DISTORTION THEOREMS FOR CLASSES OF g-PARAMETRIC STARLIKE MAPPINGS OF REAL ORDER IN Cn

In this paper,we define the class■ of g-parametric star like mappings of real order γ on the unit ball B_X in a complex Banach space X,where g is analytic and satisfies certain conditions.By establishing the distortion theorem of the Fréchet-derivative type of■ with a weak restrictive condition,we further obtain the distortion results of the Jacobi-determinant type and the Fréchet-derivative type for the corresponding classes(compared with■) defined on the unit polydisc(resp.unit ball ...     

THE UNIT BALL OF C^＊-ALGEBRA AND DIFFERENTIABILITY OF SUPPORT FUNCTION

In this paper we show that the unit ball of an infinite dimensional commutative C^*-algebra lacks strongly exposed points, so they have no predual. Also in the second part, we use the concept of strongly exposed points in the Frechet differentiability of support convex functions.     

COMPLEX HOPF BIFURCATION OF INTEGRAL SURFACES

The existence of the Hopf bifurcation of a complex ordinary differential equation system in the complex domain is studied in this paper by using the complex qualitative theory.In the complex domain,we conclude that the Hopf bifurcation appears for both directions of the parameter μ. The formulae of the Hopf bifurcation are also given in this paper.     

ON THE GROWTH AND VALUE DISTRIBUTION OF ANALYTIC SOLUTIONS OF A CLASS OF ALGEBRAIC DIFFERENTIAL EQUATIONS

In this paper, we show that the growth of meromorphic or algebroidal solutions of some algebraic differential equations can be estimated in terms of the growth of the coefficients in tho equation and the counting functions of some value peints. We point simulteneously out that the growth of algebroid solutions of certain class of differential equations can be estimated using only the growth of coefficients in the equation, and give an example which is not belonging to this class to show that the above conclusion is not true.     

EXISTENCE AND NONEXISTENCE FOR THE INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEM OF MULTIDIMENSIONAL NONLINEAR SCHRDINGER EQUATIONS WITH OPERATOR AND THEIR SOLITON SOLUTIONS

The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.     

EXISTENCE OF GENERALIZED SOLUTIONS TO A HYPERBOLIC MODEL OF COMBUSTION

In this paper we obtain the existence of the generalized solutions to the Cauchy problem for a model of combustion provided that the function f is of nonconvexity and initial values lie in the bounded, measurable class.     

DEGENERATE ELLIPTIC SYSTEMS OF CLASS Ⅰ

In this paper, we considered the first class (class Ⅰ) of elliptic systems of partial differential equations with a special kind of lower-order terms which are one-order singular. For the classical well-posedness of Dirichlet problem and skew derivative problem in the unit circle, we gave a discussion in full detail, and obtained complete results.     

INTERPOLATION OF Ba SPACES

In this paper we advance the interpolation theorems of linear operator in Ba spaces. The conception of Ba spaces was first put forward by Ding Xiaxi in his discussion on the prior estimate of Laplace operator in some classical domains and in his study of the embedding theorem of Orlicz-Sobolev spaces, higher dimensional singular     

INTERACTION OF STRONG AND WEAK SINGULARITIES FOR HYPERBOLIC SYSTEM OF CONSERVATION LAWS IN MULTIDIMENSIONAL SPACE

In this paper we study the interaction of strong and weak singularities for hyperbolic system of conservation laws in multidimensional space. Under the assumption of transversal intersect of the shock front with the bicharacteristics bearing weak singularities we proved a theorem on regularity propagation across the shock front.     

HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS

In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.     

NUMBER OF BOUNDED SOLUTIONS IN CRITICAL CASE

In this paper, using the method of linearization, we determine the number of bounded solutions of ordinary differential equations in critical case.     

GLOBAL CONVERGENCE OF THE FLETCHER-REEVES ALGORITHM WITH INEXACT LINESEARCH

In this paper, we investigate the convergence properties of the Fletcher Reeves algorithm. Under conditions weaker than those in a paper of M. A1-Baali,we get the global convergence of the Fletcher-Reeves algorithm with a low-accuracy inexact linesearch.     

THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α

The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper.From the maximum modulus principle of holomorphic functions,we obtain that the generalized Roper-Suffridge operators preserve strong and almost spirallikeness of type β and order α on the unit ball B~n in C~n and on bounded and complete Reinhardt domains.Therefore we obtain that the generalized Roper-Suffridge operators preserve strong spirallikeness of type β,strong and almost starlikeness of order α,strong starlikeness on the corresponding domains.Thus we can construct more subclasses of spirallike mappings in several complex variables.     

CALCULATION OF α_3 COEFFICIENT OF SCALAR FIELD BY POINT SEPARATION METHOD

The α_3 coefficient of scalar field in arbitrary Riemann space-time background is calculated by point separation method in this article. The primary expression of α_3 involves 25 invariants. Using the identities derived in the appendix, we can reduce α_3 from 25 invariants to 17 invariants which agree with Gilkey's formula for α_s coefficient of the scalar field derived by geometric methods and reasons. Recently we derived two important invariant identilies, using these identities we can reduce α_3 from 17 invariants to 15 invariants which would much simplify the calculation of the energymomentum tensor of vacuum polarization.     

THE EFFECT OF NUMERICAL INTEGRATION IN FINITE ELEMENT METHODS FOR NONLINEAR SOBOLEV EQUATIONS

1 IntroductionIn this paper we will continue the work in LZ' 3, 4J and analyze the effect of numerical integration for nonlinear Sobolev equationsProblems of this type have applications to the two-- temperature theory of heat conduction andsoil mechanics. The treatment of Galerkin's approximations to the solution of partial differential equations using fume element techniques results in a syStem of equations.Throughout this paper, we shall assume that the domain n is a polygonal, so that n=…     

BOUNDARY FEEDBACK CONTROL OF ELASTIC BEAM EQUATION WITH STRUCTURAL DAMPING AND STABILITY

In this paper, we consider the partial differential equation of an elastic beam with structuraldamping by boundary feedback control. First, we prove this closed system is well--posed; then weestablish tbe exponential stability for this elastic system by using a theorem whichbelongs to F. L.Huang; finally, we discuss the distribution and multiplicity of the spectrum of this system. Theseresults are very important and useful in practical applications.     

BIFURCATION OF CUBIC INTEGRABLE SYSTEM UNDER CUBIC PERTURBATION

In this paper, we consider the bifurcation for a class of cubic integrable system under cubic perturbation. Using bifurcation theory and qualitative analysis, we obtain a complete bifurcation diagram of the system in a neighbourhood of the origin for parameter plane.     

EXISTENCE OF SOLUTIONS TO NONLINEAR TWO POINTS BOUNDARY VALUE PROBLEMS OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

In this paper, we obtain some criteria for the existence of solutions to nonli-near two-point boundary value problems by constructing some Liapunov func-tions, and we give some examples for our results to this problem in the end.     

NUMERICAL ANALYSIS OF THE DYNAMICAL BEHAVIOR OF THE EQUATION OF J-J TYPE

In this paper, we have analysed the dynamical behavior of the Josephson Junction equation bynumerical computation and the theory of dynamical systems. As 0<β<2:1 ε, and ρis not sufficientlylarge, we observed the intermittent chaotic behavior and the period-doubling chaotic behavior in whichpeople are very interested recently. This implies the for some β(0<β<2:1 ε), the dynamicalbehavior of the J-J equation is rather complex.     

LONG-TIME CONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR NAVIER-STOKES EQUATIONS

1　IntroductionIn this paper,we firstprovide a generalized difference method for the two-dimension-al Navier-Stokes equations by combining the ideas of staggered scheme[6] and generalizedupwind scheme [4 ] in space,and by backward Euler time-stepping.Then we apply theabstractframework of[7] to prove its long-time convergence.The outline of this paper is as follows:In§ 2 we state the generalized differencemethod.In§ 3 we provide some lemmas.In§ 4 we study the one-sided Lipschitz condi-tio…