U INTERVALS FOR DENUMERABLE MARKOV PROCESSES

In this paper we have introdnoed the concept of U interyals for denumerable Mar- kov processes, then analysed the flying-points and U intervals for a process. We have found relations between U intervals and Kolmogoroff's backward and forward equati- ons. Using the concept of U intervals for ： a process, we can investigate the exit and entrance problems for a process more clearly and effectively.     

ON THE DISCRETE-ORDINATES METHOD FOR THE MONOENERGETIC NEUTRON TRANSPORT EQUATION IN A SLAB WITH GENERALIZED BOUNDARY CONDITIONS

This paper is devoted to discussing the discrete-ordinates method for the monoenergetic neutron transport equation in a slab with generalized boundary conditions. For homogeneous medium with isotropic scattering and fission, the convergence theorems for discrete-ordinates approximations are given respectively for critical eigenvalue problem and dominant eigenvalue problems: for inhomogeneous medium with anisotropic scattering and fission, a similar discussion and an estimation for the convergence rate are given for critical eigenvalue problems. Finally, some numerical results are given by use of this method.     

Sharp bounds for fractional one-sided operators

In this paper,we characterize the sharp boundedness of the one-sided fractional maximal function for one-weight and two-weight inequalities.Also a new two-weight testing condition for the one-sided fractional maximal function is introduced extending the work of Martín-Reyes and de la Torre.Improving some extrapolation result for the one-sided case,we get weak sharp bounded estimates for one-sided fractional maximal function and weak and strong sharp bounded estimates for one-sided fractional integral.     

AN EMBEDDED BOUNDARY METHOD FOR ELLIPTIC AND PARABOLIC PROBLEMS WITH INTERFACES AND APPLICATION TO MULTI-MATERIAL SYSTEMS WITH PHASE TRANSITIONS

The embedded boundary method for solving elliptic and parabolic problems in geometrically complex domains using Cartesian meshes by Johansen and Colella （1998, J. Comput. Phys. 147, 60） has been extended for elliptic and parabolic problems with interior boundaries or interfaces of discontinuities of material properties or solutions. Second order accuracy is achieved in space and time for both stationary and moving interface problems. The method is conservative for elliptic and parabolic problems with fixed interfaces. Based on this method, a front tracking algorithm for the Stefan problem has been developed. The accuracy of the method is measured through comparison with exact solution to a two-dimensional Stefan problem. The algorithm has been used for the study of melting and solidification problems.     

Chebfun and numerical quadrature

Chebfun is a Matlab-based software system that overloads Matlab's discrete operations for vectors and matrices to analogous continuous operations for functions and operators.We begin by describing Chebfun's fast capabilities for Clenshaw-Curtis and also Gauss-Legendre,-Jacobi,-Hermite,and-Laguerre quadrature,based on algorithms of Waldvogel and Glaser,Liu and Rokhlin.Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles,fractional derivatives and integrals,functions defined on unbounded intervals,and the fast computation of weights for barycentric interpolation.     

非线性泛函差分方程解的性质

In this paper, some sufficient and necessary conditions are established for the oscillatory of solutions for nonlinear functional difference equations, which extend and improve some corresponding results obtained and are discrete analogues of the corresponding results for the continuous version.     

SOME RECURRENCE FORMULAS FOR BOX SPLINES AND CONE SPLINES

A degree elevation formula for multivariate simplex splines was given by Micchellis[6] and extended to hold for multivariate Dirichlet splines in [8].We report similar formulae for multivariate cone splines and box splines.To this and ,we utilize a relation due to Dahmen and Micchelli[4] that connects box splines and cone splines and a degree reduction formula given by Cohen,Lyche,and Riesenfeld in [2].     

本刊英文版2012年55卷第9期摘要

Chebfun and numerical quadrature HALE Nicholas ＆ TREFETHEN Lloyd N Abstract Chebfun is a Matlab-based software system that overloads Matlab＇s discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun＇s fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation.     

