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07 April 2003, Volume 23 Issue 2 Previous Issue    Next Issue

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GENERALIZED OPERATORS ANDOPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY HUANG Zhi-Yuan, WANG Xiang-Jun, WANG Cai-Shi Acta mathematica scientia,Series B. 2003, 23 (2):  145.  Abstract ( 733 )   RICH HTML PDF (139KB) ( 1005 )   Save The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields. References | Related Articles | Metrics

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A NOTE ON OSCILLATION MODULUS OF PL-PROCESS AND ITS APPLICATIONS UNDER RANDOM CENSORSHIP ZHOU Yong Acta mathematica scientia,Series B. 2003, 23 (2):  155.  Abstract ( 588 )   RICH HTML PDF (127KB) ( 904 )   Save The strong limit results of oscillation modulus of PL-process are established in this paper when the density function is not continuous function for censored data. The rates of convergence of oscillation modulus of PL-process are sharp under week condition. These results can be used to derive laws of the iterated logarithm of random bandwidth kernel estimator and nearest neighborhood estimator of density under continuous conditions of density function being not assumed. References | Related Articles | Metrics

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BOCHNER TECHNIQUE IN REAL FINSLER MANIFOLDS ZHONG Tong-De, ZHONG Chun-Beng Acta mathematica scientia,Series B. 2003, 23 (2):  165.  Abstract ( 1058 )   RICH HTML PDF (149KB) ( 1677 )   Save Using non-linear connection of Finsler manifold M, the existence of local coordinates which is normalized at a point x is proved, and the Laplace operator △ on 1-form of M is defined by non-linear connection and its curvature tensor. After proving the maximum principle theorem of Hopf-Bochner on M, the Bochner type vanishing theorem of Killing vectors and harmonic 1-form are obtained. References | Related Articles | Metrics

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WIDTHS AND AVERAGE WIDTHS OF SOBOLEV CLASSES LIU Yong-Beng, HU Gui-Qiao Acta mathematica scientia,Series B. 2003, 23 (2):  178.  Abstract ( 567 )   RICH HTML PDF (132KB) ( 1098 )   Save This paper concerns the problem of the Kolmogorov $n$-width, the linear $n$-width, the Gel'fand $n$-width and the Bernstein $n$-width of Sobolev  classes of the periodic multivariate functions in the space $L_{\bf p} (T^d)$ and the average Bernstein $\sz$-width, average Kolmogorov $\sz$-widths, the average linear $\sz$-widths of Sobolev classes of the multivariate functions in the space $L_{\bf p}(R^d)$, where ${\bf p}=(p_1,\cdots,p_d),1\le p_j<\infty,  j=1,2,\cdots,d,$ or $p_j=\infty, j=1,2,\cdots,d$. Their weak asymptotic behaviors are established for  the corresponding quantities. References | Related Articles | Metrics

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CONSTRUCTION OF PLURIHARMONIC MAPS INTO COMPLEX GRASSMANN MANIFOLDS CHAO Xiao-Li Acta mathematica scientia,Series B. 2003, 23 (2):  185.  Abstract ( 627 )   RICH HTML PDF (115KB) ( 937 )   Save In this paper, some construction theorems of pluriharmonic maps into complex Grassmann manifolds are obtained. By these, there exists a characterization of strongly isotropic pluriharmonic maps. References | Related Articles | Metrics

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CO-ISOMETRIC SOLUTIONS OF EQUATIONCU + U*C = 2D DU Quan-Beng, HOU Jin-Chuan Acta mathematica scientia,Series B. 2003, 23 (2):  192.  Abstract ( 605 )   RICH HTML PDF (142KB) ( 985 )   Save This note discusses the co-isometric solutions of the operator equation CU + U*C = 2D, establishes a correspondence between such solutions and the self-adjoint so- lutions of the algebraic Riccati equation X^2− iDX + iXD + D^2− C^2 = 0, and gives all possible co-isometric solutions parametrically. Some mistakes of Dobovivsek’s results are corrected. References | Related Articles | Metrics

