THE BOUNDEDNESS OF INTEGRAL OPERATORS OF A CLASS

Proposition If y(t), b(t) ∈ VDF ∩ VH(μ) ([1]), then||Ky||μ≤q||b||μ||y||μ,(1)where q is a constant and Ky=-b(t)/πi _L0 y(s) (ζ(t))ds.Proof. Let w(t) =1/πi _L_0 y(s)- y(t)/s-t ds and t_1-t_0=h. Suppose a path l = t't_0 U t_0t″, we obtainBy a complicated calculation, it can be got     

A CLASS OF SPHERICAL MATRIX DISTRIBUTIONS

The class of distributions on R~m, 1≤m<∞ which are the m-dimensionalmarginal distributions of orthogonally invariant distribution on R~(m n) wascharacterized by Eaton (1981). In this paper, the class of distributions onR~(m×p), 1≤m<∞ which are the m×p marginal distributions of othogonallyinvariant distribution on R~(m n)×p is characterized.     

BLOW-UP OF A CLASS OF SEMILINEAR PARABOLIC VARIATIONAL INEQUALITIES

In this paper we study the blow-up behavior for a class of semilinear parabolic variational inequalities;whereK = {u ∈L~2(0,T;H_0~1(Ω))|u(x,t)≥ψ(x) a. e. (x,t) ∈Ω×(0,T), u(x,0) = (x)},andis a uniformly elliptic operator.We prove the following main theorem.Theorem Let u(x,t) be a local solution of problem (I),u∈C(0,T;H~2(Ω)∩H_0~1(Q)),u_i∈L~2(0,T;L~2(Ω)), and following conditions are satisfied.(1) There exists a continuously differentiable function G(x,s) and a positive number α,such that     

LYAPUNOV''''S STABILITY ON SOLUTION OF A CLASS OF SYSTEM OF INTEGRO-DIFFERENTIAL EQUATIONS AND APPLICATION IN POPULATION CONTROL WITH ILLNESS

In this paper, we will discuss a class of integro-differential system of equations. It is a mathematicalmodel which is drown from the practical problems of the population control system with illness:where 0 相似文献   

EXTENDING POMPEIU OPERATOR AND THE COMPACTNESS OF SOLUTION SET FOR A CLASS OF HIGHER ORDER PARTIAL DIFFERENTIAL EQUATIONS

This paper discusses chiefly the compactness of solution set of following equationswhere △ is the Laplacian in Sobolev's sense, a;(x),i= 0,1,…n, n≥ 3, are real square matrices of dimen-sion N×V , bounded and measurable in a bounded multiply connected domain Ω, the boundary S is as-sumed to be sufficiently smooth, u(x) is unknown vector, z = (x_1,x_2,…,x_n) Ω R~z,m≥1,|S_1|issuperficial measure of the unit sphere of R~Z, |i|=i_1+ i_2 +… + i., △~m=△(△~(m-1)). ,(Ω), ,(Ω), … denote the classes of vectors or matrices whose elements belong to L,(Ω),W,(Ω),…. A vector or a matrix is said to be continuous differentiable, bounded and measurable if so are its ele-     

A CLASS OF NONHOMOGENEOUS INVERSE RIEMANN BOUNDARY VALUE PROBLEM

ＡＣＬＡＳＳＯＦＮＯＮＨＯＭＯＧＥＮＥＯＵＳＩＮＶＥＲＳＥＲＩＥＭＡＮＮＢＯＵＮＤＡＲＹＶＡＬＵＥＰＲＯＢＬＥＭ￥ＬｉｕＳｈｉｑｉａｎｇ（刘士强）（ＮｉｎｇｘｉａＵｎｉｖｅｒｓｉｌｙ，Ｙｉｎｃｈｕａｎ７５００２１）０ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔ...     

A CLASS OF FIRST ORDER QUASILINEAR PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS TO MATHEMATICAL MODEL FOR MYOPIA ILLNESS

At present, the myopia illness of the students (including the students of university, middle schools andprimary schools) is a serious problem. For preventing and curing it, we must search for the developing lowsof myopia illness to provide the theory foundation for researches on and preventions from myopia illness.We provide the mathematial model on describing the poor eyesight of the students after analysing thedeveloping lows of the poor eyesight of the students as follows:where p(r,t) is the student's myopia falling ill rate function at time t and age r, u(r) denotes the initial stagemyopia falling ill rate function and v(t), the baby myopia falling ill rate function. It is a first order quasi-     

A CLASS OF BOUNDARY VALUE PROBLEMS OF SINGULARLY PERTURBED EQUATION WITH TURNING POINT

We consider the existence and asymptotic behavior of singularly perturbed boundary value problem;εX″= b(X,t)X′,t ∈(0, 1)(1)X(0) =α, X(1) =β, (2)where, ε>0, is a sufficiently small parameter, b(X,t) is continuous in R×[0,1 ],α,βare prescribedboundary condition, and there is a function X_0(t) satisfying the implicit equation b[X_0(t),t] 0t∈[0,1 ].Boundary value problem in this case is rarely studied by other mathematician, the auther has ever dis-cussed the autonomous equation corresponding the boundary value problem (1),(2). Generally speaking,the solution of the corresponding problem has boundary layer at each end of the time interval [0 ,1] , itsinner solution is commposed by one or several constant function, these constant is the zero point of the au-     

SYNTHESES AND CHARACTERIZATION OF A SERIES OF RARE EARTH BINUCLEAR COMPLEXES

A direct method of obtaining complexes of cobalt with respect to rare earth elements is reported. The total of 14 new compounds which are insoluble in water and general organic media have been synthesized by the reaction of RE(Ac)_3·XH_2O (RE=rare earth elements except for Ce, Pm; X=2, 5, 8) with [H_6CO_2(Gc)_5CS_2] (Gc=~-S_2CNHCH_2CO_2~-) in acetone/ water at room temperature. The complexes having the general formula, [RE_2Co_2(Gc)_5HAcCS_2·XH_2O], were characterized by elemental analyses, infrared spectra, DSC and TGA.     

A COMPARATIVE STUDY OF CHINESE AND AMERICAN COTTONS

Thirty-six Chinese cottons were investigated for their physical properties using ASTM stand-ard test methods. Conventional methods using stelometer, fibrograph, and micronaireinstrumentation provided physical properties of tenacity, elongation, length, and fineness. Varietaland regional variations were examined. The Chinese cottons were compared with upland varietiesof American cottons grown across the country. In general, American cottons were stronger, butperhaps a little shorter than Chinese cottons. American cottons were no more mature on the aver-age, and they had lower elongations than did the Chinese cottons. The American cottons alsotended toward higher length uniformity than those varieties grown in China. High yarn strengthwas strongly favored by American cottons.