共查询到20条相似文献,搜索用时 15 毫秒
1.
Boris V. Dekster 《Journal of Geometry》2004,80(1-2):48-64
A new angular measure in a d-dimensional Minkowski space M was introduced recently. It determines the lengths of rectifiable curves in the (d - 1)-dimensional topological sphere S of all directions in M. Thus, a length structure appears on S. This results in the appropriate intrinsic metric in S. The paper deals with
some properties of the length structure and the resulting metric space S. In particular, it shows that diam S 2 . 相似文献
2.
《Journal of Pure and Applied Algebra》2019,223(11):5030-5048
Take positive integers m, n and d. Let Y be an m-fold cyclic cover of ramified over a general hypersurface of degree md. In this paper we study the space of lines in Y and show that it is smooth of dimension if and . When , our result gives a formula on the number of m-contact order lines of X (see Definition 1.2). 相似文献
3.
Shizan Fang Jinghai Shao Karl-Theodor Sturm 《Probability Theory and Related Fields》2010,146(3-4):535-565
The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete characterization of the derivative processes for certain class of absolutely continuous curves. We prove existence of the gradient flow curves for the relative entropy w.r.t. the Wiener measure and identify these gradient flow curves with solutions of the Ornstein–Uhlenbeck evolution equation. 相似文献
4.
Witold Marciszewski 《Proceedings of the American Mathematical Society》2003,131(6):1965-1969
Assuming that the minimal cardinality of a dominating family in is equal to , we construct a subset of a real line such that the space of continuous real-valued functions on does not admit any continuous bijection onto a -compact space. This gives a consistent answer to a question of Arhangel'skii.
5.
Fori = 1,...,n letC(xi, ri) be a circle in the plane with centrex
i and radiusr
i. A repeated distance graph is a directed graph whose vertices are the centres and where (x
i, xj) is a directed edge wheneverx
j lies on the circle with centrex
i. Special cases are the nearest neighbour graph, whenr
i is the minimum distance betweenx
i and any other centre, and the furthest neighbour graph which is similar except that maximum replaces minimum. Repeated distance graphs generalize to any dimension with spheres or hyperspheres replacing circles. Bounds are given on the number of edges in repeated distance graphs ind dimensions, with particularly tight bounds for the furthest neighbour graph in three dimensions. The proofs use extremal graph theory.Research supported by the Natural Science and Engineering Research Council grant number A3013 and the F.C.A.R. grant number EQ1678. 相似文献
6.
Reinhold Kienzler 《PAMM》2007,7(1):1041701-1041702
In Newtonian mechanics, reciprocity relations of Betti and Maxwell are useful tools in the analysis of engineering problems. Similar reciprocity relations have been established recently in Eshelbian Mechanics. In this contribution, a defect-interaction problem is investigated and various aspects of reciprocity are studied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Gyrgy Csizmadia 《Discrete Mathematics》1996,150(1-3):81-88
A finite subset of the union of the polar axis and the equator of a sphere is called a suspension. We prove that if n points in 3-space determine the maximum number of furthest neighbours then they form a suspension. The exact maximum and the optimal arrangement are also given. This sharpens a result of Avis, Erdös and Pach. 相似文献
8.
D. I. Blokhintsev 《Theoretical and Mathematical Physics》1978,37(2):933-937
9.
Martin Schechter Kyril Tintarev 《Proceedings of the American Mathematical Society》2006,134(2):403-410
We present the most general definition of the linking of sets in a Hilbert space and, drawing on the theory given in earlier papers by Schechter and Tintarev, give a necessary and sufficient geometric condition for linking when one set is compact.
10.
V. S. Avduevskii V. I. Denisov V. M. Kovtunenko A. A. Logunov G. R. Uspenskii M. M. Tsimbalyuk 《Theoretical and Mathematical Physics》1989,78(1):1-6
Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 78, No. 1, pp. 3–10, January, 1989. 相似文献
11.
12.
An antipodal set in Euclidean n-space is a set of points with the property that through any two of them there is a pair of parallel hyperplanes supporting
the set. In this paper we discuss the various possible ways to translate this notion to hyperbolic space and find the maximal
cardinality of a hyperbolic antipodal set (according to the different definitions).
The first two authors were partially supported by the Hung. Nat. Sci. Found. (OTKA), grant no. T043556 and T037752 and the
first author was partially supported also by a Natural Sciences and Engineering Research Council of Canada Discovery Grant. 相似文献
13.
Emma Previato 《Proceedings of the American Mathematical Society》1999,127(9):2547-2556
A plane polygon inscribed in a conic and circumscribed to a conic can be continuously `rotated', as it were. One of the many proofs consists in viewing each side of as translation by a torsion point of an elliptic curve. In the -space version, involving torsion points of hyperelliptic Jacobians, there is a -dimensional family of rotations, where of the hyperelliptic curve; the polygon is now inscribed in one and circumscribed to quadrics.
14.
《Topology and its Applications》2005,146(2-3):239-244
Let E denote the real inner product space that is the union of all finite dimensional Euclidean spaces. There is a bounded nonconvex set S, that is a subset of E, such that each point of E has a unique nearest point in S. Let H denote the separable Hilbert space that is the completion of space E. A condition is given in order that a point in H have a unique nearest point in the closure of S. We shall also provide an example where the condition fails. 相似文献
15.
16.
A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on , and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorphic to Hilbert space. We do this by demonstrating that the first complete rigid space can be modified slightly to be an AR-space (absolute retract), and thus by a theorem of Dobrowolski and Torunczyk is homeomorphic to .
17.
Wang Yangeng 《数学学报(英文版)》1997,13(3):333-336
The space of continuous maps from a topological spaceX to topological spaceY is denoted byC(X,Y) with the compact-open topology. In this paper we prove thatC(X,Y) is an absolute retract ifX is a locally compact separable metric space andY a convex set in a Banach space. From the above fact we know thatC(X,Y) is homomorphic to Hilbert spacel
2 ifX is a locally compact separable metric space andY a separable Banach space; in particular,C(R
n,Rm) is homomorphic to Hilbert spacel
2.
This research is supported by the Science Foundation of Shanxi Province's Scientific Committee 相似文献
18.
Oscar Perdomo 《Journal of Mathematical Analysis and Applications》2009,353(1):403-409
Let be the three-dimensional anti-de Sitter space. In this paper we will construct new examples of complete maximal space like surfaces in . Moreover, we will prove that any complete maximal space like surface in with principal curvatures ±κ bounded away from zero must be isometric to the hyperbolic cylinder. Since the new examples that we have constructed have exactly two principal curvatures everywhere, we conclude that the condition on the principal curvatures on the previous result, i.e. the condition |κ(m)|>c>0, cannot be replaced by the condition |κ(m)|>0. 相似文献
19.
Paolo Terenzi 《Archiv der Mathematik》1984,43(5):448-459
Summary Let (x
n
) be a general sequence of a Banach space, there is given a particular representation of the elements of the space spanned by (x
n
), by means of the elements of (x
n
). Some properties of this representation are shown, also if (x
n
is minimal or normingM-basis. Moreover some open questions are solved. 相似文献
20.
In this paper, we introduce the Fock space on and obtain an isomorphism between the Fock space on and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on the Bose-Fock space and answer a question in [2]. As a physical application, we study the Gibbs state. 相似文献