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Showing papers on "Space (mathematics) published in 1991"


Journal ArticleDOI
TL;DR: This paper presents a time-efficient algorithm that produces k best ''non-intersecting'' local alignments for any chosen k that needs only O(M + N + K) space.

1,015 citations


Journal ArticleDOI
01 Jan 1991
TL;DR: In this article, the authors show that any symplectic vector space has even dimension and any isotropic subspace is contained in a Lagrangian subspace and Lagrangians have dimension equal to half the dimension of the total space.
Abstract: Proposition 1.4. (1) Any symplectic vector space has even dimension (2) Any isotropic subspace is contained in a Lagrangian subspace and Lagrangians have dimension equal to half the dimension of the total space. (3) If (V1,ω1), (V2,ω2) are symplectic vector spaces with L1, L2 Lagrangian subspaces, and if dim(V1) = dim(V2), then there is a linear isomorphism φ : V1 → V2 such that φω2 = ω1 and φ(L1) = L2.

605 citations


Journal ArticleDOI
TL;DR: The local geometry of the parameter space of Calabi-Yau manifolds has been studied in this paper, where it is shown that the parameters of the complex structure decompose into a product with the space of parameters as one factor and a complex extension of the Kahler class as the other.

538 citations


Book
30 Nov 1991
TL;DR: In this paper, the authors introduce the notion of Cp(X) as an object of topological algebra, and introduce a set of properties of function spaces over arbitrary compacta.
Abstract: 0. General information on Cp(X) as an object of topological algebra. Introductory material.- 1. General questions about Cp(X).- 2. Certain notions from general topology. Terminology and notation.- 3. Simplest properties of the spaces Cp(X, Y).- 4. Restriction map and duality map.- 5. Canonical evaluation map of a space X in the space CpCp(X).- 6. Nagata's theorem and Okunev's theorem.- I. Topological properties of Cp(X) and simplest duality theo-rems.- 1. Elementary duality theorems.- 2. When is the space Cp(X) u-compact?.- 3. "tech completeness and the Baire property in spaces Cp(X).- 4. The Lindelof number of a space Cp(X),and Asanov's theorem.- 5. Normality, collectionwise normality, paracompactness, and the extent of Cp(X).- 6. The behavior of normality under the restriction map between function spaces.- II. Duality between invariants of Lindelof number and tightness type.- 1. Lindelof number and tightness: the Arkhangel'skii-Pytkeev theorem.- 2. Hurewicz spaces and fan tightness.- 3. Frechet-Urysohn property, sequentiality, and the k-property of Cp(X).- 4. Hewitt-Nachbin spaces and functional tightness.- 5. Hereditary separability, spread, and hereditary Lindelof number.- 6. Monolithic and stable spaces in Cp-duality.- 7. Strong monolithicity and simplicity.- 8. Discreteness is a supertopological property.- III. Topological properties of function spaces over arbitrary compacta.- 1. Tightness type properties of spaces Cp(X), where X is a compactum, and embedding in such Cp(X).- 2. Okunev's theorem on the preservation of Q-compactness under t-equivalence.- 3. Compact sets of functions in Cp(X). Their simplest topological properties.- 4. Grothendieck's theorem and its generalizations.- 5. Namioka's theorem, and Ptak's approach.- 6. Baturov's theorem on the Lindelof number of function spaces over compacta.- IV. Lindelof number type properties for function spaces over compacta similar to Eberlein compacta, and properties of such compacta.- 1. Separating families of functions, and functionally perfect spaces.- 2. Separating families of functions on compacta and the Lindelof number of Cp(X).- 3. Characterization of Corson compacta by properties of the space Cp(X).- 4. Resoluble compacta, and condensations of Cp(X) into a ?*-product of real lines. Two characterizations of Eberlein compacta.- 5. The Preiss-Simon theorem.- 6. Adequate families of sets: a method for constructing Corson compacta.- 7. The Lindelof number of the space Cp(X),and scattered compacta.- 8. The Lindelof number of Cp(X) and Martin's axiom.- 9. Lindelof ?-spaces, and properties of the spaces Cp,n(X).- 10. The Lindelof number of a function space over a linearly ordered compactum.- 11. The cardinality of Lindelof subspaces of function spaces over compacta.

