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25 December 1995, Volume 15 Issue 4 Previous Issue    Next Issue

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ON THE CLASS H1* Xia Mingyuan, Liu Gang Acta mathematica scientia,Series B. 1995, 15 (4):  361-369.  Abstract ( 25 )   RICH HTML PDF (419KB) ( 19 )   Save An infinite family of H1 is obtained, that is,H1(ν)≠∅ for υ ∈ N=N1 ∪ N2 ∪ N3 where N1={5,13,17,25,37,41,61},N2{υ=32r(p1r…pxr)4:p1≡3(mod 4)prime,p1>3,r,r1≥0，i=1,2,…,n;n=1,2,…}，N3={υ1υ2:υ1∈N1 and υ2∈N2}. Using H1(υ),we give 2-(2υ;k1,k2;k1 + k2 -υ} supplementary difference sets with υ=(k1-υ)2 + (k2-υ)2. Finally. we prove that if there exists an orthogonal design OD(4t;t,t,t,t) and H1(υ) ≠∅ then a Hadamard matrix of order 4tυ can be constructed. Related Articles | Metrics

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PERIODIC ORBITS IN PERTURBED GENERALIZED HAMILTONIAN SYSTEMS Zhao Xiaohua, Li Jibin, Huang Kelei Acta mathematica scientia,Series B. 1995, 15 (4):  370-384.  Abstract ( 50 )   RICH HTML PDF (831KB) ( 19 )   Save In this paper, we develop a global perturbation technique for the study of periodic orbits in three-dimensional, time dependent and independent, perturbations of generalized Hamiltonian differential equations defined on three-dimensional Poisson manifolds. We give existence, stability and bifurcation theorems and illustrate our results with a truncated spectral model of the forced, dissipative quasi-geostrophic flow on a cyclic β-plane. Related Articles | Metrics

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α-CARLESON MEASURE AND BLOCH FUNCTIONS ON BOUNDED SYMMETRIC DOMAINS OF Cn Ouyang Caiheng Acta mathematica scientia,Series B. 1995, 15 (4):  385-393.  Abstract ( 42 )   RICH HTML PDF (449KB) ( 20 )   Save In this paper we define α-Carleson measure in the Bergman metric on bounded symmetric domains. Some necessary and sufficient conditions about it and Bloch functions on the domains are given. Related Articles | Metrics

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SMALL PERTURBATION CRAMER METHODS AND MODERATE DEVIATIONS FOR MARKOV PROCESSES Gao Fuqing Acta mathematica scientia,Series B. 1995, 15 (4):  394-405.  Abstract ( 40 )   RICH HTML PDF (606KB) ( 18 )   Save This paper presents a small perturbation Cramer method for obtaining the large deviation principle of a family of measures {μ2,ε> 0} on a topological vector space. As an application, we obtain the moderate deviation estimations for uniformly ergodic Markov processes. Related Articles | Metrics

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GLOBAL EXISTENCE FOR A PARTICULAR INHOMOGENEOUS CONVECTION DIFFUSION SYSTEM Zhu Changjiang, Zhao Huljiang Acta mathematica scientia,Series B. 1995, 15 (4):  406-414.  Abstract ( 18 )   RICH HTML PDF (417KB) ( 24 )   Save This paper considers the Cauchy problem of the following convection diffusion system （vu）t+(1)/2(bu2+2uvau2+2buv+v2)x+（g（u,v）f(u,v)）=ε(vu)xx, with initial data （vu）|t=0=(v0(x)u0(x)). A global existence result is established by employing the techniques of F. B. Weissler and the energy method. Here a,b,ε > 0 are constants. Related Articles | Metrics

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EXACT-VOLUME DIFFERENTIAL FORM DE RHAM COHOMOLOGY AND HAMILTON VARIATIONAL PRINCIPLE Wang Jichun Acta mathematica scientia,Series B. 1995, 15 (4):  415-421.  Abstract ( 38 )   RICH HTML PDF (374KB) ( 22 )   Save In this paper, we suggested exact-volume differential form (for short:EVDF) and proved four theorems correlative with them:1. existence theorem, 2. cohomology theorem,3. constant multiple theorem, and 4. equal gauge theorem. And their application were discussed also. For examlpe, we deduced the particle dynamic equation of the special theory of relativity. At the same time we analyzed and contrasted cohomology theory with Hamilton's variational principle. The contrast showed the superiority of cohomology theory. Moreover,we gave a more complete classification list of differential forms. Related Articles | Metrics

