Nonexistence of formal first integrals for general nonlinear systems under resonance

In this paper, we consider the nonintegrability for nonlinear systems under the simple resonant case, i.e., the Jacobian matrix of vector field at some fixed point has some single multiply zero eigenvalues, and some nonzero eigenvalues which are N-independent. By using the Poincaré-Dulac normal form theory, we give a necessary condition for the system under consideration to have formal first integral.     

On sum and stability of g-frames in Hilbert spaces

In this paper, we give some new results on sum and stability of g-frames in Hilbert spaces. Since the finite sum of g-frames may not be a g-frame for the Hilbert space, we give a necessary and sufficient condition and some sufficient conditions for the finite sum of g-frames to be a g-frame. We also show that every g-sequence in Hilbert space can be expanded to a tight g-frame by adding a linear bounded operator. Moreover, we obtain some sufficient conditions under which g-frames (and the finite sum of g-frames) are stable under small perturbations.     

Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions

We consider a class of analytic area-preserving mappings C^m-smoothly depending on a parameter. Without imposing on any non-degeneracy assumption, we prove a formal KAM theorem for the mappings, which implies many previous KAM-type results under some non-degeneracy conditions. Moreover, by this formal KAM theorem, we can also obtain some new interesting results under some weaker non-degeneracy conditions. Thus, the formal KAM theorem can be regarded as a general KAM theorem for areapreserving mappings.     

实四元数矩阵行列式函数的几点注记

分别对实四元数矩阵理论中出现的几种行列式函数在三个初等变换下的改变性作一些讨论,得出几种满足一定性质的行列式函数的不存在性或唯一存在性。     

On the Properties of the Solution of a Strongly Degenerate Parabolic Equation

ＯｎｔｈｅＰｒｏｐｅｒｔｉｅｓｏｆｔｈｅＳｏｌｕｔｉｏｎｏｆａＳｔｒｏｎｇｌｙＤｅｇｅｎｅｒａｔｅＰａｒａｂｏｌｉｃＥｑｕａｔｉｏｎＣｈｅｎｇＦｕｘｉａ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＴｓｉｎｇｈｕａＵｎｉｖｅｒｓｉｔ...     

Standard tensor and its applications in problem of singular values of tensors

In this paper, first we give the definition of standard tensor. Then we clarify the relationship between weakly irreducible tensors and weakly irreducible polynomial maps by the definition of standard tensor. And we prove that the singular values of rectangular tensors are the special cases of the eigen-values of standard tensors related to rectangular tensors. Based on standard tensor, we present a generalized version of the weak Perron-Frobenius Theorem of nonnegative rectangular tensors under weaker conditions. Furthermore, by studying standard tensors, we get some new results of rectangular tensors. Besides, by using the special structure of standard tensors corresponding to nonnegative rectangular tensors, we show that the largest singular value is really geometrically simple under some weaker conditions.     

Differentiability of convex measures

In this paper we consider convex measures on finite-dimensional spaces. We prove the differentiability of convex measures in the Skorokhod sense (and under some natural conditions, in the Fomin sense also). Simultaneously we give some additional results on differentiability of convex measures.Translated fromMatematicheskie Zametki, Vol. 58, No. 6, pp. 862–871, December, 1995.This research was partially supported by the Russian Foundation for Basic Research under grant No. 94-01-01556, by the Ministry of Science under grant No. M38300 and by the International Science Foundation under grant No. M38000.     

Symmetry of solutions to some systems of integral equations

In this paper, we study some systems of integral equations, including those related to Hardy-Littlewood-Sobolev (HLS) inequalities. We prove that, under some integrability conditions, the positive regular solutions to the systems are radially symmetric and monotone about some point. In particular, we established the radial symmetry of the solutions to the Euler-Lagrange equations associated with the classical and weighted Hardy-Littlewood-Sobolev inequality.

     

仿紧局部cosmic空间的一些性质

给出仿紧局部cosmic空间的一些特征,建立了仿紧局部cosmic空间的几类序列覆盖L映象的特征,证明了闭L映射和商ss映射保持仿紧局部cosmic空间的性质,此外,还给出仿紧局部cosmic空间的一些映射性质。     

Some extensions of the operator entropy type inequalities

In this paper, we define the generalised relative operator entropy and investigate some of its properties such as subadditivity and homogeneity. As application of our result, we obtain the information inequality. In continuation, we establish some reverses of the operator entropy inequalities under certain conditions by using the Mond–Pe?ari? method.     

Blow‐up phenomena for a pseudo‐parabolic equation

By the means of a differential inequality technique, we obtain a lower bound for blow‐up time if p and the initial value satisfy some conditions. Also, we establish a blow‐up criterion and an upper bound for blow‐up time under some conditions as well as a nonblow‐up and exponential decay under some other conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

APPROXIMATING ANALYSIS OF A KIND OF REPAIRABLE STANDBY SYSTEMS

ＬＩＷＥＩ（李伟）；ＣＡＯＪＩＮＨＵＡ（曹晋华）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，Ｂｅｉｊｉｎｇ１０００８０，ＣｈｉｎａａｎｄＡｓｉａ－ＰａｃｉｆｉｃＯｐｅｒａｔｉｏ...     

格中依次最短无关组与Minkowski约化基等价的充分条件

本文讨论了格中基子集、依次最短无关组及Minkowski约化基之间的向量长度关系,利用无关组与基之间的一些制约性质,给出了Minkowski约化基达到依次最短长度,以及依次最短无关组成为Minkowski约化基的一些充分条件.     

Nontrivial solutions for resonant cooperative elliptic systems via computations of the critical groups

In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature.     

Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

We study second-order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second-order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second-order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions.     

The existence of zeros of set-valued mappings in reflexive Banach spaces

In this paper, we establish the equivalence between the existence of zeros for set-valued mappings and the solvability of variational inequality, under some conditions involving the generalized projection operator. Basing on this result, we obtain some existence theorems of zeros for quasimonotone set-valued mappings. As application, we derive several fixed point theorems for generalized inward mappings in Hilbert spaces.     

$G$核开集,$G$核邻域与$G$ 核导集

在拓扑空间中, 在$G$方法意义下以$G$壳与$G$核为基础, 引入$G$壳闭集,$G$核开集,$G$核邻域与$G$核导集的概念, 讨论其相应的一些性质. 特别的, 定义了点式$G$方法, 提供了在此方法下$G$闭集与$G$壳闭集, $G$开集与$G$核开集, $G$邻域与$G$核邻域, $G$导集与$G$核导集的一致性, 丰富了拓扑空间中关于$G$闭集, $G$开集, $G$内部, $G$邻域和$G$导集的一些结果. 同时, 提出一些问题以供进一步研究.     

Invariance of statistical causality under convergence

In this paper we prove the invariance of some causality relationships between flows of information (represented by filtrations) under some types of convergence. We consider a statistical concept of causality which is based on Granger’s definition of causality, but instead of time series we focus on continuous time processes.     

Multi-dimensional central limit theorems and laws of large numbers under sublinear expectations

In this paper, we present some multi-dimensional central limit theorems and laws of large numbers under sublinear expectations, which extend some previous results.