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22 June 2004, Volume 24 Issue 3 Previous Issue    Next Issue

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Multi soliton Solutions of the mKdV-SineGordon Equation ZHANG Da-Jun, DENG Shu-Fang, CHEN Deng-Yuan Acta mathematica scientia,Series A. 2004, 24 (3):  257-264.  Abstract ( 1861 )   RICH HTML PDF (353KB) ( 1247 )   Save The bilinear equation and Backlund transformation for the mKdV-SineGordo n equation are given. The multi soliton solutions are obtained through Hirota's method, bilinear Backlund transformation and Wronskian technique. The uniformity of these solutions are shown. References | Related Articles | Metrics

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Quenching for a Nonlinear Degenerate Parabolic Equation with Time Delay CHEN You-Peng, XIE Chun-Hong Acta mathematica scientia,Series A. 2004, 24 (3):  265-274.  Abstract ( 1640 )   RICH HTML PDF (394KB) ( 1265 )   Save This paper deals with the initial boundary valu e problem of a nonlinear degenerate parabolic equation with time delay.The method of regularization and the technique of upper and lower solutions are employed to show the local existence and the continuation of the positive classical solution of the above problem.The global existence and finite time quenching are discussed, and the critical length is established.The location of the uenching points and the estimates of the quenching rate for the special case of f(u) are obtained. References | Related Articles | Metrics

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A New Sequential Systems of Linear Equations Algorithm Without Strict Complementary Slackness GAO Zi-You, Ren Hua-Ling, HE Guo-Ping Acta mathematica scientia,Series A. 2004, 24 (3):  275-284.  Abstract ( 1955 )   RICH HTML PDF (394KB) ( 1396 )   Save In this paper, a new algorithm of sequential systems of l inear equations (SSLE) with arbitrary initial point is proposed by constructing  a special active constraints set. Only one or two systems of linear equations wi th the same coefficient matrix are solved per iteration. The algorithm is global ly convergent. It worths to point out that the algorithm still has one steps uperlinear convergence under some weaker assumptions, for instance, without the s trict complementary slackness condition. References | Related Articles | Metrics

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An Asymptotic Strong Duality |Method for Integer Programming WANG Wei, XU Yi-Fan Acta mathematica scientia,Series A. 2004, 24 (3):  285-292.  Abstract ( 1287 )   RICH HTML PDF (359KB) ( 1636 )   Save Although the Lagrangian method is a powerful dual search method in integer programming, it often fails to identify the optimal solution of the prim a l problem. In this paper, a quasi dual formulation is proposed for bounded integ er programming. This formulation possesses an asymptotic strong duality property and guarantees a success for identifying an optimum solution. Its another f eatu re is that no actual dual search is needed when the parameters of the method are  set to be suitable. References | Related Articles | Metrics

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The Singular Value Decomposition for Generalized Radon Transforms |in R^n WANG Jin-Ping Acta mathematica scientia,Series A. 2004, 24 (3):  293-298.  Abstract ( 1518 )   RICH HTML PDF (341KB) ( 1299 )   Save The singular value decompositions for the generalized Radon transforms are constructed when they are restricted to function spaces which are square integrable on R^n with known weight function W_n, some results about inverse transforms of the generalized Radon transforms are given.Furthermore, the inversion formulae and characteristics of their ranges are also developed. References | Related Articles | Metrics

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On the Existence of Fixed Points for Asymptotically Nonexpansive Type Semigroups in Banach Spaces ZENG Liu-Chuan Acta mathematica scientia,Series A. 2004, 24 (3):  299-306.  Abstract ( 2095 )   RICH HTML PDF (374KB) ( 1101 )   Save Let  C be a nonempty weakly compact convex subset of a Banach space X with weak uniform normal structure. Let T={T(t):t∈S} be an asymptotically nonexpansive type semigroup for which each T(t) is continuous on C. It is shown that the following conclusions hold: (i) if X is uniformly convex then F(T) is nonempty; (ii) if T={T(t):t∈S} with liminf_{t→∞,t in S}|‖T(t)‖|<+∞ is weakly asymp totically regular on C then F(T) is nonempty, where |‖T(t)‖| is the exact Lipschitzian constant of T(t), and F(T) is the set of all common fixed points of T(t),t∈S. References | Related Articles | Metrics

