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Showing papers on "Space (mathematics) published in 1989"


MonographDOI
01 Jan 1989
TL;DR: In this paper, the authors define a mapping with bounded distortion on Riemannian spaces and define the set of branch points of such a mapping, as well as its local structure.
Abstract: Introduction Some facts from the theory of functions of a real variable Functions with generalized derivatives Mobius transformations Definition of a mapping with bounded distortion Mappings with bounded distortion on Riemannian spaces Main facts in the theory of mappings with boundd distortion Estimates of the moduli of continuity and differentiability almost everywhere of mappings with bounded distortion Some facts about continuous mappings on $R^n$ Conformal capacity The concept of the generalized differential of an exterior form Mappings with bounded distortion and elliptic differential equations Topological properties of mappings with bounded distortion Local structure of mappings with bounded distortion Characterization of mappings with bounded distortion by the property of quasiconformity Sequences of mappings with bounded distortion The set of branch points of a mapping with bounded distortion and locally homeomorphic mappings Extremal properties of mappings with bounded distortion Some further results Some results in the theory of functions of a real variable and the theory of partial differential equations Functions with bounded mean oscillation Harnack's inequality for quasilinear elliptic equations Theorems on semicontinuity and convergence with a functional for functionals of the calculus of variations Some properties of functions with generalized derivatives On the degree of a mapping.

451 citations


Journal ArticleDOI
TL;DR: In this article, the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space is investigated, and the results are applied to an infinite dimensional problem involving the symplectίc action function.
Abstract: We investigate the relation between the trajectories of a finite dimensional gradient flow connecting two critical points and the cohomology of the surrounding space. The results are applied to an infinite dimensional problem involving the symplectίc action function.

317 citations


Journal ArticleDOI
Jun Kigami1
TL;DR: A reconstruction of the well-known theory of calculus on [0, 1] will naturally bring a calculus associated with the harmonic functions, Laplace operator, Gauss-Green formula and so on, on the N-Sierpinski space whose Hausdorff dimension is (logN)/(log 2) as mentioned in this paper.
Abstract: A reconstruction of the well-known theory of calculus on [0, 1] will naturally bring a calculus associated with the harmonic functions, Laplace operator, Gauss-Green’s formula and so on, on theN-Sierpinski space whose Hausdorff dimension is (logN)/(log 2).

302 citations


Journal ArticleDOI
TL;DR: A characterization of the coset spaces on which N = 2 superconformal models can be constructed by the use of the super Kac-Moody algebra is given in this article.

221 citations


Journal ArticleDOI
TL;DR: In this paper, a variety of chaotic flows evolving in relatively high-dimensional spaces are considered, and it is shown through the use of an optimal choice of basis functions, which are consequence of the Karhunen-Loeve procedure, that an accurate description can be given in a relatively low-dimensional space.

221 citations


Book
31 Aug 1989

213 citations


Book ChapterDOI
TL;DR: The theory of non-commutative symmetric spaces was introduced by Gohberg and Krein this paper, who considered the problem of symmetrically normed ideals of bounded linear operators in Hilbert space.
Abstract: In this paper we survey some aspects of the theory of non-commutative Banach function spaces, that is, spaces of measurable operators associated with a semi- finite von Neumann algebra. These spaces are also known as non-commutative symmetric spaces. The theory of such spaces emerged as a common generalization of the theory of classical (“commutative”) rearrangement invariant Banach function spaces (in the sense of W.A.J. Luxemburg and A.C. Zaanen) and of the theory of symmetrically normed ideals of bounded linear operators in Hilbert space (in the sense of I.C. Gohberg and M.G. Krein). These two cases may be considered as the two extremes of the theory: in the first case the underlying von Neumann algebra is the commutative algebra L ∞ on some measure space (with integration as trace); in the second case the underlying von Neumann algebra is B (ℌ), the algebra of all bounded linear operators on a Hilbert space ℌ (with standard trace). Important special cases of these non-commutative spaces are the non-commutative L p-spaces, which correspond in the commutative case with the usual L p-spaces on a measure space, and in the setting of symmetrically normed operator ideals they correspond to the Schatten p-classes \( \mathfrak{S}_p \) .

172 citations


Journal ArticleDOI
TL;DR: In this paper, the moduli spaces and their symmetries of the c = 3, N = 2 supersymmetric, Landau-Ginzburg models were investigated and shown to be isomorphic to the two-sphere, divided by the tetrahedral group T.

148 citations


Journal ArticleDOI
TL;DR: In this paper, a method of obtaining compact finite-difference approximations of h4 accuracy to operators of Navier-Stokes type is considered, and the basic procedure is developed for operators in one space dimension and subsequently applied to problems in more space dimensions and in time.

