Showing papers on "Space (mathematics) published in 1995"
TL;DR: In this paper, nonperturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order $e^{-1/g_s}$ contributions, where $g s$ is the string coupling.
Abstract: Non-perturbative instanton corrections to the moduli space geometry of type IIA string theory compactified on a Calabi-Yau space are derived and found to contain order $e^{-1/g_s}$ contributions, where $g_s$ is the string coupling. The computation reduces to a weighted sum of supersymmetric extremal maps of strings, membranes and fivebranes into the Calabi-Yau space, all three of which enter on equal footing. It is shown that a supersymmetric 3-cycle is one for which the pullback of the Kahler form vanishes and the pullback of the holomorphic three-form is a constant multiple of the volume element. Quantum mirror symmetry relates the sum in the IIA theory over supersymmetric, odd-dimensional cycles in the Calabi-Yau space to a sum in the IIB theory over supersymmetric, even-dimensional cycles in the mirror.
516 citations
TL;DR: In this paper, a supersymmetric σ-model in 2D space with 't Hooft magnetic flux tumed on is presented, which maps Donaldson observables on products of two Riemann surfaces to quantum cohomology ring of moduli space of flat connections.
273 citations
TL;DR: In this article, the existence theory of isothermal flows of Navier-Stokes fluids in two and three space dimensions is extended to general polytropic pressures P(ρ) = Kργ, γ > 1, with fairly general initial data.
Abstract: We extend to general polytropic pressures P(ρ) = Kργ, γ > 1, the existence theory of [8] for isothermal (γ= 1) flows of Navier-Stokes fluids in two and three space dimensions, with fairly general initial data. Specifically, we require that the initial density be close to a constant in L2 and L∞, and that the initial velocity be small in L2 and bounded in L2n (in two dimensions the L2 norms must be weighted slightly). Solutions are obtained as limits of approximate solutions corresponding to mollified initial data. The key point is that the approximate densities are shown to converge strongly, so that nonlinear pressures can be accommodated, even in the absence of any uniform regularity information for the approximate densities.
262 citations
TL;DR: In this paper, a Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all SU(2) Chern-Simon theories defined by all choices of punctures and representations on the spatial boundary S. The integer level k of Chern-Simons theory is given by k = 6π/G2Λ+α, where Λ is the cosmological constant and α is a CP breaking phase.
Abstract: Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory in which the pullback of the curvature to the boundary is self‐dual (with a cosmological constant). A Hilbert space which describes all the information accessible by measuring the metric and connection induced in the boundary is constructed and is found to be the direct sum of the state spaces of all SU(2) Chern–Simon theories defined by all choices of punctures and representations on the spatial boundary S. The integer level k of Chern–Simons theory is found to be given by k=6π/G2Λ+α, where Λ is the cosmological constant and α is a CP breaking phase. Using these results, expectation values of observables which are functions of fields on the boundary may be evaluated in closed form. Given these results, it is natural to make the conjecture that the quantum states of the system are completely determined by measurements mad...
244 citations
TL;DR: In this article, a characterisation of hilbert spaces by orthomodular spaces is presented. But this characterization is restricted to the case of orthomorphism and it is not applicable to the HILBERT space.
Abstract: (1995). Characterization of hilbert spaces by orthomodular spaces. Communications in Algebra: Vol. 23, No. 1, pp. 219-243.
222 citations
TL;DR: In this paper, a conceptually clear and transparent derivation of the real-space screened Korringa-Kohn-Rostoker method is presented within the framework of the generalized multiple-scattering theory.
Abstract: Within the framework of the generalized multiple-scattering theory, a conceptually clear and transparent derivation of the real-space screened Korringa-Kohn-Rostoker method is presented. It is suggested that, by a suitable choice of the reference system, a fast exponential spatial decay of the structure constants can be obtained. This opens the way to treat large-scale systems in real space with a computational complexity that scales more favorably than the usual increase with the third power of the number of atoms.
