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15 July 2002, Volume 22 Issue 3 Previous Issue    Next Issue

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M¨|OBIUS INVARIANT GRADIENT AND LITTLE α-BLOCH FUNCTIONS ZHUO Wen-Xin, OU Yang-Cai-Heng Acta mathematica scientia,Series B. 2002, 22 (3):  195-301.  Abstract ( 619 )   RICH HTML PDF (127KB) ( 1070 )   Save In this paper, the authors get the characterizations of the integral and Carleson type measure both associated with the invariant gradient for little -Bloch functions in the unit ball of Cn. As a consequence, some results of Ouyang C H, Yang W S and Zhao R H in [4] and a result of Yang W S in [10] are extended. References | Related Articles | Metrics

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ON AN IDENTITY OF RAMANUJIAN DING Xia-Qi, LUO Pei-Zhu Acta mathematica scientia,Series B. 2002, 22 (3):  289-294.  Abstract ( 614 )   RICH HTML PDF (90KB) ( 870 )   Save In the present paper the authors will give a new proof of the classical Ramanujian identity by the theory of distributions References | Related Articles | Metrics

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EXISTENCE AND DECAY OF WEAK SOLUTIONS TO DEGENERATE DAVEY-STEWARTSON EQUATIONS LI Yong-Sheng, GUO Bo-Ling Acta mathematica scientia,Series B. 2002, 22 (3):  302-310.  Abstract ( 1013 )   RICH HTML PDF (136KB) ( 906 )   Save In this paper, the authors consider a system of degenerate Davey-Stewartson equations. They prove the global existence of weak solutions in some weighted function spaces and the decay of weak solutions in some anisotropic spaces for appropriate initial data. References | Related Articles | Metrics

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A NOTE ON SINGULAR VALUE DECOMPOSITION FOR RADON TRANSFORM IN R^N WANG Jin-Ping, DU Jin-Yuan Acta mathematica scientia,Series B. 2002, 22 (3):  311-318.  Abstract ( 720 )   RICH HTML PDF (128KB) ( 7835 )   Save The singular value decomposition is derived when the Radon transform is restricted to functions which are square integrable on the unit ball in Rn with respect to the weight W(x). It fulfilles mainly by means of the projection-slice theorem.The range of the Radon transform is spanned by products of Gegenbauer polynomials and spherical harmonics. The inverse transform of the those basis functions are given. This immediately leads to an inversion formula by series expansion and range characterizations. References | Related Articles | Metrics

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STABILITY OF THE RAREFACTION WAVE FOR THE GENERALIZED KDV-BURGERS EQUATION WANG Zhi-An, ZHU Chang-Jiang Acta mathematica scientia,Series B. 2002, 22 (3):  319-328.  Abstract ( 782 )   RICH HTML PDF (140KB) ( 1737 )   Save This paper is concerned with the stability of the rarefaction wave for thegeneralized KdV-Burgers equation ut + f(u)x = μuxx + uxxx, μ > 0,  2 R u|t=0 = u0(x) ! u±, x ! ±1. Roughly speaking, under the assumption that u− < u+, the solution u(x, t) to Cauchy problem (1) satisfying supx2R |u(x, t)−uR(x/t)| ! 0 as t ! 1, where uR(x/t) is the rarefaction wave of the non-viscous Burgers equation ut + f(u)x = 0 with Riemann initial data u(x, 0) =(u−, x < 0,u+, x > 0. References | Related Articles | Metrics

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ON THE CONCAVE -INEQUALITIES FOR NONNEGATIVE SUBMARTINGALES MEI Tao, LIU Pei-De Acta mathematica scientia,Series B. 2002, 22 (3):  329-334.  Abstract ( 725 )   RICH HTML PDF (113KB) ( 926 )   Save Let 1,2 be nonnegative nondecreasing functions, and 1 be concave. The authors prove the equivalence of the following two conditions: (i) E1(Mf)  cE2(Z0+A1) for every nonnegative submartingale f = (fn)n0 with it’s Doob’s Decomposition: f = Z + A, where Z is a martingale in L1 and A is a nonnegative incrasing and predictable process. (ii) There exists positive constants c, t0 such that R 1t 1(s) s2 ds  c2(t) t , 8t > t0. When 1 = 2 the condition (ii) above is equivalent to the classical condition p < 1. As a consequence, for a concave function , p < 1 if and only if E1(Mf)  cE2(Z0+A1) for every nonnegative submartingale f. References | Related Articles | Metrics

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ASYMPTOTIC BEHAVIOUR OF EIGENVALUES FOR THE DISCONTINUOUS BOUNDARY-VALUE PROBLEM WITH FUNCTIONALTRANSMISSION CONDITIONS O.Sh.Mukhtarov, Mustafa Kandemir Acta mathematica scientia,Series B. 2002, 22 (3):  335-345.  Abstract ( 776 )   RICH HTML PDF (136KB) ( 1636 )   Save In this study, the boundary-value problem with eigenvalue parameter gener-ated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and abstract linear functionals is investigated. So, the problem is not pure boundary-value.The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence of infinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found. References | Related Articles | Metrics

