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25 August 2004, Volume 24 Issue 4 Previous Issue    Next Issue

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The Nevanlinna Pick Interpolation in the Class N(E_m) and the Associated Generalized Stieltjes Moment Problem  TUN Hua-Zhang Acta mathematica scientia,Series A. 2004, 24 (4):  385-394.  Abstract ( 1417 )   RICH HTML PDF (410KB) ( 1164 )   Save Let E\-m=(-∞,∞)＼∪[DD(]m[]j=1[DD)](α\-j,β\-j). The author denotes by N(E_m) the class of all functions which e holomorphic in the upper halfplane and whose imaginary parts are nonnegative, and which are holomorphic and take real values on each  interval (α\-j,β\-j)(j=1,…,m).In this paper an onetoone correspondence between the solutions to the  NevanlinnaPick interpolation problem with finite(infinite) nodes  and the solutions to the associated nonstandard truncated(full) generalized Stieltjes moment problem is established by using Hankel vector approach. The solvability criteria for the  nonstandard truncated generalized Stieltjes moment problem and the corresponding NevanlinnaPick  problem are  obtained by the  method due to Risez. Using the limiting  process, the author deduces the necessary condition  for  the solvable Nevanlinna Pick problem with infinite interpolation nodes. References | Related Articles | Metrics

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Pointwise Multipliers between Two Holomorphic Function Spaces on C^n ZHANG Hua-Jun Acta mathematica scientia,Series A. 2004, 24 (4):  395-403.  Abstract ( 1497 )   RICH HTML PDF (366KB) ( 1166 )   Save In this paper, the author will discuss the pointwise multipliers from    Bloch type spaces β\+p to Dirichlet type spaces D\-qby using mixed norm     spaces, Bergman type operators, Carleson measure, the estamation of order and     linear functional.　At the same time,　the author will study the pointwise multipliers from    Dirichlet type spaces D\-p to little Bloch type spaces β\+q\-0 too. References | Related Articles | Metrics

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The Exact Hausdorff Function of Generalized &alpha|stable Process ZHENG Shui-Cao Acta mathematica scientia,Series A. 2004, 24 (4):  404-408.  Abstract ( 1528 )   RICH HTML PDF (349KB) ( 1141 )   Save School of Mathematical Sciences, Peking University, Beijing 100871;The Basic Teaching Department, Jimei University, Xiamen 361021) References | Related Articles | Metrics

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The Association Schemes of a Kind of 2 dimensional Subspaces of Pseudo symplectic Space F^(2v+2+l)_q and Its Structure ZHANG Geng-Sheng Acta mathematica scientia,Series A. 2004, 24 (4):  409-419.  Abstract ( 1518 )   RICH HTML PDF (381KB) ( 1093 )   Save This paper obtains a commutative and nonsymmetric association scheme of class 2q-1 by using a kind of 2dimensional nonisotropic subspaces of singularpseudosymplectic space F\+\{(2v+2+l)\-q and  discusses its structure. This scheme can be obtained by the extension of those of additive group and multiplicative group of the base fieldand some other simple association schemes. References | Related Articles | Metrics

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Laplace Operator in Finsler Geometry YAN Rong-Mu Acta mathematica scientia,Series A. 2004, 24 (4):  420-425.  Abstract ( 1799 )   RICH HTML PDF (326KB) ( 1159 )   Save In this article, the author defines an inner product of differential form in Finsler manifold, which helps him lead to δoperator and Laplace operator. The author proves that Laplace operator can be regarded here asan extension of that in Riemann manifold. Furthermore, the author gives local coordinate expression of δoperator. References | Related Articles | Metrics

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Duality in Vector Optimization of Setvalued Maps with Super Efficient Solutions CHENG Bao-Fu, ZHOU Rong-Beng, LIU San-Yang Acta mathematica scientia,Series A. 2004, 24 (4):  426-434.  Abstract ( 1840 )   RICH HTML PDF (387KB) ( 1700 )   Save A generalized KuhnTucker optimality condition of constrained vector optimization of setvalued maps  with   super efficiency is obtained with the help of the  Contingent tangent derivatives which are developed with the aid of Contingent tangent cone and the epigraphy of the setvalued map, with which the weak duality theorems, direct duality theorems and the converse the orems for Wolfe type and MondWeir type duality are established. References | Related Articles | Metrics

