Showing papers on "Space (mathematics) published in 1989"
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
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
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
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
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
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
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
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
Journal Article•
127 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.<>
Proceedings Article•
01 Jan 1989TL;DR: This work extends previous work by considering how this methodology can be applied to the optimization of quantities that are distal not only in space but also in time.
Abstract: The forward modeling approach is a methodology for learning control when data is available in distal coordinate systems. We extend previous work by considering how this methodology can be applied to the optimization of quantities that are distal not only in space but also in time.
TL;DR: This work found, as did Roughgarden et al., that two qualitatively different dynamic outcomes were possible: a stable steady state, and cyclic fluctuation in population density and space occupied.
Abstract: We study the dynamic behavior of open systems where older or larger individuals can inhibit the recruitment of juveniles into the population. Our approach is to examine the predictions of simple dynamic models. In these models, settlement rate into open space is decoupled from local population density. Our more elaborate models are special cases of Roughgarden et al.'s (1985) model for an open marine population with space—limited recruitment. We found, as did Roughgarden et al., that two qualitatively different dynamic outcomes were possible: a stable steady state, and cyclic fluctuation in population density and space occupied. The crucial factor needed to produce cyclic fluctuations is a time delay between settlement and recruitment into the adult population. The introduction of density—dependent mortality in adults serves to stabilize the limit cycle. The effect of growth or development rate on stability depends upon the relationship between these rates and individual size or age. This is because increased growth may act to increase the area occupied at equilibrium (a destabilizing factor), but can cause developmental time lags to either increase or decrease in length. As a result, an unstable system can be stabilized by either an increase or a decrease in juvenile growth rate when adults do not grow, or grow more slowly than juveniles.
TL;DR: The coupled-rearrangement-channel variational method with Gaussian-basis functions is applied to describe accurately both the short-range correlations and the asymptotic behavior of muonic molecular ions and Coulomb-interacting three-body systems.
Abstract: To the $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ ground states, we apply the coupled-rearrangement-channel variational method with Gaussian-basis functions which has successfully been used in precise calculations of muonic molecular ions, Coulomb-interacting three-body systems. The trinucleon wave function is decomposed into angular-momentum-projected three-body channels as done in the Faddeev equations method, but the interaction is fully incorporated with no partial-wave decomposition. The radial part of the channel amplitudes is expanded with a sufficient number of Gaussian-tail basis functions of the Jacobi coordinates. The Gaussian ranges are taken to be geometrical progressions which run from very short ranges through large enough ones. This ab initio variational approach is found to describe accurately both the short-range correlations and the asymptotic behavior. The Argonne ${V}_{14}$ potential is used as an example of realistic two-nucleon interactions; for $^{3}\mathrm{He}$, the Coulomb potential is included nonperturbatively. The calculation reproduces precisely the results of the Faddeev calculations for $^{3}\mathrm{H}$ and $^{3}\mathrm{He}$ for binding energy, probabilities of the S, S', P, and D states, and the S- and D-wave asymptotic normalization constants. Convergence of the present results is seen at a much smaller number of the three-body channels than in the Faddeev calculations. This is because the interaction is truncated in the angular momentum space in the Faddeev calculations but the full interaction is taken in the present method.
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.
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)).
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.
TL;DR: Rodrigues vectors are explored as a means of representing crystal orientation distributions in this article, and relationships between the Rodrigues vectors and several commonly used representations of rotations are presented.
Abstract: Rodrigues vectors are explored as a means of representing crystal orientation
distributions. Relationships between the Rodrigues vectors and several more
commonly utilized representations of rotations are presented. The restrictions which
cubic material symmetry imposes on the Rodrigues space are examined and
relationships for special equivalent configurations are developed. Common crystal
orientation distributions are presented as Rodrigues vectors and compared to the
more standard representations in terms of pole figures and Euler angles. Applications
of the Rodrigues space for illustrating misorientations between neighboring grains are also discussed.
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
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
01 Jan 1989
TL;DR: In this article, a yield function that describes the behavior of orthotropic sheets exhibiting planar anisotropy and subjected to plane stress conditions is proposed, which gives yield surface shapes in a three-dimensional space (two normal stresses and one shear stress) in rather good agreement with the ones based on polycrystal modeling.
Abstract: A yield function that describes the behavior of orthotropic sheets exhibiting planar anisotropy and subjected to plane stress conditions is proposed. This criterion gives yield surface shapes in a three-dimensional space (two normal stresses and one shear stress) in rather good agreement with the ones based on polycrystal modeling. Some examples are given to illustrate the necessity of such formulation.
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.
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.
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.
TL;DR: This paper proposes that two events so correlated are experienced as one and the same event; that is, any two quantum physically correlated events separated in time or space will constitute a single experience--an event in "consciousness."
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.
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.