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Positive Solutions for Secondorder mPoint \=Boundary Value Problems of Robin Type MA Ru-Yun Acta mathematica scientia,Series A. 2004, 24 (3):  307-318.  Abstract ( 2082 )   RICH HTML PDF (379KB) ( 1217 )   Save Let a∈C［0,1］, b∈C(［0,1］,(-∞, 0)).Let \-1(t) be the unique positive solution  of the linear problemu″+ a(t)u′+b(t)u=0 ,\=u′(0)=0, u(1)=1 .The author studies the existence of positive solutions for the nonhomogeneous mpoint boundary value problemu″+ a(t)u′+b(t)u+h(t)f(u)=0, \=u′(0)=0, u(1)-∑[DD(]m-2[]i=1[DD)]α\-i u(ξ\-i)=d,where d is a parameter, ξ\-i∈(0,1) and α\-i∈(0,∞)  are given constants satisfying∑[DD(]m-2[]i=1[DD)]α\-i\-1(ξ\-i) <1,i∈{1,\:,m-2}.Under suitable conditions, the author shows that there exists a positive number d\+* such that the problem has at least one positive solution for 0<d<d\+* and no positive solution for d>d\+*. References | Related Articles | Metrics

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Some Anzahl Theorems of Alternate Matrices \=over \$Z/p\+kZ\$ and its Application  TUN Tan, NA Ji-Zhu Acta mathematica scientia,Series A. 2004, 24 (3):  319-328.  Abstract ( 1498 )   RICH HTML PDF (388KB) ( 1259 )   Save Let \$W\-m(R)\$  be the set of alternate matrices over \$Z/p\+kZ\$ with order  \$m\$, where \$m≥2,p\$ is aprime and \$k>1\$. By determining the normal form of alternate matrices over\$Z/p\+kZ,\$ the compute \$n(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])\$  and the number of the orbits of \$W\-m(R)\$, where \$W(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])\$   denotes the set of all the alternate matrices with order \$m\$ and the invariant factors of them are \$(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)]),\$  and  \$(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:,\{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)])\$ denotes the number of elements in  \$W(2r,2t,\{r\-1,\:,r\-1\}[TXX}][DD(X]s\-1[DD)],\:, \{r\-l,\:,r\-l\}[TXX}][DD(X]s\-l[DD)]), ∑[DD(]l[]i=1[DD)]s\-i=t. \$ Furthermore, using the normal form of alternate matrices, the authors construct a Cartesian authentication code and compute the parameters of Cartesian authentication code. References | Related Articles | Metrics

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Existence of Global Weak Solution and Stabilityof a Class Nonlinear Evolution Equation ZHANG Hong-Wei, HE Jing-Yang Acta mathematica scientia,Series A. 2004, 24 (3):  329-336.  Abstract ( 1909 )   RICH HTML PDF (358KB) ( 1418 )   Save In this paper the initial boundary value problem for the nonlinear evolution equation (｜ut｜r-2ut)t-Δu-ρ(t)Δut=f(u)is considered. The existence of global weak solution and the stability are proved. References | Related Articles | Metrics

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Equivalence and Extension of (Co)reflexivity and Their Applications BO Qiang-Nian Acta mathematica scientia,Series A. 2004, 24 (3):  337-341.  Abstract ( 1182 )   RICH HTML PDF (321KB) ( 1172 )   Save Equivalence and extension are  studied. Main results are as follows: (1) core flexility and reflexivity are equivalent as categories. (2) corefle xivity and reflexivity are extensionable. These are used to generalize and simplify some works of ［1-4］ Related Articles | Metrics

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A new analytic slotion for matrix eqation AV+BW=EVF ZHANG Biao, DUAN An-Ren Acta mathematica scientia,Series A. 2004, 24 (3):  342-347.  Abstract ( 1638 )   RICH HTML PDF (314KB) ( 1538 )   Save References | Related Articles | Metrics