144 citations



Proceedings Article
01 Jan 1989
TL;DR: The proof method for the lower bound shows that the emptiness problem for one-way probabilistic finite-state machines is undecidable and some results of independent interest on the rate of convergence of time-varying Markov chains to their halting states are obtained.
Abstract: Two results on interactive proof systems with two-way probabilistic finite-state verifiers are proved. The first is a lower bound on the power of such proof systems if they are not required to halt with high probability on rejected inputs: it is shown that they can accept any recursively enumerable language. The second is an upper bound on the power of interactive proof systems that halt with high probability on all inputs. The proof method for the lower bound also shows that the emptiness problem for one-way probabilistic finite-state machines is undecidable. In the proof of the upper bound some results of independent interest on the rate of convergence of time-varying Markov chains to their halting states are obtained.<>

Journal ArticleDOI
TL;DR: In this paper, the expansion of the Casimir energy for a scalar field with mass m, in a space where one dimension has been compactified into a circle of length a, leads to a double-infinite series that can be regularized by analytic continuation in the space dimension.
Abstract: The expansion of the Casimir energy for a scalar field with mass m, in a space where one dimension has been compactified into a circle of length a, leads to a double‐infinite series that can be regularized by analytic continuation in the space dimension. The dimensionally regularized sum is then expressed as a power series in am by means of zeta‐function expansions. The two possibilities of odd and even space dimensions are distinguished. In the odd space dimension we give a power expansion for small am, in addition to the asymptotic behavior. For the even space dimension, an expansion valid for any value of am is obtained. The contribution of higher‐order terms is studied and, for the three‐dimensional space, results for different values of the compactification length are shown.

Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotic behavior in time of the solutions and the theory of scattering in the energy space for the non-linear wave equation and proved the existence of the wave operators, and showed that for small initial data and, forn≧4, the assumption onf cover the case wheref behaves slightly better than a single powerp=1+4/(n−2), both near zero and at infinity.
Abstract: We study the asymptotic behaviour in time of the solutions and the theory of scattering in the energy space for the non-linear wave equation $$\square \varphi + f(\varphi ) = 0$$ in ℝn,n≧3. We prove the existence of the wave operators, asymptotic completeness for small initial data and, forn≧4, asymptotic completeness for arbitrarily large data. The assumptions onf cover the case wheref behaves slightly better than a single powerp=1+4/(n−2), both near zero and at infinity (see (1.5), (1.6) and (1.8)).

Book
01 Jan 1989

Journal ArticleDOI
TL;DR: In this article, the bosonic and fermionic operators on Wolf coset spaces (quaternionic symmetric spaces) satisfy operator product expansions with N = 4 superconformal symmetry.
Abstract: The bosonic and fermionic operators on Wolf coset spaces (quaternionic symmetric spaces) satisfy operator product expansions with N=4 superconformal symmetry. The currents and the values of the parameters can be understood from general rules on coset space constructions.


Journal ArticleDOI
TL;DR: In this article, it was shown that many quasi-autonomous evolution equations of non monotone type associated to odd non linear operators have anti-periodic solutions provided the forcing term is antiperiodic.
Abstract: Following a recent work of H Okochi in the case of evolution equations generated by subdifferential operators in a real Hilbert space, we point out that many quasi-autonomous evolution equations of non monotone type associated to odd non linear operators have some anti-periodic solutions provided the forcing term is anti-periodic This comes from the fact that the space of anti-periodic functions is transversal to the kernel of the linear part and stable under the action of odd non linear operators The proofs of our results combine strong a priori estimates which depend very little on the non-linearities with an application of Schauder's fixed point theorem to some related dissipative equations

Journal ArticleDOI
TL;DR: In this article, the authors studied static solutions of the vacuum Einstein equations in D =m+n+2 dimensions, which have the following symmetries: the solutions are spherically symmetric in (m+2) dimensions, (or more generally the m-sphere is replace by an arbitrary m-dimensional Einstein space), while the internal space is any arbitrary n-dimensional space.
Abstract: The author studies static solutions of the vacuum Einstein equations in D=m+n+2 dimensions which have the following symmetries: the solutions are spherically symmetric in (m+2) dimensions, (or more generally the m-sphere is replace by an arbitrary m-dimensional Einstein space), while the internal space is any arbitrary n-dimensional Einstein space The global properties of all such solutions are derived by considering the equivalent dimensionally reduced system in (m+2) dimensions, and by using techniques from the theory of dynamical systems after a judicious choice of variables Apart from the trivial case of the Schwarzschild solution with constant scalar field, all solutions are found to contain naked singularities or else not to be asymptotically flat, as would be expected from the 'no hair' theorems

