共查询到20条相似文献,搜索用时 46 毫秒
1.
Let K be a closed convex subset of a q-uniformly smooth separable Banach space, T:K→K a strictly pseudocontractive mapping, and f:K→K an L-Lispschitzian strongly pseudocontractive mapping. For any t∈(0,1), let xt be the unique fixed point of tf+(1-t)T. We prove that if T has a fixed point, then {xt} converges to a fixed point of T as t approaches to 0. 相似文献
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We derive a Molchan–Golosov-type integral transform which changes fractional Brownian motion of arbitrary Hurst index K into fractional Brownian motion of index H. Integration is carried out over [0,t], t>0. The formula is derived in the time domain. Based on this transform, we construct a prelimit which converges in L2(P)-sense to an analogous, already known Mandelbrot–Van Ness-type integral transform, where integration is over (−∞,t], t>0. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are Lipschitz ?-strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. An iteration process recently introduced by Chidume and Zegeye is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
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We consider a multidimensional diffusion X with drift coefficient b(α,Xt) and diffusion coefficient ?σ(β,Xt). The diffusion sample path is discretely observed at times tk=kΔ for k=1…n on a fixed interval [0,T]. We study minimum contrast estimators derived from the Gaussian process approximating X for small ?. We obtain consistent and asymptotically normal estimators of α for fixed Δ and ?→0 and of (α,β) for Δ→0 and ?→0 without any condition linking ? and Δ. We compare the estimators obtained with various methods and for various magnitudes of Δ and ? based on simulation studies. Finally, we investigate the interest of using such methods in an epidemiological framework. 相似文献
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We give an elementary proof for Lewis Bowen’s theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our methods also show that for all compact groups K and every free product Γ of infinite amenable groups, the factor Γ?KΓ/K of the Bernoulli action Γ?KΓ by the diagonal K-action is isomorphic with a Bernoulli action of Γ. 相似文献
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Suppose X is a real q-uniformly smooth Banach space and F,K:X→X are bounded strongly accretive maps with D(K)=F(X)=X. Let u∗ denote the unique solution of the Hammerstein equation u+KFu=0. A new explicit coupled iteration process is shown to converge strongly to u∗. No invertibility assumption is imposed on K and the operators K and F need not be defined on compact subsets of X. Furthermore, our new technique of proof is of independent interest. Finally, some interesting open questions are included. 相似文献
8.
Brooks’ theorem is a fundamental result in the theory of graph coloring. Catlin proved the following strengthening of Brooks’ theorem: Let d be an integer at least 3, and let G be a graph with maximum degree d. If G does not contain Kd+1 as a subgraph, then G has a d-coloring in which one color class has size α(G). Here α(G) denotes the independence number of G. We give a unified proof of Brooks’ theorem and Catlin’s theorem. 相似文献
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We prove that if for a continuous map f on a compact metric space X, the chain recurrent set, R(f) has more than one chain component, then f does not satisfy the asymptotic average shadowing property. We also show that if a continuous map f on a compact metric space X has the asymptotic average shadowing property and if A is an attractor for f, then A is the single attractor for f and we have A=R(f). We also study diffeomorphisms with asymptotic average shadowing property and prove that if M is a compact manifold which is not finite with dimM=2, then the C1 interior of the set of all C1 diffeomorphisms with the asymptotic average shadowing property is characterized by the set of Ω-stable diffeomorphisms. 相似文献
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A d-arc-dominated digraph is a digraph D of minimum out-degree d such that for every arc (x,y) of D, there exists a vertex u of D of out-degree d such that (u,x) and (u,y) are arcs of D. Henning and Yeo [Vertex disjoint cycles of different length in digraphs, SIAM J. Discrete Math. 26 (2012) 687–694] conjectured that a digraph with minimum out-degree at least four contains two vertex-disjoint cycles of different length. In this paper, we verify this conjecture for 4-arc-dominated digraphs. 相似文献
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Let G be a connected regular graph. Denoted by t(G) and Kf(G) the total graph and Kirchhoff index of G, respectively. This paper is to point out that Theorem 3.7 and Corollary 3.8 from “Kirchhoff index in line, subdivision and total graphs of a regular graph” [X. Gao, Y.F. Luo, W.W. Liu, Kirchhoff index in line, subdivision and total graphs of a regular graph, Discrete Appl. Math. 160(2012) 560–565] are incorrect, since the conclusion of a lemma is essentially wrong. Moreover, we first show the Laplacian characteristic polynomial of t(G), where G is a regular graph. Consequently, by using Kf(G), we give an expression on Kf(t(G)) and a lower bound on Kf(t(G)) of a regular graph G, which correct Theorem 3.7 and Corollary 3.8 in Gao et al. (2012) [2]. 相似文献