218 citations
Patent•
20 Apr 1995
TL;DR: In this article, a method and a sensing device of measuring a concentration of a gas component of a measurement gas, which includes the steps of: introducing the measurement gas containing the gas component, from an external measurement-gas space into a first internal space, under a diffusion resistance; controlling an amount of oxygen in measurement gas within the first internal spaces, so as to produce an atmosphere which does not substantially affect measurement of the gas components, and which do not convert the component.
Abstract: A method and a sensing device of measuring a concentration of a gas component of a measurement gas, which method includes the steps of: introducing the measurement gas containing the gas component, from an external measurement-gas space into a first internal space, under a diffusion resistance; controlling an amount of oxygen in the measurement gas within the first internal space, so as to produce an atmosphere which does not substantially affect measurement of the gas component and which does not convert the gas component; introducing the atmosphere from the first internal space into a second internal space, under a diffusion resistance; and measuring the concentration of the gas component present in the atmosphere in the second internal space.
199 citations
TL;DR: In this article, a superposition procedure for solitons in the Skyrme model is described and an expression for the interaction potential of two soliton solutions is derived, which only involves the soliton's asymptotic fields.
Abstract: The Skyrme model can be generalised to a situation where static fields are maps from one Riemannian manifold to another. Here we study a Skyrme model where physical space is two-dimensional euclidean space and the target space is the two-sphere with its standard metric. The model has topological soliton solutions which are exponentially localised. We describe a superposition procedure for solitons in our model and derive an expression for the interaction potential of two solitons which only involves the solitons' asymptotic fields. If the solitons have topological degree 1 or 2 there are simple formulae for their interaction potentials which we use to prove the existence of solitons of higher degree. We explicitly compute the fields and energy distributions for solitons of degrees between one and six and discuss their geometrical shapes and binding energies.
183 citations
TL;DR: In this paper, the realization of the Ornstein-Uhlenbeck operator A in the space of uniformly continuous and bounded functions in Rn was studied, and it was shown that it generates a semigroup which is neither strongly continuous nor analytic, but enjoys nice smoothing properties.
181 citations
TL;DR: In this paper, Ray and Singer introduced zeta-regularized determinants for positive definite elliptic pseudo-differential operators (PDOs) of positive orders acting in the space of smooth sections of a finite-dimensional vector bundle E over a closed finite dimensional manifold M ([RS1], [RS2]).
Abstract: D.B. Ray and I.M. Singer invented zeta-regularized determinants for positive definite elliptic pseudo-differential operators (PDOs) of positive orders acting in the space of smooth sections of a finite-dimensional vector bundle E over a closed finite-dimensional manifold M ([RS1], [RS2]).
180 citations
TL;DR: In this paper, the authors studied the space of perturbations of a pair of dual supersymmetric theories based on an SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$.
Abstract: We study in detail the space of perturbations of a pair of dual $N=1$ supersymmetric theories based on an $SU(N_c)$ gauge theory with an adjoint $X$ and fundamentals with a superpotential which is polynomial in $X$. The equivalence between them depends on non-trivial facts about polynomial equations, i.e.\ singularity theory. The classical chiral rings of the two theories are different. Quantum mechanically there are new relations in the chiral rings which ensure their equivalence. Duality interchanges ``trivial'' classical relations in one theory with quantum relations in the other and vice versa. We also speculate about the behavior of the theory without the superpotential.
TL;DR: In this paper, a model system of strictly hyperbolic conservation laws which is genuinely nonlinear but for which the Riemann problem has no global solution is studied. And the authors show that approximate solutions which can be constructed by several standard methods converge in a weighted measure space and that the error in the approximation converges to zero.
TL;DR: These results give the results of Gerstenkorn and Manko: (1991) and in the case of infinite spaces, also give the correct forms of Yu's (1993) results.
TL;DR: In this paper, the invariantsJK,k of a framed knot coloured by the irreducible SU(2)q-module of dimensionk are studied as a function of k by means of the universal R-matrix.