Journal ArticleDOI
TL;DR: In this paper, the authors show that the space of external sources, and hence the response space of observable electromagnetic fields at the Earth's surface (the response space) can often be well approximated by spaces of very low dimension p. They demonstrate that the simplifying assumption of a finite dimensional external source space is required for a rigorous justification of transfer function (TF) methods in general and show that when p = 2, the response spaces is equivalent to all possible interstation and intercomponent TFs.
Abstract: In this paper we develop a new approach to the multiple-station analysis of geomagnetic array data. Our approach is based on the observation that the space of external sources, and hence the space of observable electromagnetic fields at the Earth's surface (the “response space”), can often be well approximated by spaces of very low dimension p. We demonstrate that the simplifying assumption of a finite dimensional external source space is required for a rigorous justification of transfer function (TF) methods in general and show that when p = 2, the response space is equivalent to all possible interstation and intercomponent TFs. Heuristically, estimation of the response space by the p dominant eigenvectors of the spectral density matrix (i.e., the frequency domain matrix of averaged cross products for all components measured in the array) can be easily justified. A more rigorous statistical treatment is also discussed. Our statistical model (a complex errors-in-variables model) allows for (potentially correlated) errors in all measured field components and treats all stations in a symmetric fashion. The model is thus substantially more reasonable than the usual statistical model used in TF estimation which assumes that the fields at a reference site are noise free and “normal.” We illustrate our approach with a small five-station magnetotelluric array which was run as part of the EMSLAB experiment. For this small array, p = 2 is a good approximation, and the two dominant eigenvectors provide an estimate of the response of the Earth to (approximately) uniform sources. There is, however, substantial additional structure in the spectral density matrix (SDM), and further analysis of the eigenvalues and eigenvectors of the SDM reveals that the “noise” (i.e., the portion of the data which does not fit a uniform source model) is dominated by source effects. These results illustrate a significant advantage of multiple-station techniques: they allow us to test model assumptions and to separate noise into coherent and incoherent components, allowing a clearer understanding of the problems, and possibilities, to be found in the interpretation of geomagnetic induction data.

Journal ArticleDOI
TL;DR: In this article, the authors investigate geometrical properties of a space curve and of its spherical images and they show that a Space curve is characterised by two 'phase-like' quantities and comment on the relation of these quantities to the Berry phase.
Abstract: The authors investigate geometrical properties of a space curve and of its spherical images. They show that a space curve is characterised by two 'phase-like' quantities and comment on the relation of these quantities to the Berry phase.


Journal ArticleDOI
TL;DR: In this paper, it was shown that there is a natural geometric procedure for constructing the quantum theory of a particle in a general metric-affine space with curvature and torsion.
Abstract: We point out that there is a natural geometric procedure for constructing the quantum theory of a particle in a general metric-affine space with curvature and torsion. Quantization rules are presented and expressed in the form of a simple path integral formula which specifies compactly a new combined equivalence and correspondence principle. The associated Schrodinger equation has no extra curvature nor torsion terms that have plagued earlier attempts. Several well-known physical systems are invoked to suggest the correctness of the proposed theory.

Journal ArticleDOI
TL;DR: In this paper, a one-dimensional model of nonmonocentric urban land use is extended into a two-dimensional space, and the equilibrium urban configurations in the 2D space are essentially the same as those in the 1D space except for the conditions on the parameters.
Abstract: A one-dimensional model of nonmonocentric urban land use is extended into a two-dimensional space. Under the assumption of circular symmetry, it is shown that the equilibrium urban configurations in the two-dimensional space are essentially the same as those in the one-dimensional space except for the conditions on the parameters.

Journal ArticleDOI
TL;DR: In this paper, the topology and geometry of the space of null geodesics N of a space-time M are used to study the causal structure of the time itself.
Abstract: The topology and geometry of the space of null geodesics N of a space‐time M are used to study the causal structure of the space‐time itself. In particular, the question of whether the topology of N is Hausdorff or admits a compatible manifold structure carries information on the global structure of M, and the transversality properties of the intersections of skies of points tell whether the points are conjugate points on a null geodesic.


Journal Article
TL;DR: In this paper, the conditions générales d'utilisation (http://www.compositio.nl/) implique l'accord avec les conditions generales de utilisation, i.e., usage commerciale ou impression systématique, constitutive of an infraction pénale.
Abstract: © Foundation Compositio Mathematica, 1989, tous droits réservés. L’accès aux archives de la revue « Compositio Mathematica » (http: //http://www.compositio.nl/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.


Book
01 Jan 1989
TL;DR: In this article, the authors consider the problem of holomorphic functions of several variables in the entire n space and show that the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product.
Abstract: We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space

Journal ArticleDOI
TL;DR: In this paper, it was shown that the set of economies whose equilibrium sets contain manifolds of arbitrary dimension is non-empty and open in the appropriate topology, and if the space of consumers is sufficiently small, then local uniqueness is a generic property of economies.

Journal ArticleDOI
TL;DR: In this paper, the authors constructed new vacua for the eleven-dimensional supermembrane in which spacetime is the product of four-dimensional anti-de Sitter space and a compact seven-dimensional Einstein space.