EXISTENCE AND MOMENT ESTIMATES FOR SOLUTIONS TO NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, we show the existence and uniqueness of solutions to a large class of SFDEs with the generalized local Lipschitzian coefficients. Some moment estima- tes of the solutions are given by establishing new Ito operator inequalities based on the Razumikhin technique. These estimates improve, extend and unify some related results including exponential stability of Mao （1997） [20], decay stability of Wu et al. （2010,2011） [32,33], Pavlovic et al. （2012） [24], asymptotic behavior of Luo et al. （2011） [18] and Song et al. （2013） [26]. Moreover, stochastic version of Wintner theorem in continuous space is established by the comparison principle, which improve and extend the main results of Xu et al. （2008 [39], 2013 [36]）. When the methods presented are applied to the SFDEs with impulses and SFDEs in Hilbert spaces, we extend the related results of Govindana et al. （2013） [7], Liu et al. （2007） [15], Vinod- kumar （2010） [29] and Xu et al. （2012） [35]. Two examples are provided to illustrate the effectiveness of our results.     

EXISTENCE OF WEAK SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS IN BANACH SPACES

0 IntroductionRecently, the study of ordinary differential equations in a Banach spacehas been developed extensively by using the strong topology, see [2],13],[4]. Atpresent, however, there is no reference or paper which systematically studiesweak solutions of the Cauchy problem of ordinary differential equation in theweak topology. In references [l],15],[7] and [8], several results of weak solutionsare proved. In this paper, we shall give the other results of weak solutions,some of which are…     

ON A NEW DEFINITION OF RICCI CURVATURE ON ALEXANDROV SPACES

Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we extend our research to summarize the geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume comparison and Lipschitz continuity of heat kernel, are obtained.     

具时滞人机系统的稳定性与分支分析(英文)

A mathematical model of man-machine system is considered.Based on the reference [4],the direction and stability of the Hopf bifurcation are determined using the normal form method and the center manifold theory.Furthermore,the existence of Hopf-zero bifurcation is discussed.In the end,some numerical simulations are carried out to illustrate the results found.     

Approximation by Modified Durrmeyer-Bernstein Operators

In this paper, we study the problem of simultaneous approximation by these operators and give out exact estimate. The following main results are obtained. Theorem I If f∈C~r[0,1], then, for every x∈[0,1], we have     

RELIABILITY BOUNDS FOR NBUE AND NWUE DISTRIBUTIONS

In [5], many inequalities for NBUE and NWUE life distributions are given. But, since thereare some basic observations which do not hold (see Section 1 for details), many results obtained in [5]are not true. In this note we propose some remedies and give some new results.     

Second order three-point boundary value problems in abstract spaces

In this paper we investigate the existence of solutions of the nonhomogeneous three-point boundaryvalue problem We search for solutions of the above problem in the Banach space of continuous functions C（[O, 1], E） with the Pettis integrability assumptions imposed on $. Some classes of Pettis-integrable functions are described in the paper and exploited in the proofs of main results. We stress on a class of pseudo-solutions of considered problem. Our results extend previous results of the same type for both Bochner and Pettis integrability settings. Similar results are also proved for differential inclusions i.e. when f is a multivalued function.     

GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-FUNCTION INVOLVING A GENERAL CLASS OF POLYNOMIALS

The object of this article is to study and develop the generalized fractional calculus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of ■-function, Appell functionF3 and a general class of polynomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus.On account of the general nature of the Saigo-Maeda operators, ■-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notablyH-function,I-function, Mittag-Leffler function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.     

ON THE GROWTH OF SOLUTIONS OF A CLASS OF HIGHER ORDER DIFFERENTIAL EQUATIONS

In this paper, authors investigate the order of growth and the hyper order of solutions of a class of the higher order linear differential equation, and improve results of M. Ozawa^[6], G. Gundersen^[7] and J.K. Langley^[8], Li Chun-hong^[11].     

