一类非线性椭圆方程组很弱解的正则性

本文在可控增长条件（１．２）－（１．４）下，对一类非线性椭圆方程组（１．１）改进其很弱解偏微商的可积性，使其为经典意义下的弱解。     

具非线性耗散项P系统的Cauchy问题

讨论具有非线性耗散项P系统的Caucby问题．在一些较为合理的假设下．证明了其光滑解的整体存在性及其解的奇性形成．     

扰动系统概周期解和有界解的存在性

该文研究扰动系统．在适当条件下给出扰动系统概周期解和有界解的存在性证明．     

随机回归模型线性性的拟合优度检验方法

本文研究随机多元回归模型的线性性检验．所提出的检验统计量是由两个统计量之和形成的．第一个是由最小二乘回归拟合的残差构造的，它具有渐近ｘ２分布，但在完全对立假设检验时，它不是相容的．另一个则是基于对上述残差量的回归核估计，在零假设成立时，它趋于零，在对立假设成立时，则趋于无穷大．理论结果表明，本文的检验方法在完全对立假设下仍有相容性．模拟结果显示出，此方法在许多对立假设下，具有较好的功效．     

平稳环境中马氏链的不可约性

给出若单链X^→具π-不可约性，则环境空间中的平稳分布π-是遍历的．同时也指出在单链叉的状态空间有限的前提下，该单链是强常返的，从而推广了经典马氏链相应的结论．     

线性控制系统对小时滞的鲁棒能控性

对于在Banach空间中线性控制系统对时滞的鲁棒能控性．给出一个充分条件,在这个条件下,证明对一个能控的线性系统施加某个小的时滞扰动之后,其能控性保持不变．     

随机删失下位置-刻度模型中的强相合与渐近正态估计

在删失分布未知的情形下,证明了所定义的位置─刻度模型中参数估计的强相合性与渐近正态性．在证明估计的渐近正态性时,使用了点过程鞅方法．     

一类高阶拟线性椭圆型方程奇摄动边值问题

本文讨论了一类拟线性椭圆型方程奇摄动Dirichlet边值问题．在适当的条件下，利用不动点定理，研究了边值问题解的存在唯一性及其渐近性态．     

客户回报随机过程的Markov性和时间齐次性

在客户发展关系的Markov链模型的基础上,构建了企业的客户回报随机过程．证明了：在适当假设下,客户回报过程是Markov链。甚至是时间齐次的Markov链．本文求出了该链的转移概率．通过转移概率得到了客户给企业期望回报的一些计算公式,从而为企业选定发展客户关系策略提供了有效的量化基础．     

集值向量变分不等式的严格可行性与可解性

本文研究集值向量变分不等式的严格可行性与可解性之间的关系．证明了如下结果:在一定条件下,只要集值向量变分不等式是严格可行的,那么其一定可解．     

Short Book Reviews

Problems in Linear Algebra, by I. V. Proskuryakov. Mir Publishers, Moscow, 1978= 453 pp.

Inequalities: Theory of Majorization and its Applications. by A. W. Marshall and I. Olkin. Academic Press, 1979, 569 pp.

Problems in Linear Algebra, by I. V. Proskuryakov. Mir Publishers, Moscow, 1978. 453 pp. Inequalities: Theory of Majorization and its Applications. by A. W. Marshall and I. Olkin. Academic Press, 1979, 569 pp. Introduction to Numerical Analysis. by F. Stummel and K. Hainer. Scottish Academic Press (in United States, Columbia University Press), 1980. 282 pp., soft cover.

Introduction to Numerical Analysis. by F. Stummel and K. Hainer. Scottish Academic Press (in the United States, Columbia University Press), 1980. 282 pp., soft cover.     

Binary formally self-dual odd codes

Most of the research on formally self-dual (f.s.d.) codes has been developed for binary f.s.d. even codes, but only limited research has been done for binary f.s.d. odd codes. In this article we complete the classification of binary f.s.d. odd codes of lengths up to 14. We also classify optimal binary f.s.d. odd codes of length 18 and 24, so our result completes the classification of binary optimal f.s.d. odd codes of lengths up to 26. For this classification we first find a relation between binary f.s.d. odd codes and binary f.s.d. even codes, and then we use this relation and the known classification results on binary f.s.d. even codes. We also classify (possibly) optimal binary double circulant f.s.d. odd codes of lengths up to 40.     

