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61.
In this article, we prove the existence of fixed points and the demiclosed principle for mean nonexpansive mappings in Cartan, Alexandrov and Toponogov(0) spaces. We also obtain a Δ-convergence theorem and a strong convergence theorem of Ishikawa iteration for mean nonexpansive mappings in Cartan, Alexandrov and Toponogov(0) spaces. 相似文献
62.
We define a general game which forms a basis for modelling situations of static search and concealment over regions with spatial structure. The game involves two players, the searching player and the concealing player, and is played over a metric space. Each player simultaneously chooses to deploy at a point in the space; the searching player receiving a payoff of 1 if his opponent lies within a predetermined radius r of his position, the concealing player receiving a payoff of 1 otherwise. The concepts of dominance and equivalence of strategies are examined in the context of this game, before focusing on the more specific case of the game played over a graph. Methods are presented to simplify the analysis of such games, both by means of the iterated elimination of dominated strategies and through consideration of automorphisms of the graph. Lower and upper bounds on the value of the game are presented and optimal mixed strategies are calculated for games played over a particular family of graphs. 相似文献
63.
64.
L. Shao D. Shao C. G. Shao H. Noda 《International Journal of Theoretical Physics》2008,47(6):1663-1691
Using the recoupling theorem and graph calculation in loop quantum gravity, it is demonstrated that the action of metric matrix
operator on Gaussian weave state is an eigenaction, the representation matrix elements of the metric operator and their expectation
values are calculated. The values of length of tangent vectors of edges adjacent to the vertex of Gaussian weave state, as
well as the angles between them are also obtained in the cases of k=0 and k=2. 相似文献
65.
Luigi Ambrosio Shouhei Honda Jacobus W. Portegies David Tewodrose 《Journal of Functional Analysis》2021,280(10):108968
In this paper we study the family of embeddings of a compact space into via eigenmaps. Extending part of the classical results [10], [11] known for closed Riemannian manifolds, we prove convergence as of the rescaled pull-back metrics in induced by . Moreover we discuss the behavior of with respect to measured Gromov-Hausdorff convergence and t. Applications include the quantitative -convergence in the noncollapsed setting for all , a result new even for closed Riemannian manifolds and Alexandrov spaces. 相似文献
66.
67.
Let and be graphs where the set of vertices is the set of points of the integer lattice and the set of edges consists of all pairs of vertices whose city block and chessboard distances, respectively, are 1.In this paper it is shown that the partition dimensions of these graphs are 3 and 4, respectively, while their metric dimensions are not finite. Also, for every n3 there exists an induced subgraph of of order 3n-1 with metric dimension n and partition dimension 3. These examples will answer a question raised by Chartrand, Salehi and Zhang. Furthermore, graphs of order n9 having partition dimension n-2 are characterized, thus completing the characterization of graphs of order n having partition dimension 2, n, or n-1 given by Chartrand, Salehi and Zhang. The list of these graphs includes 23 members. 相似文献
68.
Coenraad C.A. Labuschagne 《Journal of Mathematical Analysis and Applications》2008,342(2):780-797
Denote by cf(X) the set of all nonempty convex closed subsets of a separable Banach space X. Let (Ω,Σ,μ) be a complete probability space and denote by (L1[Σ,cf(X)],Δ) the complete metric space of (equivalence classes of a.e. equal) integrably bounded cf(X)-valued functions. For any preassigned filtration (Σi), we describe the space of Δ-convergent integrably bounded cf(X)-valued martingales in terms of the Δ-closure of in L1[Σ,cf(X)]. In particular, we provide a formula to calculate the join of two such martingales and the positive part of such a martingale. Our object is achieved by considering the more general setting of a near vector lattice (S,d), endowed with a Riesz metric d. By means of Rådström's embedding theorem for such spaces, a link is established between the space of convergent martingales in S and the space of convergent martingales in the Rådström completion R(S) of S. This link provides information about the former space of martingales, via known properties of measure-free martingales in Riesz normed vector lattices, applicable to R(S). We also apply our general results to the spaces of Δ-convergent ck(X)-valued martingales, where ck(X) denotes the set of all nonempty convex compact subsets of X. 相似文献
69.
We investigate the approximation rate for certain centered Gaussian fields by a general approach. Upper estimates are proved in the context of so–called Hölder operators and lower estimates follow from the eigenvalue behavior of some related self–adjoint integral operator in a suitable L 2(μ)–space. In particular, we determine the approximation rate for the Lévy fractional Brownian motion X H with Hurst parameter H∈(0,1), indexed by a self–similar set T?? N of Hausdorff dimension D. This rate turns out to be of order n ?H/D (log?n)1/2. In the case T=[0,1] N we present a concrete wavelet representation of X H leading to an approximation of X H with the optimal rate n ?H/N (log?n)1/2. 相似文献
70.
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete
(not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general
metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric
g
≥−(n−1)a
2, a≥0, then there exist constants A
n
>0,B
n
>0 only depending on the dimension, such that
where λ
k
(Ω) (k∈ℕ*) denotes the k-th eigenvalue of the Neumann problem on any bounded domain Ω⊂M of volume V=Vol (Ω,g). Furthermore, this upper bound is clearly in agreement with the Weyl law. As a corollary, we get also an estimate which
is analogous to Buser’s upper bounds of the spectrum of a compact Riemannian manifold with lower bound on the Ricci curvature.
相似文献