ON THE GENERALIZED BIRTH AND DEATH PROCESSES (Ⅰ)——THE NUMERAL INTRODUCTION,THE FUNCTIONAL OF INTEGRAL TYPE AND THE DISTRIBUTIONs OF RUNS AND PASSAGE TIMES

This paper makes a painstaking discussion for the generalized birth and death processes, describes some properties of processes in fixed quantity: Such as the uniqueness criterion of processes and the distributions of runs and passage times of the generalized birth and death processes which non—recurrent in (I); and stay time,     

ON THE GENERALIZED BIRTH AND DEATH PROCESSES (Ⅱ)——THE STAY TIME, LIMIT THEOREM AND ERGODIC PROPERTY

In this paper we follows [1] to discuss the stay time, limit distribution and ergodic property of the generalized birth and death processes. Here we use the notations involved in [1] besides special exposition.     

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.     

ON THE ACCURACY OF THE QUASICONFORMING AND GENERALIZED CONFORMING FINITE ELEMENTS

It is observed in practice that the numerical accuracy of the two unconventional plate elements, i. e., the nine parameter quasi-conforming and generalized conforming elements, is better than that of the usual Zienkiewicz in compatible cubic element and of a new element proposed recently by Specht, although all these elements have the same asymptotical rate of convergence O(h) in the energy norm. In the paper a careful error analysis for the quasi-conforming and generalized conforming elements is given. It is shown that the consistency error due to nonconformity of the two unconventional elements is of order O(h~2), one order high than that of other conventional nonconforming elements with nine parameters.     

ON THE ESTIMATION OF GENERALIZED LEBESGUE CONSTANT AND MODULUS OF GENERALIZED SINGULAR QUADRATURE FORMULAS AND ITS APPLICATION

This article, first gives the estimaties of two modulus, namely, generalized Lebesgue constant and modulus of generalized singular integral quadrature formulas, then applies them to obtain the error bounds of the operator BLmp to the operator B.     

SIMILARITY TRANSFORMATION, THE STRUCTURE OF THE TRAVELING WAVES SOLUTION AND THE EXISTENCE OF A GLOBAL SMOOTH SOLUTION TO GENERALIZED KURAMOTO SIVASHINSKY TYPE EQUATIONS

The existence of a global smooth solution for the initial value problem of generalized Kuramoto-Sivashinsky type equations have been obtained. Similarty siolutions and the structure of the traveling waves solution for the generalized KS equations are discussed and analysed by using the qualitative theory of ODE and Lie's infinitesimal transformation respectively.     

DECOMPOSITION, REPRESENTATION AND EXTENSION OF THE HARMONIC FUNCTIONS

In this paper, by using the probabilistic method, we obtained a decomposition theorem for the harmonic functions, generalized and strengthened some theorems: Doob's theorem on the limit behaviors of the superharmonic functions, Bocher's theorem on the representation of the harmonic functions and the extension theorem of the harmonic functions etc.     

MATRIX NORM VERSIONS OF THE KANTOROVICH INEQUALITY AND ITS APPLICATIONS

In this paper we discuss the generalizations of the Kantorovich inequality and obtain some generalized Kantorovich inequalities in the sense of matrix norm. We further illustrate how to use these inequalities to determine the lower bound of relative efficiency of the parameter estimate in linear model.     

HUNGARIAN SEMIGROUPS, THE ARITHMETIC OF GENERALIZED RENEWAL SEQUENCES AND SEMI-P-FUNCTIONS

In this paper the authors discuss the additional conditions under which a Hungarian semigroup is possessed of the fundamental Delphic properties. It is proved that both the positive generalized renewal sequence semigroup and the tame semi-p-function semigroup are Hungarian semigroups and possessed of the fundamental Delphic properties. Then the arithmetic properties of these two classes of the special semigroups are studied respectively.     

ON THE CENTER OF GENERALIZED LIENARD SYSTEM

This paper discusses the local and global center of the generalized Lienard system, gives two theorems which extend and improve the relative results of [1]-[3]. Moreover the lemmas in this paper are also useful to the study for the oscillation, stability and the existence of limit cycles of the generalized Lienard system.     

POTENTIALITY AND REVERSIBILITY FOR THE N-SPIN-FLIP PROCESSES AND THE N-GENERALIZED SPIN-FLIP-PROCESSES

The Markov processes with infinite particle system are one of the new branches in probability, recently it is developed rapidly. It relates not only to the statistical physics of balanced state, but also to the statistical physics of the unbalanced state and other subjectst In this paper, two kinds of Markov processes with infinite     

KANTOROVICH-TYPE INEQUALITIES AND THE MEASURES OF INEFFICIENCY OF THE GLSE

In this paper we introduce some Kantorovich inequalities for the Euclidean norm of a matrix,that is, the upper bounds to ‖ (X'B~(-1)X)~(-1)X'B~(-1)AB~(-1)X (X'B~(-1)X)~(-1)A~(-1)X‖~2and to ‖(X'AX)~(-1)X'BX (X'AX)~(-1)X'CX‖~2 are given, where ‖A‖~2=trace(A'A). In terms of these inequalities the upperbounds to the three measures of inefficiency of the generalized least squares estimator (GLSE) ingeneral Gauss-Markov models are also established.     

