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26 April 1997, Volume 17 Issue 2 Previous Issue    Next Issue

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Global Exisence of Classical Solution to the Nonlinear Wave Equations Qin Yuming Acta mathematica scientia,Series A. 1997, 17 (2):  121-128.  Abstract ( 71 )   RICH HTML PDF (457KB) ( 67 )   Save In this paper the existence and uniqueness of global Classical solution to the cauchy problem for the wave equation to uu-△u=F(u, Du) are proved. Moreover, the decaying esimates of every terms u,Du,D2u appearing in the equation are obtained, which arethe same as the corresponding homogeneous equation. The results of this paper supplementsthe results in[4] where F does not contain u explicitly. Related Articles | Metrics

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Coherent States of q-Deformed Oscillator and its Applications to SUq(3) Yang Yaping, Yu Zurong Acta mathematica scientia,Series A. 1997, 17 (2):  129-133.  Abstract ( 59 )   RICH HTML PDF (268KB) ( 78 )   Save Some of sighificant properties of coherent states of q-deformed oscillator are discussed. The coherent states of SUq(3) are constructed by using the realization of q-deformedoscillator of quantum algebra SUq(3). Related Articles | Metrics

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Appromaxlmation and Convergence of a Class of Hyperbolic Inverse Problem Liu Jijun, Wang Yuanming Acta mathematica scientia,Series A. 1997, 17 (2):  134-144.  Abstract ( 56 )   RICH HTML PDF (694KB) ( 151 )   Save This paper deals with the impedance inverse problem arising in the seismic geophysics. By spline theory, we approximate the infinite dimensional inverse problem by a problem in the finite dimensional space. With the aid of semi-group theory, we prove that the solution of apprximate problem converges the solution of original inverse problem. Related Articles | Metrics

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Harmonic Functions and Conditioned Brownian Motion in an Angular Domaln Yin Chuancun Acta mathematica scientia,Series A. 1997, 17 (2):  145-151.  Abstract ( 65 )   RICH HTML PDF (396KB) ( 67 )   Save Let Amd={x1,…,xd)∈Rd:x1>0,…,xm>0,1 ≤ m ≤ d} be the angular domain in Rd(d≥2). In this paper we obtain the Martin's representation of positive harmonic functions in Amd,the relationship between the minimal harmonic functions and a zero-one law for conditioned Brownian motion are investigated, the representaive forms of the minimal harmonic functions in Amd are also presented. Related Articles | Metrics

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Melnikov Function and Application in Supercritical Cases Zhang Jianwen, Li Qingshi Acta mathematica scientia,Series A. 1997, 17 (2):  152-162.  Abstract ( 63 )   RICH HTML PDF (545KB) ( 62 )   Save This paper deduces the formula of the third order Melnikov function. the relativc positions of the stable manifold and unstable manifold of the systems in electrical engineering are determined in supercritical cases, We make a comparison between the formulae of thesecond order Melnikov functions in[2] and[4] from studying of toral van der Pol equations)and find that the second order and the nth order formulae in[2] are wrong. Finaly,we correct this mistake. Related Articles | Metrics

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The Completeness of Generalized Eigenfunction System of the Transport Operator for a Nonhomogeneous Convex Medium Xu Genqi, Yang Mingzhu, Wang Shenghua Acta mathematica scientia,Series A. 1997, 17 (2):  163-169.  Abstract ( 57 )   RICH HTML PDF (409KB) ( 67 )   Save The completeness of generalized eigenfunction system of the transport operator for a nonhomogeneous convex medium is discussed in this paper. By terms of the relative convergent method we recreat, we give a complete characterization for the problem of the completeness of generalized eigenfunction system of the transport operator. We show that if 0∈Pσ(E(t)), where {E(t) ≥ 0 is transport semigroup, then generalized eigenfunction system of transport operator is not complete. if O∉Pσ(E(t)), then the generalized eigenfunction system is complete only and only if it satisfies the condition of relative convergence. Related Articles | Metrics

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Penalization Method for Optimal Control of Parabolic Problems with State Constraints Gong Liutang, Fei Pusheng Acta mathematica scientia,Series A. 1997, 17 (2):  170-175.  Abstract ( 64 )   RICH HTML PDF (291KB) ( 92 )   Save In this paper,we discuss a class of optimal control systems governed by parabolic evolution equations with pointwise state constraints, through the perturbation of the op timal control problem, we get the necessary condition which the state variables and control variables are choosen independently. Related Articles | Metrics