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THE STRUCTURE AND APPROXIMATION OF A.S. SELF-SIMILAR SET HU Di-He Acta mathematica scientia,Series B. 2003, 23 (2):  201.  Abstract ( 692 )   RICH HTML PDF (110KB) ( 976 )   Save The structure of any a.s. self-similar set $K(\bar{\omega})$ generated by a class of random elements $\{g^{(\bar{\omega})}_{n,\sigma }\}$ taking values in the space of contractive operators is given and  the approximation of  $K(\bar{\omega})$ by the fixed points $\{p^{(\bar{\omega})}_{n,\sigma }\}$ of $\{g^{(\bar{\omega})}_{n,\sigma }\}$ is obtained. It is useful to generate the fractal in computer. References | Related Articles | Metrics

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GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS XU Rui, CHEN Lan-Sun,M.A.J. Chaplain Acta mathematica scientia,Series B. 2003, 23 (2):  208.  Abstract ( 704 )   RICH HTML PDF (129KB) ( 1447 )   Save A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small. References | Related Articles | Metrics

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INERTIAL ALGORITHMS FOR THE STATIONARY NAVIER-STOKES EQUATIONS HOU Ting-Ren, R.M.M. Mattheij Acta mathematica scientia,Series B. 2003, 23 (2):  219.  Abstract ( 688 )   RICH HTML PDF (194KB) ( 919 )   Save Several kind of new numerical schemes for the stationary Navier-Stokes equa- tions based on the virtue of Inertial Manifold and Approximate Inertial Manifold, which we call them inertial algorithms in this paper, together with their error estimations are pre- sented. All these algorithms are constructed under an uniform frame, that is to construct some kind of new projections for the Sobolev space in which the true solution is sought. It is shown that the proposed inertial algorithms can greatly improve the convergence rate of the standard Galerkin approximate solution with lower computing effort. And some numerical examples are also given to verify results of this paper. References | Related Articles | Metrics

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EQUIVALENCE OF kama-HOPF ALGEBRAS SUN Jian-Hua Acta mathematica scientia,Series B. 2003, 23 (2):  239.  Abstract ( 516 )   RICH HTML PDF (113KB) ( 859 )   Save Some basic properties of the antipode of an N0I-graded -Hopf algebra are studied. Also, several equivalent conditions of an N0I-graded -bialgebra (-Hopf algebra) are given. References | Related Articles | Metrics

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ON THE GROWTH OF INFINITE ORDER DIRICHLET SERIES CHEN Te-Wei, SUN Dao-Chun Acta mathematica scientia,Series B. 2003, 23 (2):  247.  Abstract ( 622 )   RICH HTML PDF (92KB) ( 1067 )   Save In this paper, the property of infinite order Dirichlet series in the half-plane are investigated. The more exact growth of infinite order Dirichlet series is obtained without using logarithm argument to the type-function for the first time. References | Related Articles | Metrics

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COMPOSITION OPERATORS FROM B-{\ alpha} TO F(p, q, s) JIANG Li-Jian, HE Yo-Zan Acta mathematica scientia,Series B. 2003, 23 (2):  252.  Abstract ( 689 )   RICH HTML PDF (138KB) ( 1155 )   Save Necessary and sufficient conditions are given for a composition operator $C_{\phi}f=f \circ \phi$ to be bounded and compact from $B^{\alpha}$ to $F(p,q,s)$. References | Related Articles | Metrics

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ASYMPTOTIC BEHAVIOR OF SOLUTION FOR NONLOCAL REACTION-DIFFUSION SYSTEM LI Fu-Cai, CHEN Wei-Peng, XIE Chun-Gong Acta mathematica scientia,Series B. 2003, 23 (2):  261.  Abstract ( 779 )   RICH HTML PDF (153KB) ( 1296 )   Save This paper deals with reaction-diffusion system with nonlocal source. It is proved that there exists a unique classical solution and the solution either exists globally or blows up in finite time. Furthermore, its blow-up set and asymptotic behavior are obtained provided that the solution blows up in finite time. References | Related Articles | Metrics

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SOLVING SECOND ORDER DIFFERENTIAL EQUATIONS IN QUANTUM MECHANICS BY ORDER REDUCTION C. Ted Chen Acta mathematica scientia,Series B. 2003, 23 (2):  274.  Abstract ( 882 )   RICH HTML PDF (156KB) ( 3205 )   Save t Solving the famous Hermite, Legendre, Laguerre and Chebyshev equations requires different techniques of unique character for each equation. By reducing these differential equations of second order to a common solvable differential equation of first order, a simple common solution is provided to cover all the existing standard solutions of these named equations. It is easier than the method of generating functions and more powerful than the Frobenius method of power series. References | Related Articles | Metrics