On the solutions of a second order nonlinear system with almost periodic forcing

A second order almost periodic perturbed nonlinear system with small parameter is discussed in this paper. Based on some analytical techniques and the method of averaging, some sufficient conditions are obtained for existence of one almost periodic solution. Also some suitable conditions are given for existence of two almost periodic solutions. The obtained new results generalized the known results in Seifert [1], [3] and He [2], [4]. Finally, some applications are presented to illustrate that our results are a good generalization of the known results.     

Uniqueness results of meromorphic functions whose derivatives share four small functions

We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.     

集值映射的拟一致收敛

本文中，在拟一致空间中引入强局部对称性的概念，并讨论集值映射的拟一致收敛性．本文推广了［５］中的一些结果，同时用反例否定了［３］和［４］中的主要定理     

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.     

Approximate Radon-Nikodým representations on Riesz algebras

For the finitely additive case approximate Radon-Nikodym representations are obtained in the setting of Riesz algebras, complementing and generalizing results of Bochner [4], Fefferman [10], de Amo, Chitescu and Díaz Carrillo [1]. Furthermore the possible relations between the various spaces which appear here are given, answering a question of [1]. Various examples show that our results are sharp, there also the class of approximately representable functionals is explicitly characterized, a partial answer to another question of [1]. Finally some open questions are listed.     

Meromorphic functions sharing two or three values with their derivatives in some angular domains

We study the uniqueness of transcendental meromorphic functions sharing two or three values with their derivatives in some angular domains instead of the whole complex plane. The obtained results extend the corresponding results of Frank-Weissenborn [8] and Frank-Schick[9], and improve Theorems 1–3 from Zheng [19]. Some examples are given to show that the obtained results, in a sense, are the best possible.     

Rings characterized by injectivity classes

Recently, there are a number of well known theorems which char­acterize rings in terms of injective modules (cf. [2], [3], [5] and [8]). The purpose of this paper is to give general theorems which show that some similar results remain true when many other classes of general injective modules are considered in place of injective modules. Our results encompass several well known results by Huynh and Smith, Liu, and Xue. In particular we answer negatively the question of Yue Chi Ming [11] and an example is given to show that E—injective modules form an intermediate class between continuous and quasi-continuous modules(cf. Example 3).     

“寻找临界点的注”一文的一点改进

本文在没有 (PS) c条件的前提下 ,证明了文献 [2 ]中的两个结果仍然成立 .从而改进了 [2 ]中相应的结果 .     

Summation of almost convergent divergent sequences,topological methods

In this paper we give a characterization of the conservative matrices that sum only those divergent sequences which are not almost convergent. Such conditions are similar to those which are necessary and sufficient for a conservative matrix to sum no bounded divergent sequence (Agnew [1], Mazur-Orlicz [4], Wilansky-Zeller [6], and Zeller [7]). There are, however, some differences showing, that the results mentioned above cannot be transmitted without any restriction. Parts of this paper have been already developed by the author more detailed in [5].     

Global exponential stability of a class of retarded impulsive differential equations with applications

This paper studies the dynamics of a class of retarded impulsive differential equations (IDE), which generalizes the delayed cellular neural networks (DCNN), delayed bidirectional associative memory (BAM) neural networks and some population growth models. Some sufficient criteria are obtained for the existence and global exponential stability of a unique equilibrium. When the impulsive jumps are absent, our results reduce to its corresponding results for the non-impulsive systems. The approaches are based on Banach’s fixed point theorem, matrix theory and its spectral theory. Due to this method, our results generalize and improve many previous known results such as [3], [5], [6], [9], [17], [18], [23], [32], [38], [43], [51], [52]. Some examples are also included to illustrate the feasibility and effectiveness of the results obtained.     

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。     

G -函数与迭代阵谱半径的估计

该文应用G -函数概念, 获得了迭代矩阵谱半径新的上、下界, 所得结果推广和改进了文献[1--6]中的相应结果.这些结果适合于更广泛的矩阵类, 数值结果也表明在相同的条件下这些新界优于文献[1--6]中的界.     