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DECOMPOSITION FOR BERS-ORLICZ SPACES Zhao Ruhan Acta mathematica scientia,Series B. 1995, 15 (4):  422-430.  Abstract ( 16 )   RICH HTML PDF (468KB) ( 20 )   Save In this paper some decomposition theorems for classical weighted Orlicz spaces and Bers-Orlicz spaces are established. As applications of these decomposition theorems some estimates about the growth of the Taylor coefficients of the functions in airs-Orlicz spaces are given. Related Articles | Metrics

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SINGULAR SOLUTIONS FOR A CONVECTION DIFFUSION EQUATION WITH ABSORPTION Zhao Junning Acta mathematica scientia,Series B. 1995, 15 (4):  431-441.  Abstract ( 36 )   RICH HTML PDF (533KB) ( 24 )   Save In this paper we discuss the ekistence and nonexistence of singular solutions for a porous medium equations with convectioll and absorption terms. Related Articles | Metrics

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THE UNIQUENESS AND CONTINUOUS DEPENDENCE FOR CHARACTERISTIC CAUCHY PROBLEM OF PARTIAL DIFFERENTIAL EQUATIONS Luan Wengui, Liu Weixia Acta mathematica scientia,Series B. 1995, 15 (4):  442-457.  Abstract ( 37 )   RICH HTML PDF (827KB) ( 20 )   Save In this paper, we investigate the connection between the uniqueness and the continuous dependence for the Cauchy problem of linear partial differential equations with everywhere characteristic initial hypersurface. The local Carleman's estimate used by S. Alinhac and M. S. Baouendi to prove the uniqueness for the characteristic Cauchy problem is improved to the global estimate with a specific peaking weight factor. Using this estimate, we can prove similarly the uniqueness of the characteristic Cauchy problem. In particular, we derive also the continuous dependence for the solution of this problem in the function class that a certain norm is bounded by the aid of the same inference of proving the global estimate. Related Articles | Metrics

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APPROXIMATION OF GENERALIZED BI-AXIALLY SYMMETRIC POTENTIALS WITH FAST RATES OF GROWTH H. S. Kasana, D. Kumar Acta mathematica scientia,Series B. 1995, 15 (4):  458-467.  Abstract ( 41 )   RICH HTML PDF (506KB) ( 20 )   Save The paper deals with growth and approximation of solutions (not necessarily entire) of certain elliptic partial differential equations. These solutions are called Generalized Bi-axially Symmetric Potentials (GBSP's). The GBSP's are taken to be regular in a finite hyperball and influence of the growth of their maximum moduli on the rate of decay of their approximation errors in sup norm is studied. The authors obtain the characterizations of the q-type and lower q-type of a GBSP H ∈ HR,0 < R < ∞, in terms of rate of decay of approximation error En(H,R0), 0 < R0 <R <∞. Related Articles | Metrics

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MEAN VALUE OF ANALYTIC OPERATOR FUNCTIONS Yu Xiaopei, Jian Ming Acta mathematica scientia,Series B. 1995, 15 (4):  468-473.  Abstract ( 16 )   RICH HTML PDF (301KB) ( 20 )   Save In this paper,it is proved that if A is a normal proper contraction on Hilbert space H and F(z)=U(z)+iV(z) is operator-valued analytic on the unit disc △ and 0 < p < 1,then||F(A)||p ≤ ||F(0)||p+Cp(1-||A||)-2× sup0 < t < 1∬△||U[(At-εI)(I-εA·t)-1]||pdm(ε). Related Articles | Metrics

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ON SOME EXTREMAL PROPERTIES OF ALGEBRAIC POLYNOMIALS Xie Siqing Acta mathematica scientia,Series B. 1995, 15 (4):  474-476.  Abstract ( 42 )   RICH HTML PDF (152KB) ( 22 )   Save Let Pn be an algebraic polynomial of degree n with real coefficients. We study the extremal properties of the integral ∫-11(P"n(x)）2dx and ∫-11(1-x2)(P"n(x)2dx subject to the constraint max-1≤x≤1|Pn(x)|≤1. Related Articles | Metrics