BOUNDARY STABILIZATION OF HYPERBOLIC SYSTEM WITH NO DISSIPATIVE CONDITIONS

There has been much work (cf. [1], [4], [7]-[12]and references of [8]) on the stabilization of hyperbolic systems. Most of the papers, with the exception of [4] and[12], are concerned only with feedbacklaws such that the resulting systems are dissipative. As is pointed out at the beginning of [7], the dissipative property demands     

THE ANALYSIS OF TEMPORAL DISSIPATIVE STRUCTURE FOR THE IODATE-HYDROGEN PEROXIDE-MALONIC ACID REACTION

According to the chemical mechanism, which was suggested in the reference [7], this paper has established the bifurcation point of Briggs-Rauscher reaction, and has determined the stability of the bifurcation point.We have made the numerical computation by computer and got the projection of the limit cycle on the plane of ig [HIO_2]～lg [I~-] and lg.[Mn~(3 )]～lg[I~-] for f=0.55, f=1 and f=2, respectively. On the other hand, we have got a set of isogradientsFollowing results were obtained:The phase difference between [HIO_2] and [I~-] is equal to π, and between [Mn~(3 )] and [I~-] is nearly equal to π/2;The abrupt change of [HIO_2] is due to the change of [I~-] from 1.3×10~(-6) molar/litre to 8×10~(-7) molar/life nearly, but the change of [Mn~(3 )] is slow;The shape of the limit cycle is dependent upon f.     

求解对流扩散方程的ICT-MMOCAA差分解法

Combing the ideas of FCT^[1,2]with the MMOCAA^[3],the ICT-MMOCAA difference method,in which the transport is corrected by interpolation,is established for convection diffusion problem in the paper,The new method possesses the property of general FCT schemes and it is free from oscillation,with which the large gradient problem is solved by the MMOCAA difference method based on high-order(≥2)Lagrange interpolation^[3].Because the analysis in [3]is only suit for the scheme based on linear interpolation,the analysis method difered form [3] is used for obaining the error estimates of the new method.The numerical example is given in the paper.     

Long time behavior for damped generalized coupled nonlinear wave equations. Ⅱ.Unbounded domain

Introduction In [if, the authors established the unique existence of the smooth solution for the couplednonlinear equations. These were proposed to describe the interaction process of internal longwaves. In [2], Ito proposed a recursion operator by which he inferred that the equations possessinfinitely many symmetries and constants of motion. In [31, He established the existence ofa smooth solution to the system of coupled nonlinear KdV equations[41. We remark that'Schonbeh[sl dealt with a …     

Fixed Points of Nonexpansive Type Mappings in Topological Spaces

Recently. Penot[1] and Kirk[2]obtained the abstract versions of Kirk's fixed point theorem of [3] for nonexpansive mappings, respectively. Gille spie and Williams [4, 5] replaced the reflexive and normal structure used in Kirk [3] and Kannan [6], by uniformly normal structure to obtain the fixed point theorems for nonexpansive and Kannan mappings. Kaukich [7] also extended the result of [3] to the generalized nonexpansive mappings.     

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.     

关于带W权Drazin逆的表示定理及迭代方法

To study singular linear system, Cline and Greville[8] proposed the concept of W-weighted Drazin inverse for the rectangular matrices,where the properties were also discussed. The computation for the W-weighted Drazin inverse is of much interest, which is mainly divided into two kinds of methods: direct method[2,4,6] and iterative method[3,5,7,9,12,13]. In this paper, we study the iterative method and successive matrix squaring(SMS) method for the W-weighted Drazin inverse and generalize the main results in [12,13].     

APPLICATIONS OF THE BERNSTEIN-DURRMEYER OPERATORS IN ESTIMATING THE NORM OF MERCER KERNEL MATRICES

The paper is related to the norm estimate of Mercer kernel matrices. The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on [0, 1] × [0, 1] based on the Bernstein-Durrmeyer operator kernel are obtained, with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2 -norm for general Mercer kernel matrices on [0, 1] x [0, 1] are provided.     

A RECURSIVE ALGORITHM OF THE PARAMETER ESTIMAION WHEN THE NOISE IS COLORED

When the noise is white the recursive algorithm of the parameter estimation is discussed in [1], [2]. When the noise is n-Step correlated the recursive algorithm of the parameter estimation is discussed in [3]. In this paper when the noise is colored the recursive algorithm of the parameter estimation is discussed and the recursive algorithm is given.     