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Some Researches of Shannon-Mcmillan Theorem(Ⅱ) Liu Wen, Yang Weiguo Acta mathematica scientia,Series A. 1997, 17 (2):  176-183.  Abstract ( 88 )   RICH HTML PDF (458KB) ( 20 )   Save In this paper, a class of small-devitions theorems for the relative entropy densities of the sequence of arbitrary random variables are discussed by comparing between the sequence of arbitrary distributions and the seqence of independent distributions. As corollaries, some Shannon-Mcmillan theorems are obtained and some results for the discrete information source which has been obtained by authors before are extended. Related Articles | Metrics

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The Spherical Functions and Fourier Transform on SL(2, R) Shu Lisheng Acta mathematica scientia,Series A. 1997, 17 (2):  184-191.  Abstract ( 58 )   RICH HTML PDF (466KB) ( 13 )   Save In this paperi We will study some propcrties of spheri-cal functions on G=SL(2,R). By Virtue of these, we obtain that for each γ∈ Ǧ*, there exists a f∈Cc∞(G)such that f(γ) ≠ 0. This result plays an important role in Fourier transform on SL(2,R). Related Articles | Metrics

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A Generalization of the Poincaré-Cartan Invarian and Dirac's Conjecture Li Ziping, Tang Taiming Acta mathematica scientia,Series A. 1997, 17 (2):  192-199.  Abstract ( 60 )   RICH HTML PDF (521KB) ( 50 )   Save We generalize Poincaré-Cartan integral invariant to a system with a singular higher-order Lagrangian which depends on time t explicitly, this invariant connected with the canonical equations and canonical transformation for the generalized constrained Hamiltonian system is studied. The connection between this invariant and Dirac's conjecture is discussed.An example shows that Dirac's conjecture fails for a system with a singular higher-order LagranJian. Related Articles | Metrics

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Poisson Operators and Generalized Carleson Measure on Spaces of Homogeneous Type Liu Lanzhe Acta mathematica scientia,Series A. 1997, 17 (2):  200-206.  Abstract ( 67 )   RICH HTML PDF (379KB) ( 34 )   Save In this paper,some generalized Carleson measure and Poisson potential operators on sppaces of homogeneous type are defined, the boundedness of the operators on Lp、Hp Tent and Lorentz spaces are cbtained. Related Articles | Metrics

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Descripency of Uniform Desingn Sampling Wang Zhaojun, Zhang Runchu Acta mathematica scientia,Series A. 1997, 17 (2):  207-217.  Abstract ( 87 )   RICH HTML PDF (593KB) ( 82 )   Save This papcr provcs that the dcsripcncy ordcr of uniform dcsign sampling and randomizcd uniform design id O(n-1(ln n)d). At last the simulation results are given. Related Articles | Metrics

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The Representation of the Multicomponent q Coherent States for the Quantum Algebra SUq(4) He Huiyong, Li Guanghua Acta mathematica scientia,Series A. 1997, 17 (2):  218-224.  Abstract ( 68 )   RICH HTML PDF (382KB) ( 128 )   Save The rnulticompomponent q coherent states of SUq(4) are presented. The representation of the density operator in this multicomponent q coherent state space and inhomogeneous differential realization of the generators is discussed. Related Articles | Metrics

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Reconstructing Properties of Neighborhood Pseudo-similar Vertices Xie Litong, Liu Guizhen Acta mathematica scientia,Series A. 1997, 17 (2):  225-228.  Abstract ( 55 )   RICH HTML PDF (263KB) ( 83 )   Save Let G be a simple connected graph and let v be any vertex of G. In this paper it is proved that the number of neighborhood pseudo-similar vertices of v in G is reconstructed. Furthermore, some open problems are presented. Related Articles | Metrics

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Measures and Martingales on Infinite State Spaces Chen Zeqian Acta mathematica scientia,Series A. 1997, 17 (2):  229-234.  Abstract ( 44 )   RICH HTML PDF (381KB) ( 69 )   Save The Radon-Nikodym theorem and Riesz representation theorem on infinite state spaces are built. Then we introduce the notion of measure-valued martingales. The measure-valued martingales are different from the usual vector-valued inartingales and can be applied to superprocesses. Related Articles | Metrics

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On Boundedness of a Class of Singular Integral Operator in Banach-Valued Hardy Space Wei Dan Acta mathematica scientia,Series A. 1997, 17 (2):  235-240.  Abstract ( 63 )   RICH HTML PDF (295KB) ( 135 )   Save This paper gives the boundedness of a class of singular integral operator in Banach-valued Hardy space HB1(Rn). Related Articles | Metrics