GENERALIZATIONS OF THE MEAN VALUES AND THEIR INEQUALITIES

Some generalizations of the classical Mean Values and their inequalities are presented inthis paper,using B-spline functions.The new generalized Means can be applied to nonlineardifference schemes for solving O.D.E.and P.D.E.with singularities([6,7,8]).     

ASYMPTOTIC BEHAVIOR OF POSITIVE RADIAL SOLUTIONS FOR THE GENERALIZED EMDEN-FOWLER EQUATION WITH APPLICATION

In this paper, we consider a class of semilinear parabolic differential equation where nonlinear term has local bounded coefficients. Under some assumptions, we get the existence and uniqueness of solution. Terminate to the time variable, we obtain the so called generalized Emden-Fowler equation and the asymptotic behavior of positive radial solutions have been given in all dimensions. At the end of this paper, we give its application to critical branching Brownian motion (also called measure-valued branching processes).     

NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF PERIODIC SOLUTIONS OF RICCATI'S EQUATION WITH PERIODIC COEFFICIENTS

In this paper, the concept of generalized ω-periodic solution is given for Riccati's equationy'=a(t)y~2 b(t)y c(t)with perriodic coefficients, the relation between generalized ω-periodicsolutions and the characteristic numbers of system x'_1=c(t)x_2, x'_2=-a(t)x_1-b(t)x_2 is indicated, andseveral necessary and sufficient conditions are given using the coefficients. Moreover, in the case of a(t)without zero, the relation between the number of continuous ω-periodic solutions of y'=a(t)y~2 b(t)y c(t) δand the parameter δ is given; thus the problem on the existence of continuous ω-periodic.solutions is basically solved.     

THE BIRTH AND DEATH PROCESSES WITH ZERO AS THEIR ABSORBING BARRIER

Let E=(0,1,…),Q~b=(q_(ij)),i,j=0,1,…,where q_(i,i-1)=a_i,q_(i,i+1)=b_i,q_(ii)=-(a_i+b_i),q_(ij)=0,when|i-j|>1.a_0=0,b_0=b>0,a_i,b_i>0(i>0).Letting b=0 in Q~b,we get the matrix Q~0.The time homogeneous Markov process X~b={x~b(t,ω),0≤t<σ~b(ω)}(X~0={x~0(t,ω),0≤t<σ~0(ω)}),with Q~b(Q~0,respectively)as its density matrix and with E as its state space,is called Q~b(Q~0,respectively)process in this paper.Q~b and Q~0 processes are all called the birth and death processes,with zero being the reflecting barrier of Q~b processes,the absorbing barrier of Q~0 processes.All the Q~b processes have been constructed by both probability and analytical methods(Wang [2],Yang[1]).In this paper,the Q~0 processes are“imbedded.”into Q~b processes and all the Q~0 processesare directly constructed from the Q~b processes.The main results are:Let b>0 be arbitrarily fixed,then there is a one to one correspondence between the Q~0 processesand the Q~b processes(in the sense of transition probability).The Q~0 process is uni     

THE STATIONARY DISTRIBUTIONS AND THE STEADY PROBABILITY CURRENTS OF ONEDIMENSIONAL DIFFUSION PROCESSES UNDER NON-LOCAL BOUNDARY CONDITIONS

In the present paper we study the limit distributions of one-dimensional diffusion processes under non-local boundary conditions. We obtain the existence conditions for the non-trivial stationary distributions, get their concrete formulas in all cases according to boundary classification, and give the results of some probability explanations. One-dimensional diffusion processes, which provide a simple mathematical model for studying irreversible steady systems, show that the basic characteristic of an irreversible stationary state is the occurrence of the probability current, i. e. the circulation phenomenon.     

ON THE FRACTAL NATURE OF INCREMENTS OF THE INFINITE SERIES OF OU PROCESSES RELATED TO THE CHUNG LIL

The author proves that the set of points where the Chung type LIL fails for the path of the infinite series of independent Ornstein-Uhlenbeck processes is a random fraetal, and evaluates its Hausdorff dimension.     

ON THE EXISTENCE AND UNIQUENESS THEOREMS OF SOLUTIONS FOR THE SYSTEMS OF MIXED MONOTONE OPERATOR EQUATIONS WITH APPLICATIONS

The existence, uniqueness and non-symmetric iterative approximation of solutions for a class of systems of mixed monotone operator equations are discussed. As an appplication, we utilize the results presented in this paper to study the existence and uniqueness problems of common solutions for a class of systems of functional equations arising in dynamic programming of multistage decision processes and a class of systems of nonlinear integral equations. The results obtained in this paper not only answer an open question suggested in [3] but also generalize the corresponding results of.     

ASYMPTOTIC SOLUTIONS OF THE REDUCED WAVE EQUATION IN THE VICINITY OF A HIGHER CAUSTIC

In this paper the asymptotic solutions of the reduced wave equation (1) in the vicinity of a higher caustic have been found out by means of asymptotic expansions of the generalized Airy function, and the order (or the singularity inder) and the phase's increment of solutions on the higher caustic have been obtained, too.