A method of numerical solution of functional equations

Approximate solutions of some functional equations as the best approximation of the exact solutions in some suitable spaces have been obtained and some applications given.     

关于局部随机吸引子若干性质的注记(英文)

In this note, we study some properties of local random pull-back attractors on compact metric spaces. We obtain some relations between attractors and their fundamental neighborhoods and basins of attraction. We also obtain some properties of omega-limit sets, as well as connectedness of random attractors. A simple deterministic example is given to illustrate some confusing problems.     

高阶非线性常微分方程的可积类型

本文借助于Leibniz公式、复合函数的高阶导数公式以及变量替换的方法,给出了较为广泛的高阶非线性常微分方程的可积类型,有的还提供了通积分的表达式.所得结论推广了文献中的结果.最后列举了实例.     

Continuity of sublinear operators on F-spaces

In this note, some of the fundamental theorems concerning the automatic continuity of positive linear functionals and positive linear operators (see [9,14,21]) as well as certain uniform boundedness type theorems (see [5,13,15,19]) will be extended to derive various continuity properties of (even discontinuous) sublinear operators from some metrizable topological vector space to some ordered topological vector space.     

课堂教学评估中权重的制定方法探讨

本文介绍了多元统计分析在教学评估体系指标权重制定中的应用。结合具体例子用wilcox onsigned rank检验法和spearman相关系数对各种结果作了比较,并根据实际意义选出其中较好的结果作为评估函数。     

Generalization of some results concerning eigenvalues of a certain class of matrices and some applications

In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices and doubly stochastic matrices as well as on graph spectra and graph energy.     

Heavy-traffic approximations for fractionally integrated random walks in the domain of attraction of a non-Gaussian stable distribution

We prove some heavy-traffic limit theorems for processes which encompass the fractionally integrated random walk as well as some FARIMA processes, when the innovations are in the domain of attraction of a non-Gaussian stable distribution.     

关于r-平均凸函数的一些性质

继续研究r-平均凸函数,得到了r-平均凸函数的几个等价条件及若干个性质,并改进了相关文献的结果,同时对基本不等式进行了加细.     

SF-环的内射性

研究了SF-环与P-内射环的关系,构造了SF-环成为P-内射环的一系列条件.证明了SF-环R只要满足其中之一:R的每个极大左理想是有限生成的;特殊右零化子的降链条件;对R的每个极大左理想M,l(M)在R中是本质的,那么R就是P-内射环.在此基础上,利用一定条件下SF-环的P-内射性,发展了SF-环的若干新结果,这些结果部分地拓展了有关文献中的结果.     

Online mathematics teacher education: overview of an emergent field of research

Online mathematics teacher education is characterized as an emergent area of research in mathematics education. We identify some key topics that require further research: communities and networks of teachers in online environments; sustainability of these communities and kinds of organizational structures; knowledge-building practices in technology-mediated work group interactions; and online interactions among teachers. The emergence of new research issues also gives rise to new theoretical approaches or the adaptation of existing theoretical perspectives that are presented in this special issue. We summarize some of these theoretical perspectives and attempt to show how online environments have changed them, as well as some theoretical problems that remain to be solved.     

On the energy and Estrada index of strongly quotient graphs

In this paper, we consider the strongly quotient graphs and obtain some better results for the energy and Estrada index of these graphs, as well as some relations between Estrada index and the graph energy.     

On the use of alternating chains and hypergraphs in edge coloring

Existence of some generalized edge colorings is proved by using the properties of hypergraphs as well as alternating chain methods. A general framework is given for edge colorings and some general properties of balancing are derived.     

Generalizations of Hardy's integral inequality

The purpose of this paper is to obtain some general inequalities which contain as special cases some recently established extensions of Hardy's integral inequality.     

(δ,)-等距的稳定性

本文讨论了Banach空间之间非满射、非线性的弱等距逼近问题.在某些条件假设下,对(δ,(?))-等距算子的稳定性给出了一些肯定的结果,从而修正并推广了文[1—4]中的一些结果.     

Some Results on the Growth of Polynomials

In this paper,we have studied the Lacunary type of polynomials and proved a result which generalizes as well as refines some well-known polynomial inequalities regarding the growth of polynomials not vanishing inside a circle.Further the paper corrects the proofs of some already known results.     

On the behaviour of the periodic Coxeter Laplacian in some representations related to the antiferromagnetic asymptotic mode and continual limits

We consider some problems related to the asymptotic behaviour of the so-called periodic Coxeter Laplacian (a distinguished operator in the group algebra of the symmetric group essentially coinciding with the Hamiltonian of the XXX Heisenberg model of spins) in some representations corresponding to the antiferromagnetic asymptotic mode, as well as in some related continual limits. Bibliography: 9 titles.     

Some properties of skew codes over finite fields

After recalling the definition of some codes as modules over skew polynomial rings, whose multiplication is defined by using an endomorphism and a derivation, and some basic facts about them, in the first part of this paper we study some of their main algebraic and geometric properties. Finally, for module skew codes constructed only with an automorphism, we give some BCH type lower bounds for their minimum distance.     

Enumeration of strings in Dyck paths: A bijective approach

The statistics concerning the number of appearances of a string τ in Dyck paths as well as its appearances in odd and even level have been studied extensively by several authors using mostly algebraic methods. In this work a different, bijective approach is followed giving some known as well as some new results.     

On the regularity of the critical point infinity of definitizable operators

In this note necessary and sufficient conditions for the regularity of the critical point infinity of a definitizable operator A are given. Using these criteria it is proved that the regularity of the critical point infinity is preserved under some additive perturbations as well as for some operators which are related to A. Applications to indefinite Sturm-Liouville problems are indicated.