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Let R be a commutative ring with identity. We will say that an R-module M satisfies the weak Nakayama property, if IM=M, where I is an ideal of R, implies that for any x∈M there exists a∈I such that (a−1)x=0. In this paper, we will study modules satisfying the weak Nakayama property. It is proved that if R is a local ring, then R is a Max ring if and only if J(R), the Jacobson radical of R, is T-nilpotent if and only if every R-module satisfies the weak Nakayama property. 相似文献
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Mustapha Chellali Teresa W. Haynes Stephen T. Hedetniemi Alice McRae 《Discrete Applied Mathematics》2013
A subset S⊆V in a graph G=(V,E) is a [j,k]-set if, for every vertex v∈V?S, j≤|N(v)∩S|≤k for non-negative integers j and k, that is, every vertex v∈V?S is adjacent to at least j but not more than k vertices in S. In this paper, we focus on small j and k, and relate the concept of [j,k]-sets to a host of other concepts in domination theory, including perfect domination, efficient domination, nearly perfect sets, 2-packings, and k-dependent sets. We also determine bounds on the cardinality of minimum [1, 2]-sets, and investigate extremal graphs achieving these bounds. This study has implications for restrained domination as well. Using a result for [1, 3]-sets, we show that, for any grid graph G, the restrained domination number is equal to the domination number of G. 相似文献
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We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces, and we define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and cone-to-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (in the classical sense) and K-monotone functions defined by Borwein, Burke and Lewis to mappings with domains and ranges of higher dimensions. First, using results of Veselý and Zají?ek, we show some relationships between these classes. Then, we show that every K-monotone function f:X→R, where X is any Banach space, is continuous outside of a set which can be covered by countably many Lipschitz hypersurfaces. This sharpens a result due to Borwein and Wang. As a consequence, we obtain a similar result for K-monotone dominated and cone-to-cone monotone mappings. Finally, we prove several results concerning almost everywhere differentiability (also in metric and w∗-senses) of these mappings. 相似文献
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Let R(G) be the graph obtained from G by adding a new vertex corresponding to each edge of G and by joining each new vertex to the end vertices of the corresponding edge, and Q(G) be the graph obtained from G by inserting a new vertex into every edge of G and by joining by edges those pairs of these new vertices which lie on adjacent edges of G. In this paper, we determine the Laplacian polynomials of R(G) and Q(G) of a regular graph G; on the other hand, we derive formulae and lower bounds of the Kirchhoff index of these graphs. 相似文献
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Let ηt be a Poisson point process of intensity t≥1 on some state space Y and let f be a non-negative symmetric function on Yk for some k≥1. Applying f to all k-tuples of distinct points of ηt generates a point process ξt on the positive real half-axis. The scaling limit of ξt as t tends to infinity is shown to be a Poisson point process with explicitly known intensity measure. From this, a limit theorem for the m-th smallest point of ξt is concluded. This is strengthened by providing a rate of convergence. The technical background includes Wiener–Itô chaos decompositions and the Malliavin calculus of variations on the Poisson space as well as the Chen–Stein method for Poisson approximation. The general result is accompanied by a number of examples from geometric probability and stochastic geometry, such as k-flats, random polytopes, random geometric graphs and random simplices. They are obtained by combining the general limit theorem with tools from convex and integral geometry. 相似文献
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In many applications it has been observed that hybrid-Monte Carlo sequences perform better than Monte Carlo and quasi-Monte Carlo sequences, especially in difficult problems. For a mixed s-dimensional sequence m, whose elements are vectors obtained by concatenating d-dimensional vectors from a low-discrepancy sequence q with (s−d)-dimensional random vectors, probabilistic upper bounds for its star discrepancy have been provided. In a paper of G. Ökten, B. Tuffin and V. Burago [G. Ökten, B. Tuffin, V. Burago, J. Complexity 22 (2006), 435–458] it was shown that for arbitrary ε>0 the difference of the star discrepancies of the first N points of m and q is bounded by ε with probability at least 1−2exp(−ε2N/2) for N sufficiently large. The authors did not study how large N actually has to be and if and how this actually depends on the parameters s and ε. In this note we derive a lower bound for N, which significantly depends on s and ε. Furthermore, we provide a probabilistic bound for the difference of the star discrepancies of the first N points of m and q, which holds without any restrictions on N. In this sense it improves on the bound of Ökten, Tuffin and Burago and is more helpful in practice, especially for small sample sizes N. We compare this bound to other known bounds. 相似文献