On Meromorphic Starlike Multivalent Functions

In this paper we introduce and study some new subclasses of meromorphic starlike multivalentfunctions.Inclusion relations are established,Integral transforms of functions in these classes are alsoconsidered.In particular,our results include or improve several results due to Mogra et al.[2],Mogra[3],Goel and Sohe[4]and Bajpai[5].     

The Error Estimates of Semi-discrete Galerkin Methods for some Non-linear Parabolic Equations

1. Introduction Concerning the finite element analysis for linear and nonlinear parabolic equa tions there are a lot of papers, however, only a few of them devoted to the parabolic problems with mixed boundary conditions. In[1],[2] and [3], the finite element methods for some non-linear parabolic problems are systematically considered, but they are mainly restriced to the cases in which the boundary conditions are of Dirichlet     

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.     

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.     

PERIODIC OSCILLATORY SOLUTION TO DELAYED BAM NEURAL NETWORKS WITH PERIODIC COEFFICIENTS

In this paper,using the continuation theorem of coincidence degree theory,Lyapu- nov functionals and some new inequality techniques,some new sufficient criteria are obtained to ensure the existence and global exponential stability of periodic solution. Our results are less restrictive than previous works and more effective than those in [12],which plays a significant role in designing globally exponentially stable and peri- odic oscillatory BAM neural networks with periodic coefficients.One example is al...     

Absolute stability of general lurie type indirect control systems

1. IntroductionThe absolute stability problem is one of the central topics of the stability theory for itstheoretical and engineering importance. UP to date, this problem has been studied by manyauthors [1--9], and many sufficient conditions and some necessary and sufficiellt conditions inspecial cases for absolute stability are obtained. In papers [7,8], Liao gave a necessary andsufficient condition for absolute stability for partial arguments. In this paperg by using anew concept of absolut…     

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.     

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.     

Generllzation of Direct Product and Generation of Sets of Orthogonal Functions

Two new kinds of direct product of matrices are defined. Their properties are investigated. Direct products of matrix and set of continuous functions are also defined. Many complete sets of orthogonal functions, such as those sets given by Walsh [2], Paley [3], Chrestenson[4], and Watari [5], may be generated by these newkinds of direct product. Direct products are also applicable to the generation of sets of piecewise orthogonal functions.     

AN EXTRAGRADIENT METHOD FOR RELAXED COCOERCIVE VARIATIONAL INEQUALITY AND EQUILIBRIUM PROBLEMS

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansive mappings, the set of an equilibrium problem and the set of solutions of the variational inequality prob- lem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao[17], Takahashi[12] and many others.     

ON COUPLING OF JUMP PROCESSES

This is a sequel to the paper [3] in which the marginality, regularity and orderpreservation for couplings of jump processes are studied. The main purpose of this note is to present a criterion and some practical suffcient conditions for the success of couplings and some criteria for the monotonicity of jump processes.     

Three-Step Iterative Sequences with Errors for Uniformly Quasi-Lipschitzian Mappings

The purpose of this paper is to investigate some sufficient and necessary conditions for three-step Ishikawa iterative sequences with error terms for uniformly quasi-Lipschitzian mappings to converge to fixed points. Our results extend and improve the recent ones announced by Liu [3,4], Xu and Noor [5], and many others.     

GLOBALLY CONVERGENT INEXACT GENERALIZED NEWTON METHODS WITH DECREASING NORM OF THE GRADIENT

AbstractIn this paper, motivated by the Martinez and Qi methods[l], we propose one type of globally convergent inexact generalized Newton methods to solve unconstrained optimization problems in which the objective functions are not twice differentiable, but have LC gradient. They make the norm of the gradient decreasing. These methods are implementable and globally convergent. We prove that the algorithms have superlinear convergence rates under some mile conditions.The methods may also be used to solve nonsmooth equations.     

Enumeration of maps on the projective plane

1. IntroductionA lnap is rooted if an edge is distinguished togetl1er with an end and a side of the edge.An edge belo11ging to only one face is called double (or 8ingular by some author), al1 othersbelonging to exactly two faces are called s1ngle. The enumeration of rooted p1anar maps wasfirst introduced by Tutte['], Techniques originated by Tutte [2,3l for enumerating variousclasses of rooted Inaps on tIle sphere are here applied to the c1asses of alI rooted maps onthe projective plane. Th…     

NUMERICAL STUDIES OF 2D FREE SURFACE WAVES WITH FIXED BOTTOM

AbstractThe motion of surface waves under the effect of bottom is a very interesting and challenging phenomenon in the nature, we use boundary integral method to compute and analyze this problem. In the linear analysis, the linearized equations have bounded error increase under some compatible conditions. This contributes to the cancellation of instable Kelvin-Helmholtz terms. Under the effect of bottom, the existence of equations is hard to determine, but given some limitations it proves true. These limitations are that the swing of interfaces should be small enough, and the distance between surface and bottom should be large enough. In order to maintain the stability of computation, some compatible relationship must be satisfied like that of [5]. In the numerical examples, the simulation of standing waves and breaking waves are calculated. And in the case of shallow bottom, we found that the behavior of waves are rather singular.     

Stability for several type of interval matrices

The robust stability for some types of tlme-varying interval raatrices and nonlineartime-varying interval matrices is considered and some sufficient conditions for robust stability of such interval matrices are given, The main results of this paper are only related to the verticesset of a interval matrices, and therefore, can be easily applied to test robust stability of interval matrices. Finally, some examples are given to illustrate the results.     

ON ThE OPTIMUM MASS RATIOS OF STEP-ROCKETS

In this paper, the writer will give a concrete counter-example to show that an important argument in [1]and [2](i. e. in this problem the extreme-point and the optimum mass Rat ios were the same) was Somewhat incorrect in general.Then how to find the optimum mass Ratios in Reneral situation? To do this, The writer went a step further to discuss the work of [1], [2], and obtained not only some important new results such as the existance and uniqueness of the extreme-points in[2], but also proposed the idea of theoretical permissible region as well as the idea of practical permissible region etc. Then proposed a method for determining the optimum mass Ratios, Hence some results in [1] and[2] were improved and perfected.     

BOUNDEDNESS IN p-NFDES

1 IntroductionRecently, the papers (cf [1], [2]) have established stabi1ity of p-NFDEsusing Liapunov-Razumikhin functionaJs. However, in order to study the limtset and the existence of periodic solutions of p-NFDEs, we need to know notonly the stability but ajso the boundedness of solutions. In this paper, weshal1 discuss the boundedness properties of P-NFDEs by Liapunov functionals,which improve some boundedness conditions for FDEs in the literature. Someexamples are also worked out t…     

行分块矩阵值域上正交投影的展开式

We give in this note some expansion formulas for the orthogonal projectors onto the range of the row block matrix [ A, B ], and use the expansion formulas to examine relations among the orthogonal projectors onto the ranges of A, B and [A, B]. In particular, we present some identifying conditions for a pair of orthogonal projectors of the same size to commute.     

Some Optimal Block-Factorial Designs

The theory of optimal design plays a fundamental role in experimental design. Some of the results have been widely applied to the realistic world. In[1], Kiefer proved the optimality of some block designs. In this paper some block-factorial designs are discussed. When a block design d_2(v_2,b,k) is superimposed on other block design d_1(v_1,b,k), the resulting structure is called a block-factorial design and is abbreviated as d_1*d_2. The collection of all such designs is denoted by π(v_1,v_2, bk) or Ω. If d_1,d_2 are uniform and they are orthogonal to each other, the structure can be considered as an orthogonal design with three factors. In[2] Cheng pointed out that