ON THE EXISTENCE OF INFINITELY MANY CRITICAL POINTS OF THE EVEN FUNCTIONAL integral from n=Ω to (F(x, u, Du)dx) IN W_0~(1,p)

§1. Introduction In the paper [1], Pacella and Tricarico proved that the existence of infinitely many critical points of even functional integral from Ω to (F(x,u,Du)dx) in space W_0~(1,2). As far as our knowledge goes, the paper [1] is the first investigation of general functional integral from Ω to (F(x,u,Du)dx) in Hilbert space W_0~(1,2), but the techniques used in the paper[1], was restricted to Hilbert space. In the same year as when [1] had published, we independently proved [2] the     

MULTI-DIMENSIONAL GEOMETRIC BROWNIAN MOTIONS, ONSAGER-MACHLUP FUNCTIONS, AND APPLICATIONS TO MATHEMATICAL FINANCE

1 IntroductionThe solution of the following stochastic differential equationis called the geometric Brownian motion, where a(t), b(t) are deterministic functions of ti ac isa Brownian motion, and ddt is the It6 integral. This equation has been successfully applied tothe financial problems such as modeling the prices of stocks, sc.e for example, [81, [7], [14], [13],[19], [21]. When the initial condition is given, i.e. xo = x, the solution isIt is known that in the financial market, it is als…     

INFINITE ELEMENT METHOD FOR THE EXTERIOR PROBLEMS OF THE HELMHOLTZ EQUATIONS

1. IntroductionThe infinite element method has been successfully applied to some boundary valueproblems of partial differential equations, where the solutions possess corner singularpoints or the domains are exterior ones. If the equations are invariant under similaritytransformation the approaches have been given in [11] [131 for singular solutions, and in[12][15][181119] for the exterior problems. If the equations do not admit the above invariant property? one approach has been given in [14]…     

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.     

Applications of the Bernstein-Durrmeyer operators in estimating the norm of Mercer kernel matrices

The paper is related to the norm estimate of Mercer kernel matrices.The lower and upper bound estimates of Rayleigh entropy numbers for some Mercer kernel matrices on[0,1]×[0,1]based on the Bernstein-Durrmeyer operator kernel ale obtained,with which and the approximation property of the Bernstein-Durrmeyer operator the lower and upper bounds of the Rayleigh entropy number and the l2-norm for general Mercer kernel matrices on[0,1]×[0,1]are provided.     

Predictor-Corrector Smoothing Methods for Monotone LCP

In this paper, we analyze the global and local convergence properties of two predictor-corrector smoothing methods, which are based on the framework of the method in [1], for monotone linear complementarity problems (LCPs). The difference between the algorithm in [1] and our algorithms is that the neighborhood of smoothing central path in our paper is different to that in [1]. In addition, the difference between Algorithm 2.1 and the algorithm in [1] exists in the calculation of the predictor step. Comparing with the results in [1],the global and local convergence of the two methods can be obtained under very mild conditions. The global convergence of the two methods do not need the boundness of the inverse of the Jacobian. The superlinear convergence of Algorithm 2.1‘ is obtained under the assumption of nonsingularity of generalized Jacobian of Φ(x,y) at the limit point and Algorithm 2.1 obtains superlinear convergence under the assumption of strict complementarity at the solution. The efficiency of the two methods is tested by numerical experiments.     

RADIUS OF STARLIKENESS FOR THE CLASS S(α,n)

In this paper we shall investigate the bound of starlikeness r for the classS(α, n) in [1]. We obtain the following sharp result:where α_0 is the unique solution of the equationα[1+(1-2α)r~(2n)]/1-r~(2n)={1-(1-2α)r~n/1+r~n}~2with respect to α in the open interval (0, 1). This result is also the extension of somewell-known ones in [2], [3, Theorem 1] and [4, Theorem 2]     

Stability of Fredholm Integral Equation of the First Kind in Reproducing Kernel Space

It is well known that the problem on the stability of the solutions for Fredholm integral equation of the first kind is an ill-posed problem in C[a,b] or L2[a,b].In this paper,the representation of the...     

THE SUPER-BIHAMILTONIAN REDUCTION ON C~∞(S~1, OSP(1|2))

In this article, we will show that the super-bihamiltonian structures of the Kuper- KdV equation in [3], the Kuper-CH equation in [17, 18] and the super-HS equation in [11, 16, 19] can be obtained by applying a super-bihamiltonian reduction of different super-Poisson pairs defined on the loop algebra of osp（1｜2）.     

三次系统的蚶形曲线分界线环(英文)

The fol1owing eight kinds of algebraic curves al1 can be the algebraic se-paratrix cycle containing focus for quadratic system, they are the lune fOr-med by hyperbola and equatorial arc['], the entire parabola['], the heterocIinicorbits formed by parabola and straight lineI3], the non-return mapping sepa-ratrix cycle formed by entire e1lipse['], the homoc1inic orbits of cubic curvey' -- 4xs + 3x -- 1 = 0['], the homoc1inic orbits or the non-return mappingseparatrix cycle forrned by quartic cur…     

SOME REMARKS ON THE NULL CONDITION FOR NONLINEAR ELASTODYNAMIC SYSTEM

The author derives the same null condition as in[1]for the nonlinear elastodynamic systemin a simpler way and proves the equivalence of the null conditions introduced in[1]and[7]respectively.