Abstract: The invariantsJK,k of a framed knotK coloured by the irreducibleSU(2)q-module of dimensionk are studied as a function ofk by means of the universalR-matrix. It is shown that whenJK,k is written as a power series inh withq=eh, the coefficient ofhd is an odd polynomial ink of degree at most 2d+1. This coefficient is a Vassiliev invariant ofK. In the second part of the paper it is shown that ask varies, these invariants span ad-dimensional subspace of the space of all Vassiliev invariants of degreed for framed knots. The analogous questions for unframed knots are also studied.
TL;DR: This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form.
Abstract: Powered by TCPDF (www.tcpdf.org) This material is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Seitsonen, A.P.; Puska, M.J.; Nieminen, R.M.
Abstract: By considering a (partial) topological twisting of supersymmetric Yang-Mills compactified on a 2d space with `t Hooft magnetic flux turned on we obtain a supersymmetric $\sigma$-model in 2 dimensions. For N=2 SYM this maps Donaldson observables on products of two Riemann surfaces to quantum cohomology ring of moduli space of flat connections on a Riemann surface. For N=4 SYM it maps $S$-duality to $T$-duality for $\sigma$-models on moduli space of solutions to Hitchin equations.
TL;DR: For all radial weights which are not decreasing too fast, the space of harmonic functions is isomorphic to c 0 as mentioned in this paper, and for the weights that are completely characterized, the Riesz projection, mapping the weighted space of the harmonic functions onto the corresponding space of holomorphic functions is bounded.
Abstract: Weighted spaces of harmonic and holomorphic functions on the unit disc are studied. We show that for all radial weights which are not decreasing too fast the space of harmonic functions is isomorphic to c0. For the weights that we consider we completely characterize those spaces of holomorphic functions which are isomorphic to c0. Moreover, we determine when the Riesz projection, mapping the weighted space of harmonic functions onto the corresponding space of holomorphic functions, is bounded.
TL;DR: In this paper, it was shown that there are no 4D bicovariant differential calculi, which are Lorentz covariant, and that there exists a five-dimensional differential calculus, which satisfies both requirements.
TL;DR: The main result of as mentioned in this paper is that the hypersurface M is holomorphically nondegenerate at the origin if there is no holomorphic vector field tangent to M in a neighborhood of the origin.
Abstract: Let M be an analytic real hypersurface through the origin in C n+1 and let hol ( M ) denote the space of vector fields X =Re Z |M tangent to M in a neighborhood of the origin, where Z is a holomorphic vector field defined in a neighborhood of the origin. The hypersurface M is holomorphically nondegenerate at the origin if there is no holomorphic vector field tangent to M in a neighborhood of the origin. The main result of the paper is that hol ( M ) is finite dimensional if and only if M is holomorphically nondegenerate at the origin.
TL;DR: The universal Teichm\\Pi$ as discussed by the authors is an equivariant injective holomorphic immersion of $T(1)$ into Universal Siegel Space, which is a universal parameter space for all Riemann surfaces.
Abstract: The Universal Teichm\\\"uller Space, $T(1)$, is a universal parameter space for all Riemann surfaces. In earlier work of the first author it was shown that one can canonically associate infinite- dimensional period matrices to the coadjoint orbit manifold $Diff(S^1)/Mobius(S^1)$ -- which resides within $T(1)$ as the (Kirillov-Kostant) submanifold of ``smooth points'' of $T(1)$. We now extend that period mapping $\\Pi$ to the entire Universal Teichm\\\"uller space utilizing the theory of the Sobolev space $H^{1/2}(S^1)$. $\\Pi$ is an equivariant injective holomorphic immersion of $T(1)$ into Universal Siegel Space, and we describe the Schottky locus utilizing Connes' ``quantum calculus''. There are connections to string theory. Universal Teichm\\\"uller Space contains also the separable complex submanifold $T(H_\\infty)$ -- the Teichm\\\"uller space of the universal hyperbolic lamination. Genus-independent constructions like the universal period mapping proceed naturally to live on this completion of the classical Teichm\\\"uller spaces. We show that $T(H_\\infty)$ carries a natural convergent Weil-Petersson pairing.
13 Dec 1995
TL;DR: In this paper, the authors proved that every minimizer is either a helicoidal arc or of the form C, S, CS, SC, CSC, CCC, where S stands for "circle" and S for "segment", respectively.