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The Solution of Singular Integral Equations with a Translation on the Line HU Yong-Jia, DU Jin-Yuan Acta mathematica scientia,Series A. 2004, 24 (3):  348-353.  Abstract ( 1502 )   RICH HTML PDF (331KB) ( 1162 )   Save The paper discusses the solution of singular integral equations with a real or complex translation on the real axis. The uniqueness of the solution isobtained and the solvable conditions are given. References | Related Articles | Metrics

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Existence and Uniqueness of Positive Solutions for a Class ofElliptic Problems  DAN Qi-Kang Acta mathematica scientia,Series A. 2004, 24 (3):  354-361.  Abstract ( 1392 )   RICH HTML PDF (344KB) ( 1209 )   Save In this paper, the author studies the existence and uniqueness of positive solutions for the quasilinear elliptic problem\$\$u|\-\{Ω=0: -div［(d+|u|\+2)\+\{〖SX(〗p〖〗2〖SX)〗-1u］=λ\-1u\+\{p-1+g(x,u)〓 x∈Ω,\$\$where \$Ω\$ is a bounded domain in \$R\+N,λ\-1\$ is the firsteigenvalue of \$△\-P\$ on \$Ω\$ subject to zero Dirichlet boundary conditions, and \$g(x,t)\$satisfies the growth condition \$ lim[DD(X]t→+∞[DD)]〖SX(〗g(x,t)〖〗t\+\{p-1〖SX)〗=0, p>1, 0≤d<+∞.\$ References | Related Articles | Metrics

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Comparations of stochastic decisions YAN Zai-Zai, NIE Zan-Kan Acta mathematica scientia,Series A. 2004, 24 (3):  362-368.  Abstract ( 1700 )   RICH HTML PDF (352KB) ( 926 )   Save There have been many alternativerandomized response strategies for implementing survey on sensitive question so far. And most of these strategies have improved survey efficiency by choosing approprite design parameters. However, two different procedures with common design parameter values are of diferent  protection degree to the respondents. Some earlier comparisons of those strategies are unfair  because those comparisons do not provide the same degree of protection to the respondents in the two models. In this paper, theauthors compare exactly the efficiency of some earlier strategies under same protection degree to respondents.  The obtained results show that these earlier randomized response strategies must be  reevaluated. References | Related Articles | Metrics

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A Note on the Polysums of Rooted Bitrees HAO Rong-Xia, LIU Pan-Pei, HE Wei-Li Acta mathematica scientia,Series A. 2004, 24 (3):  369-374.  Abstract ( 1388 )   RICH HTML PDF (323KB) ( 1175 )   Save In this paper, the chrosum equation of rooted bitrees with the valency of rooted vertex, the number of isthmus and the number of loops is gotten, and also the authers  present the explicit formulae for such maps with up to above three parameters and their degenerating cases. References | Related Articles | Metrics

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Schatten Class of Small Hankel Operators \=on Weighted Bergman Spaces LIU Yong-Min Acta mathematica scientia,Series A. 2004, 24 (3):  375-380.  Abstract ( 1444 )   RICH HTML PDF (324KB) ( 1178 )   Save The  small Hankel operators on weighted Bergman spaces  of bounded symmetric domains Ω in  C\+n with symbols in  L\+2(Ω, dV\-λ) are studied. Characterizations for the membership in the  Schatten  classes  of the small Hankel operators   h\-Φ  are presented in  terms of a certain integral transform of the symbol Φ. References | Related Articles | Metrics

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The Exponent Set of Primitive Simple Hypergraphs MIAO Zheng-Ke Acta mathematica scientia,Series A. 2004, 24 (3):  381-384.  Abstract ( 1856 )   RICH HTML PDF (305KB) ( 1115 )   Save Let H be a hypergraph. The author uses the notations H\+* and L(H) to mean the dual hypergraph and line graph of H respectively. The adjacent graph of H, denoted by G\-H, is defined to be the graph which consist of L(H\+*) and the loops of H. If G\-H is primitive, then H is called primitive, and γ(G\-H) is called the exponent of H. In this paper, the author obtains that the exponent set of primitive simple hypergraphs of order n and the exponent set of primitive simple hypergraphs of order n with rank at least 3. Further, the extremal hypergraphs are described. References | Related Articles | Metrics