Adaptive-Additive Multilevel Methods for Hypersingular Integral Equation

In this article we present the combined adaptive-additive multilevel methods for the Galerkin approximation of hypersingular integral equation on the interval o = ( m 1,1). We also derive an efficient and reliable a posteriori error estimate for the error between the exact solution u and the approximated multilevel solution $ \tilde u_ {\cal M} $ , measuring locally the quality of $ \tilde u_ {\cal M} $ . The algorithm is carefully designed to obtain minimal complexity. A limitation of our analysis approach is that the meshes must be assumed to be quasi-uniform.     

Quantitative approximation of certain stochastic integrals

We approximate certain stochastic integrals, typically appearing in Stochastic Finance, by stochastic integrals over integrands, which are path-wise constant within deterministic, but not necessarily equidistant, time intervals. We ask for rates of convergence if the approximation error is considered in L 2 . In particular, we show that by using non-equidistant time nets, in contrast to equidistant time nets, approximation rates can be improved considerably.     

Spectral Integral Variations of Degree Maximal Graphs

The concept of the spectral integral variation was introduced by Fan [Fan Yizheng (2002). On spectral integral variations of graphs. Linear and Multilinear Algebra , 50 , 133-142] to study the general graphs with all changed eigenvalues moving up by integers when an edge is added. Here we consider the spectral integral variations of maximal graphs G , and successfully give an equivalent condition for the spectral integral variation of G occurring in two places by adding an edge e . We also characterize whether the graph G + e is maximal so that an explicit interpretation of the above condition is obtained, where G + e denotes the graph obtained from G by adding an edge e .     

Spectral Integral Variations of Degree Maximal Graphs

The concept of the spectral integral variation was introduced by Fan [Fan Yizheng (2002). On spectral integral variations of graphs. Linear and Multilinear Algebra , 50 , 133-142] to study the general graphs with all changed eigenvalues moving up by integers when an edge is added. Here we consider the spectral integral variations of maximal graphs G , and successfully give an equivalent condition for the spectral integral variation of G occurring in two places by adding an edge e . We also characterize whether the graph G + e is maximal so that an explicit interpretation of the above condition is obtained, where G + e denotes the graph obtained from G by adding an edge e .     

一类Lupas-Baskakov积分算子的点态逼近阶

引入一类Ｌｕｐａｓ－Ｂａｓｋａｋｏｖ积分算子，给出它对有界变差函数的点态逼近度，并指出精确的逼近阶．     

On a Conjecture on a Laplacian Matrix with Distinct Integral Spectrum

In a paper Fallat et al. (J Graph Theory 50 (2005), 162–174) consider the question of the existence of simple graphs on n vertices whose Laplacian matrix has an integral spectrum consisting of simple eigenvalues only in the range , 0 always being, automatically, one of the eigenvalues. They completely characterize the case when n is one of the eigenvalues, but for the case when n is not, they conjecture that there are no such graphs. In that paper it is shown that, indeed, there are no such graphs for . In this paper we show that the conjecture is true for We actually consider the nonexistence of graphs whose Laplacians are realized by more general spectra , with , , , , and , subject to certain trace conditions. We show that, indeed, for sufficiently large n such graphs do not exist. Our methods are both graph theoretical and algebraic. In certain cases we refine the Cauchy interlacing theorem. Finally, rather than work with Laplacians which have nonpositive off‐Diagonal entries, we transform the problems to the realizability of spectra of nonnegative matrices which we term anti‐Laplacians.     

Lebesgue-Stieltjes形式的Choquet积分Ⅱ

研究了Lebesgue-Stieltjes形式的Choquet积分的收敛性定理,如单调收敛定理、法都引理、控制收敛定理等.     

Finite dimensional approximation to solutions of minimization problems in functional spaces

In this paper we consider minimization problems whose objectives are defined on functional spaces. The integral global optimization technique is applied to characterize a global minimum as the limit of a sequence of approximating solutions on finite dimensional subspaces. Necessary and sufficient optimality conditions are presented. A variable measure algorithm is proposed to find such approximating solutions. Examples are presented to illustrate the variable measure method     

积分凸性及其应用

该文在Banach空间中通过向量值函数的Bochner积分引进集合与泛函的积分凸性以及集合的积分端点等概念. 文章主要证明有限维凸集、开凸集和闭凸集均是积分凸集，下半连续凸泛函与开凸集上的上半连续凸泛函均是积分凸的, 非空紧集具有积分端点, 对紧凸集来说其积分端点集与端点集一致, 最后给出积分凸性在最优化理论方面的两个应用.     

q-Hermite Polynomials and a q-Beta Integral

The main object of the present paper is to derive a formula for the q-Hahn.polynomials by using the q-Mehler formula about the q-Hermite polynomials.This result, together with other properties of the q-Hermite polynomials, provides an evalution of a q-beta integral.Both the celebrated Askey-Wilson integral and the Ismail-Stanton-Viennot integral are special cases of this integral.     

Integral representation with weights II, division and interpolation

Let f be a r×m-matrix of holomorphic functions that is generically surjective. We provide explicit integral representation of holomorphic ψ such that ϕ=f ψ, provided that ϕ is holomorphic and annihilates a certain residue current with support on the set where f is not surjective. We also consider formulas for interpolation. As applications we obtain generalizations of various results previously known for the case r=1. The author was partially supported by the Swedish Research Council     

Star-shaped approximation approach for stochastic programming problems with probability function

Star-shaped probability function approximation is suggested. Conditions of log-concavity and differentiability of approximation function are obtained. The method for constructing stochastic estimates of approximation function gradient and stochastic quasi-gradient algorithm for probability function maximization are described in the paper     

Diffusion approximation of controlled branching processes with random environments

Conditions are established under which a sequence of density dependent branching processes with random environments converges weakly to a diffusion process. The limiting diffusion process can be obtained as a solution of a stochastic differential equation     

Pointwise analog of the jackson approximation theorem

The pointwise version of the Jackson theorem on the best approximation by trigonometric polynomials is proved. Some application of the result is also presented.     

Integral circulant graphs

In this note we characterize integral graphs among circulant graphs. It is conjectured that there are exactly 2^τ(n)-1 non-isomorphic integral circulant graphs on n vertices, where τ(n) is the number of divisors of n.     

On Spectral Integral Variations of Graphs

Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge.     

Choquet积分的收敛定理

Murofushi、Sugeno等学者已对关于模糊测度的Choquet积分进行了详细的研究,但关于积分的收敛理论是不够的。本文讨论这一问题,给出Choquet积分的一些收敛定理,包括广义单调收敛定理、Fatou引理等。从中可以看出,Choquet积分与Sugeno模糊积分具有相同的收敛定理。     

On Spectral Integral Variations of Graphs

Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge.     

Noor积分算子的一些应用

引入用Hadamard卷积定义的算子In p-1并给出了它的某些具体应用．     

An improved approximation algorithm for requirement cut

This note presents improved approximation guarantees for the requirement cut problem: given an n-vertex edge-weighted graph G=(V,E), and g groups of vertices X₁,…,X_g⊆V with each group X_i having a requirement r_i between 0 and |X_i|, the goal is to find a minimum cost set of edges whose removal separates each group X_i into at least r_i disconnected components. We give a tight Θ(logg) approximation ratio for this problem when the underlying graph is a tree, and show how this implies an O(logk⋅logg) approximation ratio for general graphs, where .