Free boundary problems in the theory of fluid flow through porous media: Existence and uniqueness theorems

Summary Elliptic free boundary problems in the theory of fluid flow through porous media are studied by a new method, which reduces the problems to variational inequalities: existence and uniqueness theorems are proved. Entrata in Redazione il 3 agosto 1972. Research supported by C.N.R. in the frame of the collaboration between L.A.N. of Pavia and E.R.A. 215 of C.N.R.S. and of Paris University. ? Laboratorio di Analisi Numerica del C.N.R. di Pavia ? and ? Università di Pavia ?. ? Università di Pavia ? and ? G.N.A.F.A. del C.N.R. ?.     

Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces

By using viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for the iterative sequence to converging to a common fixed point are obtained. The results presented in the paper extend and improve some recent results in [H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl. 298 (2004) 279-291; H.K. Xu, Remark on an iterative method for nonexpansive mappings, Comm. Appl. Nonlinear Anal. 10 (2003) 67-75; H.H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; J.S. Jung, Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 302 (2005) 509-520; P.L. Lions, Approximation de points fixes de contractions', C. R. Acad. Sci. Paris Sér. A 284 (1977) 1357-1359; A. Moudafi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl. 241 (2000) 46-55; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 128-292; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491].     

The multidimensional plateau problem in Riemannian varieties

This paper is the author's abstract of his dissertation for the degree of Doctor of Physico-Mathematical Sciences. The dissertation was defended on September 29, 1972 at a session of the Council of the Mechanico-Mathematical Faculty of M. V. Lomonosov Moscow University. The official opponents were Prof. V. M. Alekseev, Doctor of Phys.-Mat. Sci.; Prof. D. V. Anosov, Doctor of Phys.-Mat. Sci.; and Prof. M. M. Postnikov, Doctor of Phys.-Mat. Sci.Translated from Matematicheskie Zametki, Vol. 13, No. 1, pp. 159–167, January, 1973.     

Sensitivity analysis for parametric generalized implicit quasi-variational-like inclusions involving P-η-accretive mappings

In this paper, using proximal-point mapping technique of P-η-accretive mapping and the property of the fixed-point set of set-valued contractive mappings, we study the behavior and sensitivity analysis of the solution set of a parametric generalized implicit quasi-variational-like inclusion involving P-η-accretive mapping in real uniformly smooth Banach space. Further, under suitable conditions, we discuss the Lipschitz continuity of the solution set with respect to the parameter. The technique and results presented in this paper can be viewed as extension of the techniques and corresponding results given in [R.P. Agarwal, Y.-J. Cho, N.-J. Huang, Sensitivity analysis for strongly nonlinear quasi-variational inclusions, Appl. Math. Lett. 13 (2002) 19-24; S. Dafermos, Sensitivity analysis in variational inequalities, Math. Oper. Res. 13 (1988) 421-434; X.-P. Ding, Sensitivity analysis for generalized nonlinear implicit quasi-variational inclusions, Appl. Math. Lett. 17 (2) (2004) 225-235; X.-P. Ding, Parametric completely generalized mixed implicit quasi-variational inclusions involving h-maximal monotone mappings, J. Comput. Appl. Math. 182 (2) (2005) 252-269; X.-P. Ding, C.L. Luo, On parametric generalized quasi-variational inequalities, J. Optim. Theory Appl. 100 (1999) 195-205; Z. Liu, L. Debnath, S.M. Kang, J.S. Ume, Sensitivity analysis for parametric completely generalized nonlinear implicit quasi-variational inclusions, J. Math. Anal. Appl. 277 (1) (2003) 142-154; R.N. Mukherjee, H.L. Verma, Sensitivity analysis of generalized variational inequalities, J. Math. Anal. Appl. 167 (1992) 299-304; M.A. Noor, Sensitivity analysis framework for general quasi-variational inclusions, Comput. Math. Appl. 44 (2002) 1175-1181; M.A. Noor, Sensitivity analysis for quasivariational inclusions, J. Math. Anal. Appl. 236 (1999) 290-299; J.Y. Park, J.U. Jeong, Parametric generalized mixed variational inequalities, Appl. Math. Lett. 17 (2004) 43-48].     

On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings

The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357-1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351-358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767-773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911-921].     

