关于挠自由群分次环的注记

本文推广ＣＮａｓｔａｓｅｃｕ，Ｆ．ＶａｎＯｙｓｔａｅｙｅｎ的有关结果，并在一定条件下回答了Ｋ．Ｒ．Ｆｕｌｌｅｒ等人的公开问题．     

A note on the units of semigroup rings

In [2] Coleman and Enochs obtained results about the units of the polynomial ring R[x] for rings R satisfying a condi-tion which is, in some sense, a generalization of commutativity. In [3] some of these results were extended to group rings over an ordered group. In this note a class of rings larger than the class considered in [2] is used to extend the results in [2] and 3] to the semigroup ring RG, G an u.p, semigroup.

In the last section we give a necessary and sufficient condi-tion for an element to be a divisor of zero in RG where G is an u.p. semigroup.     

关于M—矩阵等价表征的注记

「２」指出了「１」的某些错误,并给出了修正的结果。本继续「２」的讨论,给出了Ｍ－矩阵等价表征的进一步结果。     

NOD随机变量阵列加权乘积和的强极限定理

本文研究了行为NOD随机变量阵列加权乘积和的完全收敛性和强稳定性,推广和改进了文献[1]和[2]在NA情形时的结果以及[4]在独立同分布情形时的结果.     

B值随机元和的完全收敛性

在B值随机元随机有界于一非负随机变量的情况下．讨论了B值独立随机元序列非随机足标和的完全收敛性，作为应用，得到了随机足标和完全收敛性的相应结果，将[5]中的一些结果推广到B值独立随机无情形，同时使[3]（d=1），[4]，[6]的相应结果成为特例．     

亚纯函数微分多项式f~kQ[f]+P[f]的零点分布

文[4]对简单形式的微分多项式fkf’+a的零点分布进行了讨论,文[1]对一般形式的微分多项式fkQ[f]+P[f]的零点分布进行了讨论.但由于极点给证明带来的困难,这些工作主要是对整函数来做的.本文证明了任一满足δ(∞,f)>k+2ΓQ+3ΓP+2/2k+2ΓQ+1的超越亚纯函数f,微分多项式fkQ[f]+P[f]在不含f,Q[f]极点和P[f]零、极点的可数个圆盘并集之外有无穷多个零点,其中k≥3Γp+2,而ΓQ,ΓP分别是f的微分多项式Q[f],P[f]的权.文[1]和[2,4,6]中的结论是本文结论的特殊情况.     

Global bifurcation of waves

In this note it will be shown how a theorem of Alexander [1] and Ize [9] together with computational results of Alexander and Yorke [4] and Alexander and Fitzpatrick [2] may be used to generalize the existence theorem for, and to prove some global results about, certain wave-like solutions of nonlinear systems of partial differential equations.The equations to be studied are weakly coupled parabolic systems of equations defined on a bounded axisymmetric domain. Such equations are often called reaction-diffusion equations (or interaction-diffusion equations) and arise in many parts of biology and chemistry. The question as to how wave-like solutions of these equations may bifurcate from a family of trivial solutions was studied by Auchmuty [5] and the results will be considerably extended here.     

关于对Fuzzy弱自反关系证明的注记

陈贻源［１］和张文修［２］分别引入了Ｆｕｚｚｙ弱自反关系的定义和有关的证明。本文在［１］和［２］给出Ｆｕｚｚｙ弱自反关系定义的基础上，对［１］和［２］的有关Ｆｕｚｚｙ弱自反关系证明提出了异议，并给出了新的证明。     

M—矩阵的等价表征

本文引进了按环路弱不约非零元素对角占优的概念，讨论了Ｍ－矩阵的等价条件，给出了Ｍ－矩阵的两个等价表征，改进与推广了（１），（２），（５），（９）的相应结果。     

Remarks on the “Reply to Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems,Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978””

In this letter, we show that the main results of the reply paper [1] are wrong. We demonstrate that the authors of Delavari et al. (2012) [1] have carried out an essential flaw in the proof approach of the system stability. Therefore, we prove that the defects of the paper [2] which have been described in the comment paper [3] are still continued. In this regard, we conclude that the results of our comment paper [3] are correct.     

Existence of Classical Solution of a Quasilinear Stefan-Signorini Problem

In this paper, we consider an one-phase quasilinear Stefan-Signorini problem. In [1] X. Liu has proved the existence and the uniqueness of this problem by the traditional penalty method (see [3] and [4]). Here we use the Mixed Scheme in [2] which is more suitable to the Stefan-Signorini problem and obtain more natural existence results.     

