the structure of such spaces is controlled by the structure of an associated 'primitive' space. In the case of primitive spaces it is shown that m and n are bounded by functions of r and that these bounds are tight.
TL;DR: In this paper, the properties of fluctuations inμ space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation, and the results are compared with those obtained in the extensive literature, which is reviewed in some detail.
Abstract: The properties of fluctuations inμ space in or outside thermal equilibrium are obtained by solving hierarchies of equations derived either from the Liouville or the Master equation. In particular we study the one-, two-, etc., time correlation functions that describe the spatial and temporal behavior of the fluctuations inμ space. Explicit solutions are obtained for a dilute gas. The Langevin approach is briefly discussed. Our results are compared with those obtained in the extensive literature, which is reviewed in some detail.
TL;DR: In this paper, a polymer chain configuration space renormalization group method is developed for application to the polymer diffusion equation for a single continuous polymer chain with excluded volume and unaveraged hydrodynamic interactions.
Abstract: A polymer chain configuration space renormalization group method is developed for application to the polymer diffusion equation for a single continuous polymer chain with excluded volume and unaveraged hydrodynamic interactions The method builds upon our chain configuration space equilibrium formulation which is based on a coarse graining procedure which utilized small chain contour length loop excluded volume interactions to define the renormalization procedure This approach is generalized to include small loop hydrodynamic interactions within the renormalization scheme Our coarse graining treatment is combined with the methods of Kawasaki and Gunton, designed to consider dynamical critical phenomena, to provide the chain configuration space renormalization group theory Calculations are explicitly presented to order e = 4−d, where d is the dimensionality of space However, we show that the dynamical exponent can be obtained exactly from a consideration of the general renormalization scheme without th
01 Jul 1981
TL;DR: Theorem 2 is a characterization of such isometries for 1 ≤ p ≤ ∞, ≠ 2 as discussed by the authors, where φ is a faithful semifinite normal trace on a von Neumann algebra.
Abstract: The spaces Lp(, φ) for 1 ≤ p ≤ ∞, where φ is a faithful semifinite normal trace on a von Neumann algebra , are defined in (10),(2),(14). The problem of determining the general form of an isometry of one such space into another has been studied in (i), (6), (9), (12), (5). Our main result, Theorem 2, is a characterization of such isometries for 1 ≤ p ≤ ∞, ≠ 2. The method of proof is based on that of (7), where isometries between Lp function spaces are characterized. The main step in the proof is Theorem 1, which gives the conditions under which equality holds in Clarkson's inequality.
TL;DR: In this article, the complete f 7 2 f 5 2 p 3 2 p 1 2 model space is presented for the M1 excitation of the ground states of 42,44,48Ca.
TL;DR: In this article, it was shown that a similar geometric construction is also possible in the quantum case, and the fundamental formulae of quantum case are given (they differ in some details from the classical ones), and possible physical applications are shortly sketched.
TL;DR: In this paper, it was shown that every subspace of LI contains a subspace isomorphic to some lq. The proof depends on a fixed point theorem for random measures.
Abstract: It is shown that every subspace of LI contains a subspace isomorphic to some lq. The proof depends on a fixed point theorem for random measures.