Conjugacy separability of Seifert 3-manifold groups over non-orientable surfaces

Scott (1978) [12] showed Seifert 3-manifold groups are subgroup separable. Niblo (1992) [9] improved this result by showing that these groups are double coset separable. In Allenby, Kim and Tang (2005) [2] it was shown that all but two types of groups in the orientable case are conjugacy separable. Martino (2007) [7] using topological results showed that Seifert groups are conjugacy separable. Here we use algebraic method to show that Seifert groups over non-orientable surfaces are conjugacy separable.     

Kinematic-wave analysis of particle settling in tube centrifuges

The kinematic-wave theory of particle settling in tube centrifuges is subject to controversy. G. Anestis and W. Schneider [1] made the common assumption that the flow in a rotating tube of large length/diameter ratio can be treated in one-dimensional approximation. Their results have been found in agreement with measurements [2], [3]. However, M. Ungarish [4] performed an analysis of the two-dimensional settling process in the limit of vanishing particle concentration and obtained results that are not in accord with the one-dimensional flow approximation, irrespective of the length/diameter ratio. It is the aim of the present investigation to gain a better understanding of the process. According to this analysis, quasi-one-dimensional kinematic waves are embedded in a two-dimensional bulk flow that is governed by the boundary conditions at the walls of the tube. The results are compared with those of the one-dimensional flow approximation. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Remarks, du côté de chez Tarski, on symmetric ternary relations

We point out that the results in [12] are the model-theoretic counterpart of results established syntactically in [3] and [10], and that Martin’s theorem for the Euclidean 3- or higher-dimensional case, established in [5], does not depend on the Beckman-Quarles theorem, and can be rephrased as a result about axiomatizability and definability.     

关于一类抛物型Monge-Ampère方程解的注记

本文讨论如下抛物型Monge-Ampere方程的第一初边值问题-ut+det1/n D2u=g(χ,t),(χ,t)∈Q=Ω×(0,T),u= (χ,t),(χ,t)∈ pQ,其中Ω为Rn中有界凸集.证明了在更一般的结构条件下[3,7]的结果仍然成立.证明中重要的一点是在Rn × R中非柱型域上“冻结问题”的可解性.     

Improving the order and rates of convergence for the Super-Halley method in Banach spaces

In this study we are concerned with the problem of approximating a locally unique solution of an equation on a Banach space. A semilocal convergence theorem is given for the Super-Halley method in Banach spaces. Earlier results have shown that the order of convergence is four for a certain class of operators [4], [5], [8]. These results were not given in affine invariant form, and made use of a real quadratic majorizing polynomial. Here, we provide our results in affine invariant form showing that the order of convergence is at least four. In cases that it is exactly four the rate of convergence is improved. We achieve these results by using a cubic majorizing polynomial. Some numerical examples are given to show that our error bounds are better than earlier ones.     

On the Determination of a Density Function by Its Autoconvolution Coefficient

We investigate eigenvalues and eigenvectors of certain linear variational eigenvalue inequalities where the constraints are defined by a convex cone as in [4], [7], [8], [10]-[12], [17]. The eigenvalues of those eigenvalue problems are of interest in connection with bifurcation from the trivial solution of nonlinear variational inequalities. A rather far reaching theory is presented for the case that the cone is given by a finite number of linear inequalities, where an eigensolution corresponds to a (+)-Kuhn-Tucker point of the Rayleigh quotient. Application to an unlaterally supported beam are discussed and numerical results are given.     

Weak convergence conditions for Inexact Newton-type methods

We establish a new semilocal convergence results for Inexact Newton-type methods for approximating a locally unique solution of a nonlinear equation in a Banach spaces setting. We show that our sufficient convergence conditions are weaker and the estimates of error bounds are tighter in some cases than in earlier works [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30] and [31]. Special cases and numerical examples are also provided in this study.     

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．