随机泛函分析中可交换映象的随机不动点定理

随机不动点定理在随机泛函分析中是一重要问题.在可分完备的度量空间中的随机不动点定理Bharucha-Reid,王梓坤,?pa?ek,Han?,Itoh及作者等都曾进行过讨论(见[1-5,15-20,21]).在本文中我们对概率分析中可交换映象的随机不动点定理得出了几个新的结果,它推广了前述诸人工作中某些重要结果.在确定性情形也推广了Jungck[6,7,8],Das,Naik[9],Rhoades[10],及Ciric[11]的结果.     

非对称不定问题的非协调多重网格法

１．引言设　是Ｒｄ（ｄ＝２;３）中的有界多角形区域,α是它的边界．考虑下列模型问题此处ｆ∈ＥＬ２（Ω）,系数ＡＥ（Ｃ１（Ω））ｄ×ｄ满足下列一致椭园条件此处α０是正常数．此外假设Ｂ∈（Ｃ１（Ω）ｄ和ｃ∈Ｃ０（Ω）（［１４］）．（１．１）式的变分形式是：找ｕ∈Ｈ０（Ω）使得最近,非对称不定问题的非协调多重网格法吸引了众多的研究,详见问,［７］;［１０］．考虑非协调元多重网格的一个重要原因是混合元和非协调元之间存在着紧密的联系（详见【几问,问）．设ＦＩ是ｆｉ拟一致的Ｈ角形或矩形剖分,是由连接Ｆ'－'（…     

A refined theorem concerning the conditioning of semidefinite programs

Using a weaker version of the Newton-Kantorovich theorem [6] given by us in [3], we show how to refine the results given in [8] dealing with the analyzing of the effect of small perturbations in problem data on the solution. The new results are obtained under weaker hypotheses and the same computational cost as in [8].     

拟非线性发展方程的B解

利用Ｋｕｒａｔｏｗｓｋｉ非紧致测度及［５］中有关结果，本文证明了Ｂａｎａｃｈ空间拟非线性发展方程Ｂ解的存在性，并且讨论了Ｂ解的一些性质。例子表明［５］及［２］的结论为本文结果之推论。     

B值随机元阵列的完全收敛性及大数定律

该文在随机元阵列随机有界于某非负随机变量的条件下，得到了B值随机元阵列完全收敛性的一般性结论，并讨论了随机元阵列加权和的收敛性，使[5][6]中的结果得到了改进和推广．同时讨论了完全收敛性与Banach空间p型（1＜P≤2）性质的等价性，使[14]，[15]中的结果得到进一步的改进．     

Existence of pseudo-equilibria in a financial economy

We prove the existence of a pseudo-equilibrium in a financial economy with incomplete markets in which the agents may have nonordered preferences. We use a fixed-point-like theorem of [5] that generalizes the results by Hirsch, Magill and Mas-Colell [18] and Husseini, Lasry and Magill [19] to encompass the framework considered by Gale and Mas-Colell ([14], [15]).     

A Fixed Point Theorem for Multi-valued Composite Increasing Operators in Partially Ordered Spaces

DefinitionlLl]I,etXbeaHausdorffTopologicalspacewhichhaspartiallyorderedstructure.WesayXisasemiorderedTopologicalSpace,ifforanytwonets{x.Ir6T}and{YrlrET}inX,x,相似文献   

Théorèmes du type Ingham et application à la théorie du contrôle

Ingham [4] improved a previous result of Wiener [10] on nonharmonic Fourier series. Modifying his weight function we obtain optimal results improving several earlier theorems of Kahane [7], Castro and Zuazua [2] and of Jaffard, Tucsnak, and Zuazua [5]. Then we apply these results to simultaneous observability problems.     

Ingham-Beurling type theorems with weakened gap conditions

Completing a series of works begun by Wiener [34], Paley and Wiener [28] and Ingham [9], a far-reaching generalization of Parseval"s identity was obtained by Beurling [4] for nonharmonic Fourier series whose exponents satisfy a uniform gap condition. Later this gap condition was weakened by Ullrich [33], Castro and Zuazua [5], Jaffard, Tucsnak and Zuazua [11] and then in [2] in some particular cases. In this paper we prove a general theorem which contains all previous results. Furthermore, applying a different method, we prove a variant of this theorem for nonharmonic Fourier series with vector coefficients. This result, partly motivated by control-theoretical applications, extends several earlier results obtained in [15] and [2]. Finally, applying these results we obtain an optimal simultaneous observability theorem concerning a system of vibrating strings. This revised version was published online in June 2006 with corrections to the Cover Date.