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We consider renewal shot noise processes with response functions which are eventually nondecreasing and regularly varying at infinity. We prove weak convergence of renewal shot noise processes, properly normalized and centered, in the space D[0,∞) under the J1 or M1 topology. The limiting processes are either spectrally nonpositive stable Lévy processes, including the Brownian motion, or inverse stable subordinators (when the response function is slowly varying), or fractionally integrated stable processes or fractionally integrated inverse stable subordinators (when the index of regular variation is positive). The proof exploits fine properties of renewal processes, distributional properties of stable Lévy processes and the continuous mapping theorem. 相似文献
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In this paper, the wrap-around L2-discrepancy (WD) of asymmetrical design is represented as a quadratic form, thus the problem of constructing a uniform design becomes a quadratic integer programming problem. By the theory of optimization, some theoretic properties are obtained. Algorithms for constructing uniform designs are then studied. When the number of runs n is smaller than the number of all level-combinations m, the construction problem can be transferred to a zero–one quadratic integer programming problem, and an efficient algorithm based on the simulated annealing is proposed. When n≥m, another algorithm is proposed. Empirical study shows that when n is large, the proposed algorithms can generate designs with lower WD compared to many existing methods. Moreover, these algorithms are suitable for constructing both symmetrical and asymmetrical designs. 相似文献
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For a Tychonoff space X , we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelöf Σ-property of X in terms of Cp(X), we extend Okunev?s results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then υY is a Lindelöf Σ-space (respectively K-analytic) if υX has this property. In the second part, applying Christensen?s theorem, we extend Pelant?s result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space. We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by ?p-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and ?p-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented. 相似文献
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This paper studies the coincidence of the τω and τδ topologies on the space of holomorphic functions defined on an open subset U of a Banach space. Dineen and Mujica proved that τω=τδ when U is a balanced open subset of a separable Banach space with the bounded approximation property. Here, we study the τω=τδ problem for several types of non-balanced domains U. 相似文献
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We conjecture that the balanced complete bipartite graph K⌊n/2⌋,⌈n/2⌉ contains more cycles than any other n-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k. For k=1, we show that any such counterexamples have n≤91 and are not homomorphic to C5; and for any fixed k there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P-complete problem in general) in a special case used by our bounds. 相似文献
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We introduce (n+1)-preprojective algebras of algebras of global dimension n. We show that if an algebra is n-representation-finite then its (n+1)-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)-preprojective algebra is (n+1)-Calabi–Yau, and, more precisely, it is the (n+1)-Amiot cluster category of the stable n-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)-cluster tilting object. We show that even if the (n+1)-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}) the results above still hold for the stable category of Cohen–Macaulay modules. 相似文献
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Let T:D⊂X→X be an iteration function in a complete metric space X. In this paper we present some new general complete convergence theorems for the Picard iteration xn+1=Txn with order of convergence at least r≥1. Each of these theorems contains a priori and a posteriori error estimates as well as some other estimates. A central role in the new theory is played by the notions of a function of initial conditions of T and a convergence function of T. We study the convergence of the Picard iteration associated to T with respect to a function of initial conditions E:D→X. The initial conditions in our convergence results utilize only information at the starting point x0. More precisely, the initial conditions are given in the form E(x0)∈J, where J is an interval on R+ containing 0. The new convergence theory is applied to the Newton iteration in Banach spaces. We establish three complete ω-versions of the famous semilocal Newton–Kantorovich theorem as well as a complete version of the famous semilocal α-theorem of Smale for analytic functions. 相似文献
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Let G be a countable discrete group with an orthogonal representation α on a real Hilbert space H . We prove Lp Poincaré inequalities for the group measure space L∞(ΩH,γ)?G, where both the group action and the Gaussian measure space (ΩH,γ) are associated with the representation α . The idea of proof comes from Pisier?s method on the boundedness of Riesz transform and Lust-Piquard?s work on spin systems. Then we deduce a transportation type inequality from the Lp Poincaré inequalities in the general noncommutative setting. This inequality is sharp up to a constant (in the Gaussian setting). Several applications are given, including Wiener/Rademacher chaos estimation and new examples of Rieffel?s compact quantum metric spaces. 相似文献
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We utilize the classical hypercircle method and the lowest-order Raviart–Thomas H(div) element to obtain a posteriori error estimates of the P1 finite element solutions for 2D Poisson's equation. A few other estimation methods are also discussed for comparison. We give some theoretical and numerical results to see the effectiveness of the methods. 相似文献