502 citations



Book ChapterDOI
01 Aug 1991
TL;DR: The notion of extensibility of a finite set of Laurent polynomials is shown to be central in the construction of wavelet decompositions by decomposition of spaces in a multiresolution analysis.
Abstract: We study basic questions of wavelet decompositions associated with multiresolution analysis. A rather complete analysis of multiresolution associated with the solution of a refinement equation is presented. The notion of extensibility of a finite set of Laurent polynomials is shown to be central in the construction of wavelets by decomposition of spaces. Two examples of extensibility, first over the torus and then in complex space minus the coordinate axes are discussed. In each case we are led to a decomposition of the fine space in a multiresolution analysis as a sum of the adjacent coarse space plus an additional space spanned by the multiinteger translates of a finite number of pre-wavelets. Several examples are provided throughout to illustrate the general theory.

321 citations


01 Aug 1991

303 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigate macroscopic loop amplitudes (at genus zero) using the matrix model and the Liouville theories of two-dimensional quantum gravity, and resolve several apparent discrepancies between the matrix models and LiOUville theory.

280 citations


Journal ArticleDOI
TL;DR: In this paper, the authors deal with non-commutative objects based on the Weyl algebra from the differential geometric point of view, where the basic object is not a point of a space but certain sections of bundles.

269 citations


Journal ArticleDOI
TL;DR: In this paper, the space (S ∗ of Hida distributions is characterized in terms of analytic properties of the Fourier transformation of its elements, and the space is characterized by the Fouriers transformation of the elements.

241 citations


Journal ArticleDOI
TL;DR: The model provides a quantitative measure of anisotropy by a fractional dimension, as viewed from exciton dynamics, which can be determined experimentally from interband optical spectra.
Abstract: Wannier-Mott excitons in anisotropic or confined systems are studied using the model of fractional-dimensional space. The excitons in an anisotropic solid are treated as ones in an isotropic fractional-dimensional space, where the dimension is determined by the degree of anisotropy. By solving the simple hydrogenic Schr\"odinger equation in the fractional-dimensional space, exciton wave functions, bound energies, and associated optical spectra are obtained as a function of spatial dimensionality. Dimensional behavior in binding energy, radial density, and angular momentum is discussed. The model provides a quantitative measure of anisotropy by a fractional dimension, as viewed from exciton dynamics, which can be determined experimentally from interband optical spectra. The results obtained here are also applicable to hydrogenic impurities in anisotropic solids.

Journal ArticleDOI
TL;DR: In this paper, the ground-state properties of the heavy nuclei were analyzed in the three-dimentional deformation space {βλ, γ = 2, 4, 6}.

Journal ArticleDOI
TL;DR: In this paper, it was shown that the equations of general relativity remain well defined even in the limit that the metric becomes degenerate, and that there exist smooth solutions to these equations on manifolds in which the topology of space changes.
Abstract: In a first-order formulation, the equations of general relativity remain well defined even in the limit that the metric becomes degenerate. It is shown that there exist smooth solutions to these equations on manifolds in which the topology of space changes. The metric becomes degenerate on a set of measure zero, but the curvature remains bounded. Thus if degenerate metrics play any role in quantum gravity, topology change is unavoidable.

Proceedings ArticleDOI
01 Apr 1991
TL;DR: The space of both deep and bushy trees is easier to optimize than the space of left-deep trees alone, and it is discussed how Iterative Improvement, Simulated Annealing, and Two Phase Optimization perform on these spaces.
Abstract: We present a combination of analytical and experimental results that shed some light into the shape of the cost function of the strategy spaces that query optimizers must deal with. These are the space that includes only left-deep trees and the space that includes koth deep and bushy trees. We conclude that the cost functions of both spaces essentially form a “well” but of a distinctly different quality. Based on this result, we discuss how Iterative Improvement, Simulated Annealing, and Two Phase Optimization perform on these spaces. We conclude that the space of both deep and bushy trees is easier to optimize than the space of left-deep trees alone.

