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.     

RESOLUTION OF SINGULARITY AND OSCILLATORY INTEGRAL(Ⅰ)

Oscillatory integral such as ∫_(B~2) e~((itf)(x))g(x)dx is studied and asymptotic behavior of theoscillatory integral is obtained.The phase f(x)is analytic and has only isolated criticalpoint in B~2,while g(x)is smooth and compactly supported in B~2.     

THE KERNELS OF PRODUCT TYPE ON LOCAL FIELDS(Ⅱ)

In paper[4],the kernel of product type on θ is introduced.It was shown in[4]that λ_n(x;r;s)is an approxi-mate identity.The purpose of this paper is to prove the directand inverse approximation theorems for the singular integral     

ON GENERALIZED LIENARD EQUATION AND THE UNIQUENESS OF LIMIT CYCLES IN GAUSS－TYPE PREDATOR－PREY SYSTEM

ＯＮＧＥＮＥＲＡＬＩＺＥＤＬＩＥＮＡＲＤＥＱＵＡＴＩＯＮＡＮＤＴＨＥＵＮＩＱＵＥＮＥＳＳＯＦＬＩＭＩＴＣＹＣＬＥＳＩＮＧＡＵＳＳ－ＴＹＰＥ　ＰＲＥＤＡＴＯＲ－ＰＲＥＹ　ＳＹＳＴＥＭＳｈａｏＭｉｎｇｈｕａ（邵明华）（ＨａｎｇｚｈｏｕＴｅａｃｈｅｒｓ＇Ｃ...     

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.     

ON THE RELATION BETWEEN THE METHODS(C,α)AND(A,n,p)OF SUMMABILITY OF SERIES

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ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

1.IntroductionRecentlythestudyofdiscontinuoussolutionforthesystemofconservationlawsinhigherdimensionalspacehasbeenconsiderablydeveloped.In[1,W12]thelocalekistenceof8olutionforsuclisystemwithdiscontinuityinvolvingsingleshock,rarefactionwaveorsoundwav(gradientwave)hasbeenestablished.In[2Jand[14]theproblemsoninteractionoftwoshocksorinteractionofweaksingularitiesarealsoconsidered.Itisnaturaltoaskwhatabouttheresultwhenashockisinteractedbyawavewitliweakersillgularities,particularly,forthenbynsystem…     

ON THE RELATIVE POSITION OF LIMIT CYCLES FOR THE EQUATION OF TYPE(Ⅱ)τ=0

In this paper,we consider the relative position of limit cycles for the system(dx)/(dt)=δx-y mxy-y~2,(dy)/(dt)=x-ax~2, (1)under the conditiona<0,0<δ≤m,m≤1/a-a.(2)The main result is as follows:(i)Under Condition(2),if δ=m/2 m~2/(4a)≡δ_0,then system(1)_(δ_0)has no limit cycles andon singular closed trajectory through a saddle point in the whole plane.(ii)Under condition(2),the foci O and R'cannot be surrounded by the limit cyclesof system(1)simultaneously.     

LOCAL WELL-POSEDNESS AND ILL-POSEDNESS ON THE EQUATION OF TYPE □u= u~k(u)~α

This paper undertakes a systematic treatment of the low regularity local well-posedness and ill-posedness theory in H3 and Hs for semilinear wave equations with polynomial nonlinearity in u and (?)u. This ill-posed result concerns the focusing type equations with nonlinearity on u and (?)tu.     

THEORY OF INTERPOLATION ON INFINITE INTERVAL—Ⅰ(UNIFORM CONVERGENCE OF STABLE INTERPOLATION PROCESSES)

§1. Preliminaries and Results Let us begin by defining a triangular matrix L whose n-th row consists of n distinct points x_(vn), v=1, n; n=1, 2, … such that 0相似文献   

SINGULAR INTEGALS IN SEVERAL COMPLEX VARIABLES(Ⅳ)——THE DERIVATIVE OF CAUCHY INTEGRAL ON SPHERE

The aim of this paper is to study the boundary properties of the derivative of Cauchyintegral on the sphere.Using the concept of the Hadamard principal value of singularintegral of higher order introduced in [I],the author obtains the corresponding Plemeljformula expressed by Hadamard principal value.     

ON THE TRANSFORMATIONS OF THE POTENTIALS,INTEGRABLE EVOLUTION EQUATIONS AND B(A|¨)CKLUND TRANSFORMATIONS

The generalization of the AKNS method,Calogero method and Konopelchenkomethod is given in three respects,First,the new fundamental relations associated with thematrix spectral problem and a new explicit expression related to the matrixes B and Cwhich are contained in the transformations of the transition matrixes are obtained.Thenthe wide classes of the integrable evolution equations are conveniently derived withoutimproperly assuming B=C.Finally,an important property of the operator L_A is showed,the conditions connected with the temporal half of the B(a|¨)cklund transformations and thenew simple expressions of the integrals of motion are deduced.     

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     

ON THE CROSSING NUMBER OF THE COMPLETE TRIPARTITE GRAPH K_(1,8,n)

The well known Zarankiewicz' conjecture is said that the crossing number of the complete bipartite graph Km,n (m≤n) is Z(m,n). where Z(m,n) = [m/2] [(m-1)/2] [n/2] [(n-1)/2](for and real number x, [x] denotes the maximal integer no more than x). Presently, Zarankiewicz' conjecture is proved true only for the case m≤G. In this article, the authors prove that if Zarankiewicz' conjecture holds for m≤9, then the crossing number of the complete tripartite graph K1,8,n is Z(9, n) 12[n/2].     

A THEOREM ON THE 1-FACTORS OF (m, n)-TREES

In this paper a necessary and sufficient condition for a (m, n)-tree to have a 1-factor is given. Tutte's theorem in which the given graph is a tree is generalized.     

REGULARITY AND EXPLICIT REPRESENTATION OF (0,1,…,m - 2,m) INTERPOLATION ON THE ZEROS OF (1-x)P_(n-1)~(α,β)(x)

A necessary and sufficient condition of regularity of (0,1,…,m - 2,m) interpolation on the zeros of (1-x)P_(n-1)~(α,β)(x) (α> -1,β≥- 1) in a manageable form is established, where P_(n-1)~(α,β)(x) stands for the (n-1)th Jacobi polynomial. Meanwhile, the explicit representation of the fundamental polynomials when they exist, is given.     

REGULARITY OF (0,1,…,r-2,r)INTERPOLATION ON THE UNIT CIRCLE

The object of this paper is to show regularity of(0,1,...,r-2,r) interpolation on the set obtained by projecting vertically the zeros of (1-x2)pn(x)(λ≥1/2)onto the unit circle,where Pn(x)stands for the nth ultraspherical polynomial.     

THE BOUNDEDNESS OF BO CHNER-RIESZ MEANS B_R~δ(f)ON THE SPACES■_p~(α,q)

Let 0J-2/n+1-min{α,0},where J=n/min{p,q}.The above results cann't be improved,if α≥0 and p≤q.     

PROPER SPLITTINGS FOR RESTRICTED LINEAR EQUATIONS AND THE GENERALIZED INVERSE A_(T,S)~2

This paper presents a proper splitting iterative method for comparing the general restricted linear euqations Ax=b, x ∈T (where, b ∈AT, and T is an arbitrary but fixed subspace of C~m) and the generalized in A_(T,S) For the special case when b ∈AT and dim(T)=dim(AT), this splitting iterative methverse A_(T,S) hod converges to A_(T,S)b (the unique solution of the general restricted system Ax=bx ∈T).