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ON PSEUDOSYMMETRY TYPE HYPERSURFACES OF SEMI-EUCLIDEAN SPACES I Kadri Arslan, Ryszard Deszcz, Ridvan Ezentas., Cengizhan Murathan, Cihan Ozgur Acta mathematica scientia,Series B. 2002, 22 (3):  346-358.  Abstract ( 798 )   RICH HTML PDF (163KB) ( 1407 )   Save In this paper the authors investigate hypersurfaces M of a semi-Euclidean space En+1 s , n  4, satisfying ( C + R) · H = LkQ(g,Hk), k = 1, 2, 3. Using obtained results they show additional curvature properties of investigated hypersurfaces References | Related Articles | Metrics

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GAUSSIAN WHITE NOISE CALCULUS OF GENERALIZED EXPANSION CHEN Ze-Qian Acta mathematica scientia,Series B. 2002, 22 (3):  359-368.  Abstract ( 622 )   RICH HTML PDF (140KB) ( 1103 )   Save A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators @t and its dual, creation operators @t . References | Related Articles | Metrics

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A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP ZHU Li Acta mathematica scientia,Series B. 2002, 22 (3):  369-378.  Abstract ( 768 )   RICH HTML PDF (133KB) ( 1531 )   Save In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the Lp-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group. References | Related Articles | Metrics

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A VANISHING THEOREM ON L2 HARMONIC FORMS CHEN Zhi-Hua, ZHOU Chao-Hui Acta mathematica scientia,Series B. 2002, 22 (3):  379-387.  Abstract ( 555 )   RICH HTML PDF (128KB) ( 904 )   Save This paper is concernod with the L2 harmonic forms of a complete noncompact Riemannian manifold, i.e. If M has a pole Q, let 0 < p < n 1+p2 or p2n 1+p2 < p < n, and assume the radial section curvatures satisfy −c(1−c) r 2  Kr  c(1−c) 2 on M − {Q}, where 1 > c > (1+p2)p−1 n−1 , then Hp = {0}. If M has a soul, then similar result is obtained References | Related Articles | Metrics

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ON CERTAIN CLASS OF ANALYTIC FUNCTIONS DEFINED BY DIFFERENTIAL SUBORDINATION LIU Ming-Sheng Acta mathematica scientia,Series B. 2002, 22 (3):  388-392.  Abstract ( 679 )   RICH HTML PDF (98KB) ( 1146 )   Save In this paper, the new subclass Bn(, ,A,B) of analytic functions is introduced.Its subordination relations, inclusion relations, the inequality properties andconvering theorem are discussed. The results obtained in this paper are sharp, which generalize the related works of some authors and some other new results are obtained. References | Related Articles | Metrics

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ON THE HOLOMORPHIC SOLUTION OF NON-LINEAR TOTALLY CHARACTERISTIC EQUATIONS WITH SEVERAL SPACE VARIABLES CHEN Hua, LUO Zhuang-Chu Acta mathematica scientia,Series B. 2002, 22 (3):  393-403.  Abstract ( 683 )   RICH HTML PDF (143KB) ( 1190 )   Save In this paper the authors study a class of non-linear singular partial differential equation in complex domain Ct×Cn x. Under certain assumptions, they prove the existence and uniqueness of holomorphic solution near origin of Ct × Cn x. References | Related Articles | Metrics

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COMPOSITION OPERATOR ON BERS-TYPE SPACES HE Wei-Xiang, JIANG Li-Jian Acta mathematica scientia,Series B. 2002, 22 (3):  404-412.  Abstract ( 701 )   RICH HTML PDF (132KB) ( 1262 )   Save Necessary and sufficient conditions are established for a composition operator C'f = f ?' to be bounded or compact on the Bers-type space H1 and the little Bers-type space H1 . The boundedness and compactness of the composition operator C' on A1(') are characterized, which generalize the case of C' on H1 References | Related Articles | Metrics

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BESOV SPACES B ^α,p_p ON DOMAINS AND LAPLACE OPERATORS GUI Yi-Qing, LIU Shan-Tian, YANG Da-Chun Acta mathematica scientia,Series B. 2002, 22 (3):  413-418.  Abstract ( 698 )   RICH HTML PDF (114KB) ( 962 )   Save Let  be a bounded smooth domain. In this paper, the authors define the Besov spaces ˙B ,pp on , establish the atomic decomposition of these spaces, and obtain the regularity estimate of the Dirichlet problem and the Neumann problem for the Laplaceoperator on these spaces. References | Related Articles | Metrics

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KKM TYPE THEOREMS AND COINCIDENCE THEOREMS ON L-CONVEX SPACES DING Xie-Ping Acta mathematica scientia,Series B. 2002, 22 (3):  419-426.  Abstract ( 652 )   RICH HTML PDF (116KB) ( 1074 )   Save Some KKM theorems and coincidence theorems involving admissible set-valued mappings and the set-valued mappings with compactly local intersection property are proved in L-convex spaces. As applications, some new fixed point theorems are obtained in L-convex spaces. These theorems improve and generalize many important known results in recent literature. References | Related Articles | Metrics

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YANG-BAXTER OPERATORS AND TENSOR TRANSFORMATIONS WANG Zhen-Hua Acta mathematica scientia,Series B. 2002, 22 (3):  427-432.  Abstract ( 546 )   RICH HTML PDF (110KB) ( 871 )   Save The author considers relations between Yang-Baxter operators and tensor transformations, and proves that all tensor transformations over the category of modules of a Yang-space form a group References | Related Articles | Metrics