一些特殊三角剖分上分片线性样条的最佳逼近问题

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

Tchebyshev Approximation by S~0_1(△) over Some Special Triangulations

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

Tchebyshev Approximation by S01（△） over Some Special Triangulations

The critical point set plays a central role in the theory of Tchebyshev approximation.Generally,in multivariate Tchebyshev approximation,it is not a trivial task to determine whether a set is critical or not.In this paper,we study the characterization of the critical point set of S 0 1(△) in geometry,where is restricted to some special triangulations(bitriangular,single road and star triangulations).Such geometrical characterization is convenient to use in the determination of a critical point set.     

APPROXIMATION OF BOCHNER-RIESZ MEANS 0F CONJUGATE FOURIER INTEGRALS BEL0W THE CRITICAL INDEX

In this paper we study the approximation on set of full measure for functions in Sobolev spacesL_m~1 (R~n) (m∈N) by Bochner-Riesz means of conjugale Fourier integrals below the critical index. Atheorem concerning the precise approximation orders with relation to the number m of space L_m~1 (R~n) andthe index of Bochner-Riesz means is obtained.     

3阶不可约符号模式的精细惯量极小临界集

Let S be a nonempty, proper subset of all possible refined inertias of real matrices of order n. The set S is a critical set of refined inertias for irreducible sign patterns of order n,if for each n × n irreducible sign pattern A, the condition S ? ri(A) is sufficient for A to be refined inertially arbitrary. If no proper subset of S is a critical set of refined inertias, then S is a minimal critical set of refined inertias for irreducible sign patterns of order n.All minimal critical sets of refined inertias for full sign patterns of order 3 have been identified in [Wei GAO, Zhongshan LI, Lihua ZHANG, The minimal critical sets of refined inertias for 3×3 full sign patterns, Linear Algebra Appl. 458(2014), 183–196]. In this paper, the minimal critical sets of refined inertias for irreducible sign patterns of order 3 are identified.     

A conjecture on k-factor-critical and 3-γ-critical graphs

For a graph G =(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination number γ(G) of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,if γ(G-v) γ(G) for any vertex v in G.A graph G is domination edge critical,if γ(G ∪ e) γ(G) for any edge e ∈/E(G).We call a graph G k-γ-vertex-critical(resp.k-γ-edge-critical) if it is domination vertex critical(resp.domination edge critical) and γ(G) = k.Ananchuen and Plummer posed the conjecture:Let G be a k-connected graph with the minimum degree at least k+1,where k 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is k-factor-critical.In this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph.     

AN EFFICIENT SEQUENTIAL DESIGN FOR SENSITIVITY EXPERIMENTS

In sensitivity experiments, the response is binary and each experimental unit has a critical stimulus level that cannot be observed directly. It is often of interest to estimate extreme quantiles of the distribution of these critical stimulus levels over the tested products. For this purpose a new sequential scheme is proposed with some commonly used models. By using the bootstrap repeated-sampling principle, reasonable prior distributions based on a historic data set are specified. Then, a Bayesian strategy for the sequential procedure is provided and the estimator is given. Further, a high order approximation for such an estimator is explored and its consistency is proven. A simulation study shows that the proposed method gives superior performances over the existing methods.     

The Approximation Theorem of Convolution Operator in △~p Set-valued Function Space

The paper is a contribution to the problem of approximating random set with values in a separable Banach space. This class of set-valued function is widely used in many areas.We investigate the properties of p-bounded integrable random set. Based on this we endow it with △p metric which can be viewed as a integral type hausdorff metric and present some approximation theorem of a class of convolution operators with respect to △p metric. Moreover we also can establish analogous theorem for other integral type operator in △p space.     

THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET

The structure of any a.s. self-similar set K(w) generated by a class of random elements {gn,wσ} taking values in the space of contractive operators is given and the approximation of K(w) by the fixed points {Pn,wσ} of {gn,ow} is obtained. It is useful to generate the fractal in computer.     

APPROXIMATE COMMON DIVISORS OF POLYNOMIALS AND DEGREE REDUCTION FOR RATIONAL CURVES

This paper deals with how to perturb a given set of polynomials so as to include a common linear factor. An algorithm is derived for determining such a set of perturbation polyrlomials which are subject to certain constrains at the endpoints of a prescribed parametric interval and minimized in a certain sense. This result can be combined with subdivision technique to obtain a continuous piecewise approximation to a rational curve.     

Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

正August 10-14,2015Beijin,China The International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

FRACTIONAL INTEGRALS OF THE WEIERSTRASS FUNCTIONS： THE EXACT BOX DIMENSION

The present paper investigates the fractal structure of fractional integrals of Weierstrass functions. The ezact box dimension for such functions many important cases is established. We need to point out that, although the result itself achieved in the present paper is interesting, the new technique and method should be emphasized. These novel ideas might be useful to establish the box dimension or Hausdorff dimension (especially for the lower bounds) for more general groups of functions.     

English Series

正1 Aims and Scope Acta Mathematicae Applicatae Sinica(English Series)is a quarterly journal established by the Chinese Mathematical Society.The journal publishes high quality research papers from all branches of applied mathematics,particularly welcomes those from partial differential equations,computational mathematics,applied probability,mathematical finance,statistics,dynamical systems,optimization and management science.     

CHINESE ANNALS OF MATHEMATICS SERIES B Volume 35 · 2014 TOTAL CONTENTS

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Congruences,ideals and annihilators in standard QBCC-algebras

We characterize congruence lattices of standard QBCC-algebras and their connection with the congruence lattices of congruence kernels. Work on the paper was supported by Council of Czech Government No J14/98:153100011.     

A decomposition of continuity via ideals

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.      

When a compact (countably compact) set is closed. II

We obtain (a) necessary and sufficient conditions and (b) sufficient conditions for a compact (countably compact) set to be closed in products (sequential products) and subspaces (sequential subspaces) of normal spaces. As a consequence of these, sufficient conditions are obtained for (i) the closedness of arbitrary (countable) union of closed sets and (ii) the equality of the union of the closures and the closure of the union of arbitrary (countable) families of sets in these spaces. It is also shown that these results do not hold for quotients of even T ₄,-spaces.     

ASYMPTOTIC BEHAVIOR OF ECKHOFF＇S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION

The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called ＂jumps＂ is studied and asymptotic L2 constants of the rate of convergence of the method are computed.