Abstract: We present the solution of the three-dimensional case of a problem regarding the structure of minimum-length paths with a prescribed curvature bound and prescribed initial and terminal positions and directions. In particular, we disprove a conjecture, according to which every minimizer is a concatenation of circles and straight lines. We show that there are many minimizers-the "helicoidal arcs"-that are not of this form. These arcs are smooth and are characterized by the fact that their torsion satisfies a second-order ordinary differential equation. The solution is obtained by applying optimal control theory. An essential feature of the problem is that it requires the use of optimal control on manifolds. The natural state space of the problem is the product of three-dimensional Euclidean space and a two-dimensional sphere. Although the problem is obviously embeddable in 6-dimensional Euclidean space, the maximum principle for the embedded problem yields no information, whereas a careful application of the maximum principle on manifolds yields a very strong result, namely, that every minimizer is either a helicoidal arc or of the form C, S, CS, SC, CSC, CCC, where C, S stand for "circle" and "segment", respectively.
22 Jan 1995
TL;DR: It is shown that any Euclidean graph over a set V of n points in k-dimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., has weight O(1) .
Abstract: In this paper, we show that any Euclidean graph over a set V of n points in k-dimensional space that satisfies either the leapfrog property or the isolation property has small weight, i.e., has weight O(1) . wt(SMT), where SMT is a Steiner minimal tree of V. Both the leapfrog property as well as the isolation property constrain the way the edges of the graph are configured in space. Our main application is to prove that certain Euclidean graphs known as t-spanners can be constructed with optimal weight of O(1) + wt(SMT), an intriguing open problem that has attracted much attention recently. The main tool in obtaining the above weight bounds is a theorem that proves the existence of long edges in a Steiner minimal tree on a restricted set of points in k-dimensional space. We also generalize this theorem for Steiner minimal trees on arbitrary point sets. Since very little is known about high-dimensional Steiner minimal trees, these results are of independent interest.
TL;DR: In this article, the authors studied the geometry of convex surfaces embedded in ℝ4 through their generic contacts with hyperplanes and proved that the inflection points on them are the umbilic points of their families of height functions.
Abstract: We study the geometry of the surfaces embedded in ℝ4 through their generic contacts with hyperplanes. The inflection points on them are shown to be the umbilic points of their families of height functions. As a consequence we prove that any generic convexly embedded 2-sphere in ℝ4 has inflection points.
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TL;DR: In this article, the authors show that every separable Tychonoff submaximal space is totally disconnected and show that pseudo-Lindelof sub-maximal spaces are Lindelof spaces.
TL;DR: In this paper, it is shown that the modified Hotelling's model does have a subgame perfect equilibrium in pure strategies and that the equal distance location pattern is an equilibrium, where the linear space is replaced by a one-dimensional bounded space without a boundary.
Book•
21 Apr 1995
TL;DR: In this paper, the space of heegaard graphs is defined for handlebodies and generalized one-relator 3-manifolds and N-relaton 3-mansifolds.
Abstract: Handlebodies.- Relative handlebodies.- Generalized one-relator 3-manifolds.- N-relaton 3-manifolds.- The space of heegaard graphs.
TL;DR: In this paper, the authors considered the multidimensional cosmological model describing the evolution of n Einstein spaces in the presence of a multicomponent perfect fluid and the dynamics of the model near the singularity were reduced to a billiard on the (n-1)-dimensional Lobachevsky space.
Abstract: The multidimensional cosmological model describing the evolution of n Einstein spaces is considered in the presence of a multicomponent perfect fluid. When certain restrictions on the parameters of the model are imposed, the dynamics of the model near the singularity are reduced to a billiard on the (n-1)-dimensional Lobachevsky space . The geometrical criterion for the finiteness of the billiard volume and its compactness is suggested. This criterion reduces the problem to the problem of illumination of an (n-2)-dimensional sphere by point-like sources. Some generalizations of the considered scheme (including scalar field and quantum generalizations) are considered.