UNDERSTANDING SCHUBERT’S BOOK(Ⅰ)

Hilbert Problem 15 required an understanding of Schubert’s book[1],both its methods and its results.In this paper,following his idea,we prove that the formulas in§6,§7,§10,about the incidence of points,lines and planes,are all correct.As an application,we prove formulas 8 and 9 in§12,which are frequently used in his book.     

一类完备Riemann流形的正调和函数

本文主要讨论一类完备Ｒｉｅｍａｎｎ流形上的调和函数所组成的线性空间．推广了Ｐ．Ｌｉ及Ｌ．Ｆ．Ｔａｍ^{[5], [7]}和和Ｇｒｅｅｎｅ－Ｗｕ^[3]中的结果．     

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.     

Uniqueness of entire functions sharing one value

We deal with the problem of entire functions sharing one value weakly. Moreover, we improve and generalize some former results obtained by J.-F.Chen, et al. [6], Y.Xu and H.L.Qiu [4], M.L. Fang [5], C.C. Yang, and X.H. Hua [3].     

Order-homomorphisms on fuzzes

In this paper, basic properties of the concept of order-homomorphisms on fuzzes [4], which is a proper generalization of the concept of fuzz functions [1], are studied. Conditions for fuzz functions to be functions of Zadeh's type are obtained. Moreover, the concepts of continuous, closed and open order-homomorphisms are introduced and studied.     

调和函数和完备流形的结构

主要通过讨论调和函数来研究完备流形的几何性质,并推广了[1,9]中的结果．     

Meromorphic functions sharing two sets

In the paper we discuss the uniqueness problem for meromorphic functions that share two sets and prove five theorems which improve and supplement some results earlier given by Yi and Yang [13], Lahiri and Banerjee [5].     

Loewner Chains and Univalence criteria related with Ruscheweyh and Salagean derivatives

In this paper we obtain, by the method of Loewner chains, some sufficient conditions for the analyticity and the univalence of the functions defined by an integral operator. These conditions involves Ruscheweyh and Salagean derivative operator in the open unit disk. In particular cases, we find the well-known conditions for univalency established by Becker [3], Ahlfors [2], Kanas and Srivastava [8] and others for analytic mappings f : U ! C: Also,we obtain the corresponding new, useful and simpler conditions for this integral operator.     

On the positivity of symmetric polynomial functions. Part III: Extremal polynomials of degree 4

In this paper, which is a continuation of [V. Timofte, On the positivity of symmetric polynomial functions. Part I: General results, J. Math. Anal. Appl. 284 (2003) 174-190] and [V. Timofte, On the positivity of symmetric polynomial functions. Part II: Lattice general results and positivity criteria for degrees 4 and 5, J. Math. Anal. Appl., in press], we study properties of extremal polynomials of degree 4, and we give the construction of some of them. The main results are Theorems 9, 13, 15, 16, and 18.     

Galois环和Z/(m)环上完全非线性函数的性质

本文把完全非线性函数推广到了有限Abel群上,利用特征谱讨论了Z/(m)上Bent函数与GF(pe)上bent函数以及完全非线性函数定义之间的关系;给出Galois环与Z/(m)上最佳线性逼近的特征谱表示,得到完全非线性函数在某种程度上能抵抗最佳线性逼近攻击的结论;并给出一种Galois环与Z/(m)环上完全非线性函数的构结方法.     

Value sharing results for shifts of meromorphic functions

In this paper, we deal with the value distribution of difference products of entire functions, and present some result on two difference products of entire functions sharing one value with the same multiplicities. The research findings also include an analogue for shift of a well-known conjecture by Brück. Our theorems improve the results of I. Laine and C.C. Yang [I. Laine, C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007) 148-151], K. Liu and L.Z. Yang [K. Liu, L.Z. Yang, Value distribution of the difference operator, Arch. Math. 92 (2009) 270-278], and J. Heittokangas et al. [J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, J.L. Zhang, Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009) 352-363]. Moreover, we show by illustrating a number of examples that our results are best possible in certain senses.