Book ChapterDOI
TL;DR: In this article, an account of the extension of the classical general equilibrium model to an infinite dimensional setting is given, where the authors follow the methodology of functional analysis and attack the existence problem.
Abstract: Publisher Summary This chapter summarizes the account of the extension of the classical general equilibrium model to an infinite dimensional setting. The classical finite dimensional theory, the commodity space is the canonical finite dimensional linear space R n . By contrast, there is no canonical infinite dimensional linear space. Different economic applications require models involving different infinite dimensional linear spaces. The mathematical discipline of functional analysis has already been well developed as a tool for the abstract study of linear spaces. The chapter follows the methodology of functional analysis and attacks the existence problem. Advantage of this method is that it yields general results, capable of application in a wide variety of specific models. An important line of research in classical general equilibrium theory has been the relationship of the core to the set of competitive allocations. In the infinite dimensional setting, an extensive body of work has been developed, which centers around the infinite-dimensional version of the Debreu–Scarf core convergence theorem.

Journal ArticleDOI
TL;DR: In this article, the authors developed the theory of equilibrium states for the class of Holder continuous functions f for which the pressure is larger than sup f. They showed that there exist a unique conformal measure (reference measure) and a unique equilibrium state, which is equivalent to the conformal measures with a positive continuous density.
Abstract: Let T be a rational map of degree d>or=2 of the Riemann sphere C=C union ( infinity ). The authors develop the theory of equilibrium states for the class of Holder continuous functions f for which the pressure is larger than sup f. They show that there exist a unique conformal measure (reference measure) and a unique equilibrium state, which is equivalent to the conformal measure with a positive continuous density. The associated Perron-Frobenius operator acting on the space of continuous functions is almost periodic and they show that the system is exact with respect to the equilibrium measure.

Journal ArticleDOI
TL;DR: In this paper, an estimate of a local field energy distribution, denoted F(ω,k), which specifies how the field energy observed by a limited number of satellites is distributed with regard to the angular frequency ω and to the wave number k, is derived from a generalization of the Capon [1969] high-resolution method.
Abstract: The best method was sought for defining locally an electrostatic or an electromagnetic turbulence in a space plasma, based on the simultaneous measurement of several wave field components at several points in space. The turbulent field is supposed to be stationary in time and homogeneous in space. An estimate of a local field energy distribution, denoted F(ω,k), which specifies how the field energy observed by a limited number of satellites is distributed with regard to the angular frequency ω and to the wave number k, is derived from a generalization of the Capon [1969] high-resolution method. The Quality of this estimate is deemed sufficient, as shown by examples of application to synthetic data.

Journal ArticleDOI
TL;DR: In this paper, the algebraic finite-mode hydrodynamic type systems that have O( N ) integrals of motion for O(N × N ) modes and are intrinsically connected with two-dimensional ideal fluid flows are studied.


Journal ArticleDOI
TL;DR: In this paper, the authors introduced metric independent field theories, which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold, and have invariance of solutions of field equations under arbitrary functional redefinitions of the field quantities.
Abstract: Metric independent $\sigma$ models are constructed. These are field theories which generalise the membrane idea to situations where the target space has fewer dimensions than the base manifold. Instead of reparametrisation invariance of the independent variables, one has invariance of solutions of the field equations under arbitrary functional redefinitions of the field quantities. Among the many interesting properties of these new models is the existence of a hierarchical structure which is illustrated by the following result. Given an arbitrary Lagrangian, dependent only upon first derivatives of the field, and homogeneous of weight one, an iterative procedure for calculating a sequence of equations of motion is discovered, which ends with a universal, possibly integrable equation, which is independent of the starting Lagrangian. A generalisation to more than one field is given.