RESEARCH ANNOUNCEMENTS The New Necessary and Sufficient Conditions for the Uniformly Continuous and Continuous of Duality Mappings

In[1],Ma shaoqin gave the necessary and sufficient condition for the uniformlycontinuous and continuous of duality mappings.In the note,We give very simplecriteria for the uniformly continuous and continuous of duality mappings.And by[1],the necessary and sufficient conditions for the norm of a real Banach Space to beuniformly Frechet differentiable and Frechet differentiable are described.     

Parity-factor and its Covering

Amahashi gives a necessary and sufficient condition for a graph to have a {1,3, … , 2n-1} -factor. Here we give some necessary and sufficient conditions for a graph to contain a parity-factor,and also we obtain a necessary and sufficient condition for a graph to have parity-factor covering.     

Determinants of matrices over semirings

In this paper, the concept of determinants for the matrices over a commutative semiring is introduced, and a development of determinantal identities is presented. This includes a generalization of the Laplace and Binet–Cauchy Theorems, as well as on adjoint matrices. Also, the determinants and the adjoint matrices over a commutative difference-ordered semiring are discussed and some inequalities for the determinants and for the adjoint matrices are obtained. The main results in this paper generalize the corresponding results for matrices over commutative rings, for fuzzy matrices, for lattice matrices and for incline matrices.     

Stokes方程的压力梯度局部投影间断有限元法

本文对定常的Stokes方程提出了一种新的间断有限元法,通过将通常的间断Galerkin有限元法与压力梯度局部投影相结合,建立了一个稳定的间断有限元格式,对速度和压力的任意分片多项式空间P_l(K),P_m(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L~2范数的最优误差估计.     

微分、差分方程的机械化方法

介绍了微分与差分方程机械化方法研究若干最新进展.主要结果包括: 微分、差分方程的特征列理论与算法,微分、差分方程系统的分解算法以及微分、差分方程解析解求解算法.     

Superconvergence of mixed finite element semi-discretizations of two time-dependent problems

We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation for the error in the space discretization can be performed in the same way as for the underlying elliptic problem.     

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

‘Strong’-‘weak’ precedence in scheduling: Extensions to series-parallel orders

We examine computational complexity implications for scheduling problems with job precedence relations with respect to strong precedence versus weak precedence. We propose a consistent definition of strong precedence for chains, trees, and series-parallel orders. Using modular decomposition for partially ordered sets (posets), we restate and extend past complexity results for chains and trees as summarized in Dror (1997) [5]. Moreover, for series-parallel posets we establish new computational complexity results for strong precedence constraints for single- and multi-machine problems.     

Pricing strategies for perishable products: the case of Vienna and the hotel reservation system hrs.com

Consider a retailer who sells perishable products for which there is uncertain demand. Yield management with dynamic pricing is a standard practice that firms use for revenue management. For perishable products, recent analysis has focused on the distribution of flight capacity, referred to as ticket sales. Other non- storable, non-transportable, immaterial hospitality products include hotel capacity. The article discusses the extent to which hotel pricing strategies vary within the internet distribution system hrs.com. This study focuses on the distribution of hotel rooms available for booking on the internet for Vienna and gives an outlook to Euroland capitals. The main research interests are the underlying pricing models and the setting of the end price. Data was taken from hrs.com, which is the most important specialist for hotel room internet distribution in Germany according to recent studies by KMPG and others. The results include the identification of different pricing strategy clusters with regard to hotel category and hotel availability over a 22-day period for Vienna and one city from all Euroland countries (the capitals were studied for all cases except for the Netherlands, for which data was collected for Amsterdam). The study took the arrival days Mondays, Tuesdays, Wednesdays and Thursdays into account, and used data for all these days from the 11th of July, 2005, to the 10th of October, 2005, for Vienna, and the first and the last of these dates as a comparison base for the other Euroland cities.     

SOR-like Methods for Augmented Systems

Several SOR-like methods are proposed for solving augmented systems. These have many different applications in scientific computing, for example, constrained optimization and the finite element method for solving the Stokes equation. The convergence and the choice of optimal parameter for these algorithms are studied. The convergence and divergence regions for some algorithms are given, and the new algorithms are applied to solve the Stokes equations as well.