On Impulsive Hyperbolic Differential Inclusions with?Nonlocal Initial Conditions

This paper is focused mainly upon existence of solutions for a second-order impulsive hyperbolic differential inclusions with nonlocal initial conditions. By using some well-known fixed-point theorems, existence theorems are established when the multivalued map has convex or nonconvex values. As applications of these main theorems, some consequences are given for the sublinear growth cases. Y.-K. Chang was supported by “Qing Lan” Talent Engineering Funds (QL-05-16A), by Lanzhou Jiaotong University, the Scientific Research Fund of Gansu Provincial Education Department (0704-14). J.J. Nieto was supported by Ministerio de Educacion y Ciencia and FEDER, Project MTM2007-61724, and by Xunta de Galicia and FEDER, Project PGIDIT05PXIC20702PN.     

The Schur Transformation for Generalized Nevanlinna Functions: Interpolation and Self-Adjoint Operator Realizations

The Schur transformation for generalized Nevanlinna functions has been defined and applied in [2]. In this paper we discuss its relation to a basic interpolation problem and study its effect on the minimal self-adjoint operator (or relation) realization of a generalized Nevanlinna function. D. Alpay acknowledges with thanks the Earl Katz family for endowing the chair which supported this research and the Netherlands Organization for Scientific Research, NWO (grant B 61-524). The research of A. Dijksma and H. Langer was partly supported by the Center for Advanced Studies in Mathematics, CASM, of the Department of Mathematics of Ben-Gurion University, that of H. Langer also by the Austrian Science Fund, Project P15540-N05. Received: September 25, 2006. Accepted: October 11, 2006.     

Classical orthogonal polynomials in two variables: a matrix approach

Classical orthogonal polynomials in two variables are defined as the orthogonal polynomials associated to a two-variable moment functional satisfying a matrix analogue of the Pearson differential equation. Furthermore, we characterize classical orthogonal polynomials in two variables as the polynomial solutions of a matrix second order partial differential equation. AMS subject classification 42C05, 33C50Partially supported by Ministerio de Ciencia y Tecnología (MCYT) of Spain and by the European Regional Development Fund (ERDF) through the grant BFM2001-3878-C02-02, Junta de Andalucía, G.I. FQM 0229 and INTAS Project 2000-272.     

Hile-yeh estimates of eigenvalues of polyharmonic operators

The new bounds of eigenvalues of polyharmonic operators are deduced. This work is a generalization of some kind of estimates of the biharmonic operator. Project supported by the Fund of NNSC.     

A new proof of <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates for the parabolic polyharmonic equations

In this paper we obtain local L ^p estimates for the parabolic polyharmonic equations by a straightforward approach. Yao was supported by the Innovation Foundation of Shanghai University (Grant No. A10-0101-08-905), Shanghai Leading Academic Discipline Project (Grant No. J50101) and Key Disciplines of Shanghai Municipality (Grant No. S30104). Zhou was supported by the National Basic Research Program of China (Grant No. 2006CB705700), National Natural Science Foundation of China (Grant No. 60532080), and the Key Project of Chinese Ministry of Education (Grant No. 306017)     

Hybrid Proximal-Point Methods for Common Solutions of Equilibrium Problems and Zeros of Maximal Monotone Operators

The purpose of this paper is to introduce and study two hybrid proximal-point algorithms for finding a common element of the set of solutions of an equilibrium problem and the set of solutions to the equation 0∈Tx for a maximal monotone operator T in a uniformly smooth and uniformly convex Banach space X. Strong and weak convergence results of these two hybrid proximal-point algorithms are established, respectively. The research of L.C. Ceng was partially supported by the National Science Foundation of China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), Science and Technology Commission of Shanghai Municipality Grant (075105118), Innovation Program of Shanghai Municipal Education Commission (09ZZ133), and Shanghai Leading Academic Discipline Project (S30405). The research of J.C. Yao was partially supported by Grant NSC 97-2115-M-110-001. Research was carried on within the agreement between National Sun Yat-Sen University of Kaohsiung, Taiwan and Pisa University, Pisa, Italy, 2008.     

Systems of proportionally modular Diophantine inequalities

The set of integer solutions to the inequality ax mod b≤c x is a numerical semigroup. We study numerical semigroups that are intersections of these numerical semigroups. Recently it has been shown that this class of numerical semigroups coincides with the class of numerical semigroups having a Toms decomposition. The first author was (partially) supported by the Centro de Matemática da Universidade do Porto (CMUP), financed by FCT (Portugal) through the programmes POCTI and POSI, with national and European Community structural funds. The last three authors are supported by the project MTM2004-01446 and FEDER funds. The authors would like to thank the referee for her/his comments and suggestions.     

The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets

In this paper we investigate multivariate integration in reproducing kernel Sobolev spaces for which the second partial derivatives are square integrable. As quadrature points for our quasi-Monte Carlo algorithm we use digital (t,m,s)-nets over which are randomly digitally shifted and then folded using the tent transformation. For this QMC algorithm we show that the root mean square worst-case error converges with order for any ɛ > 0, where 2 ^m is the number of points. A similar result for lattice rules has previously been shown by Hickernell. Ligia L. Cristea is supported by the Austrian Research Fund (FWF), Project P 17022-N 12 and Project S 9609. Josef Dick is supported by the Australian Research Council under its Center of Excellence Program. Gunther Leobacher is supported by the Austrian Research Fund (FWF), Project S 8305. Friedrich Pillichshammer is supported by the Austrian Research Fund (FWF), Project P 17022-N 12, Project S 8305 and Project S 9609.     

Reproducing Kernel Hilbert Spaces Associated with Analytic Translation-Invariant Mercer Kernels

In this article we study reproducing kernel Hilbert spaces (RKHS) associated with translation-invariant Mercer kernels. Applying a special derivative reproducing property, we show that when the kernel is real analytic, every function from the RKHS is real analytic. This is used to investigate subspaces of the RKHS generated by a set of fundamental functions. The analyticity of functions from the RKHS enables us to derive some estimates for the covering numbers which form an essential part for the analysis of some algorithms in learning theory. The work is supported by City University of Hong Kong (Project No. 7001816), and National Science Fund for Distinguished Young Scholars of China (Project No. 10529101).     

On Pairs of Linear Equations in Three Prime Variables

In this paper, we consider the simultaneous representation of pairs of integers as linear combinations in three prime variables and obtain a related numerical bound.