Journal Article
TL;DR: In this paper, it was shown that in non-Euclidean spaces of constant holomorphic sectional curvature the curvature-adapted (real) hypersurfaces are exactly the Hopf hypersurface.
Abstract: Obviously, every totally umbilical hypersurface of a Riemannian manifold is curvature-adapted. In spaces of constant sectional curvature every hypersurface is curvature-adapted. But in other ambient spaces our definition is restrictive. For example, in non-Euclidean spaces of constant holomorphic sectional curvature the curvature-adapted (real) hypersurfaces are exactly the Hopf hypersurfaces (see [3] for the notion of Hopf hypersurfaces). In locally Symmetrie spaces it turns out that for the investigation of the geometry of curvature-adapted hypersurfaces Jacobi field theory may be very useful ( s can be seen in section 5).

Journal ArticleDOI
TL;DR: In this article, an adaptive refinement algorithm is presented and interpreted as the selective enrichment of a finite-element space through the hierarchical basis, where each elemental division corresponds exactly to the inclusion of a small number of new basis functions, while existing basis functions remain unchanged.



Journal ArticleDOI
TL;DR: It is proved that it is impossible to parameterize any real plane curve, other than a straight line, by rational functions of its arc length.

Journal ArticleDOI
TL;DR: In this paper, the first results from a Hilbert space, multireference coupled-cluster (CC) method in an incomplete model (active) space are reported for the five lowest states of LiH.
Abstract: The first results from a Hilbert space, multireference coupled‐cluster (CC) method in an incomplete model (active) space are reported for the five lowest states of LiH. The active space is spanned by several configurations at the level of single and double excitations, where the configuration(s) causing intruder state problems are excluded from the complete Hilbert reference space. Full inclusion of single‐ and double‐excitation operators is considered in the expansion for the cluster operator, with all quadratic terms in the renormalization part. The multireference CC results for the ground (X 1Σ+) and four low‐lying excited states (a 3Σ+, A 1Σ+, a 3Π, A 1Π ) of LiH are compared with the corresponding full configuration‐interaction (FCI) energies. The agreement between FCI and CC values within a few hundredths of mH for the Π states proves the feasibility of the present method to describe, quantitatively, the quasicomplete reference space problem. Deviations of the incomplete multireference results from ...

Journal ArticleDOI
TL;DR: In this paper, an energy functional for a strut on a nonlinear softening foundation is worked into two different lagrangian forms, in fast and slow space respectively, and the developments originate independently of the underlying differential equation, and carry some quite general features.
Abstract: An energy functional for a strut on a nonlinear softening foundation is worked into two different lagrangian forms, in fast and slow space respectively. The developments originate independently of the underlying differential equation, and carry some quite general features. In each case, the kinetic energy is an indefinite quadratic form. In fast space, this leads to an escape phenomenon with fractal properties. In slow space, kinetic energy is added to a potential contribution that is familiar from modal formulations. Together, and in conjunction with a recent set of numerical experiments, they illustrate the extra complexities of localized, as opposed to distributed periodic, buckling.

Journal ArticleDOI
TL;DR: In this article, the authors describe the one-parameter deformation of the phase space of a quantum mechanical system and show that this twisted phase space is covariant under the action of the symplectic quantum group.
Abstract: We describe the one-parameter deformation of the phase space of a quantum mechanical system and show that this twisted phase space is covariant under the action of the symplectic quantum group. The...

Journal ArticleDOI
TL;DR: A variable-order time discretization in Hilbert space based on a multiplicative error correction allows us to separate space and time errors and further to solve fewer elliptic subproblems with less effort.
Abstract: In continuation of part I this paper develops a variable-order time discretization in Hilbert space based on a multiplicative error correction. Matching of time and space errors as explained in part I allows to construct an adaptive multilevel discretization of the parabolic problem. In contrast to the extrapolation method in time, which has been used in part I, the new time discretization allows us to separate space and time errors and further to solve fewer elliptic subproblems with less effort—a feature which is essential in view of the application to space dimensions greater than one. Numerical examples for space dimension one are included which clearly indicate the improvement.