Recent advances in linear analysis of convergence for splittings for solving ODE problems

In the nineties, Van der Houwen et al. (see, e.g., [P.J. van der Houwen, B.P. Sommeijer, J.J. de Swart, Parallel predictor–corrector methods, J. Comput. Appl. Math. 66 (1996) 53–71; P.J. van der Houwen, J.J.B. de Swart, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput. 18 (1997) 41–55; P.J. van der Houwen, J.J.B. de Swart, Parallel linear system solvers for Runge–Kutta methods, Adv. Comput. Math. 7 (1–2) (1997) 157–181]) introduced a linear analysis of convergence for studying the properties of the iterative solution of the discrete problems generated by implicit methods for ODEs. This linear convergence analysis is here recalled and completed, in order to provide a useful quantitative tool for the analysis of splittings for solving such discrete problems. Indeed, this tool, in its complete form, has been actively used when developing the computational codes BiM and BiMD [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164–165 (2004) 145–158. Code available at: http://www.math.unifi.it/~brugnano/BiM/index.html; L. Brugnano, C. Magherini, F. Mugnai, Blended implicit methods for the numerical solution of DAE problems, J. Comput. Appl. Math. 189 (2006) 34–50]. Moreover, the framework is extended for the case of special second order problems. Examples of application, aimed to compare different iterative procedures, are also presented.     

IFS on a metric space with a graph structure and extensions of the Kelisky-Rivlin theorem

We develop the Hutchinson-Barnsley theory for finite families of mappings on a metric space endowed with a directed graph. In particular, our results subsume a classical theorem of J.E. Hutchinson [J.E. Hutchinson, Fractals and self-similarity, Indiana Univ. Math. J. 30 (1981) 713-747] on the existence of an invariant set for an iterated function system of Banach contractions, and a theorem of L. Máté [L. Máté, The Hutchinson-Barnsley theory for certain non-contraction mappings, Period. Math. Hungar. 27 (1993) 21-33] concerning finite families of locally uniformly contractions introduced by Edelstein. Also, they generalize recent fixed point theorems of A.C.M. Ran and M.C.B. Reurings [A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto and R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], and A. Petru?el and I.A. Rus [A. Petru?el, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] for contractive mappings on an ordered metric space. As an application, we obtain a theorem on the convergence of infinite products of linear operators on an arbitrary Banach space. This result yields new generalizations of the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space C[0,1] as well as its extensions given recently by H. Oruç and N. Tuncer [H. Oruç, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory 117 (2002) 301-313], and H. Gonska and P. Pi?ul [H. Gonska, P. Pi?ul, Remarks on an article of J.P. King, Comment. Math. Univ. Carolin. 46 (2005) 645-652].     

Stability of iterative procedures with errors for approximating common fixed points of a couple of q-contractive-like mappings in Banach spaces

Recently, Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447] introduced the new iterative procedures with errors for approximating the common fixed point of a couple of quasi-contractive mappings and showed the stability of these iterative procedures with errors in Banach spaces. In this paper, we introduce a new concept of a couple of q-contractive-like mappings (q>1) in a Banach space and apply these iterative procedures with errors for approximating the common fixed point of the couple of q-contractive-like mappings. The results established in this paper improve, extend and unify the corresponding ones of Agarwal, Cho, Li and Huang [R.P. Agarwal, Y.J. Cho, J. Li, N.J. Huang, Stability of iterative procedures with errors approximating common fixed points for a couple of quasi-contractive mappings in q-uniformly smooth Banach spaces, J. Math. Anal. Appl. 272 (2002) 435-447], Chidume [C.E. Chidume, Approximation of fixed points of quasi-contractive mappings in Lp spaces, Indian J. Pure Appl. Math. 22 (1991) 273-386], Chidume and Osilike [C.E. Chidume, M.O. Osilike, Fixed points iterations for quasi-contractive maps in uniformly smooth Banach spaces, Bull. Korean Math. Soc. 30 (1993) 201-212], Liu [Q.H. Liu, On Naimpally and Singh's open questions, J. Math. Anal. Appl. 124 (1987) 157-164; Q.H. Liu, A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings, J. Math. Anal. Appl. 146 (1990) 301-305], Osilike [M.O. Osilike, A stable iteration procedure for quasi-contractive maps, Indian J. Pure Appl. Math. 27 (1996) 25-34; M.O. Osilike, Stability of the Ishikawa iteration method for quasi-contractive maps, Indian J. Pure Appl. Math. 28 (1997) 1251-1265] and many others in the literature.