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Multiple Positive Solutions for BVP ofa Singular Fourth Order System XI Chi-Jing, LI Fu-Xi Acta mathematica scientia,Series A. 2004, 24 (4):  435-441.  Abstract ( 1969 )   RICH HTML PDF (338KB) ( 1414 )   Save In this paper, the authors  study the existence and multiplicity of two point BVP for a singular nonlinear fourth order ordinary differential system by using the fixedpoint index theory.The existence and multiplicity theorems on positive solutionsare established by using the first eigenvalue of the corresponding linear problems. References | Related Articles | Metrics

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Sensitivity Analysis of Conditional Value at Risk LIU Xiao-Mao, LI Chu-Lin Acta mathematica scientia,Series A. 2004, 24 (4):  442-448.  Abstract ( 1587 )   RICH HTML PDF (374KB) ( 1495 )   Save This paper gives the Conditional Value at Risk (CVaR) of portfolio under the normality and t distribution respectively, and analyzes the sensitivity of CVaR with respect to portfolio allocation. The economic implications are also discussed. References | Related Articles | Metrics

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A Note on Hayman's Problem and the Sharing Value LIN Wei-Chuan, HUANG Bin Acta mathematica scientia,Series A. 2004, 24 (4):  449-453.  DOI: 30D35； 30D45 Abstract ( 1740 )   RICH HTML PDF (316KB) ( 1434 )   Save Let f(z) be a nonconstant entire function, n be a positive integer grea ter than one, and a be a nonzero finite complex number. If f^n and (f^n)^(k) share a, then nf′=ωf, where ω  is the root of  equation t^k=1. References | Related Articles | Metrics

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A Characterized Theorem of the Differential of Generalized Operator L-Valued Functions WANG Xiang-Jun, WANG Cai-Shi Acta mathematica scientia,Series A. 2004, 24 (4):  454-458.  Abstract ( 1154 )   RICH HTML PDF (341KB) ( 1216 )   Save In this paper, the authors  discuss the differential of generalized operator valued function. A charaterized theorem is obtained, some examples and applications are given . References | Related Articles | Metrics

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The Skew symmetric Solutions of Linear Matrix Equation B^TXB=D on Some Linear Manifolds DENG Yuan-Bei, HU Xi-Yan, ZHANG Lei Acta mathematica scientia,Series A. 2004, 24 (4):  459-463.  Abstract ( 1959 )   RICH HTML PDF (313KB) ( 1422 )   Save This paper discusses the skew symmetric solutions and the skew symmetric opti mal approximation solution of the linear matrix equation B^TXB=D on some  linear manifolds. The expressions of the general solutions and the unique optima l approximation solution to a given matrix X～ are obtained. References | Related Articles | Metrics

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Complete Space like Submanifolds with Flat Connection of Normal Bundle in the de Sitter Space SHU Shi-Chang, LIU San-Yang Acta mathematica scientia,Series A. 2004, 24 (4):  464-468.  Abstract ( 1516 )   RICH HTML PDF (304KB) ( 926 )   Save Let M be a complete n demensional space like submanifold in the de Sitter space S^(n^p)_p(c) with parallel mean curvature vector and constant scalar curvature, if the connection of normal bundle is flat and K(M)<0, or ‖σ‖<n^2H^2/(n-1)-2c, then M is a totally umbilical submanifold. References | Related Articles | Metrics

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A Necessary and Sufficient Condition for Determining a Hilbert Basis of P_n(Γ) CEN Yan-Meng, CEN Yi-Gang Acta mathematica scientia,Series A. 2004, 24 (4):  469-474.  Abstract ( 1448 )   RICH HTML PDF (349KB) ( 1198 )   Save Let Γ be a compact Lie group acting on R^n and P_n(Γ) the ring of Γ invariant polynomial germs under Γ. Hilbert-Weyl theorem shows that there is a Hilbert basis consisting of Γ invariant homogeneous polynomial germs for P_n(Γ). However, it is not clear, how to choose a Hilbert basis from Γ invariant homogeneous polynomial germs and how to determine that a finite set of Γ invariant homogeneous polynomial germs is a Hilbert basis of P_n(Γ).  In this paper, by means of some fundamental properties of Noether's ring and invariant integration as well as the relevant theorems in the theory of singularities, a necessary and sufficient condition is  proved for determining a Hilber basis of P_n(Γ). This will provide a new way to determine of a Hilbert basis for some P_n(Γ). References | Related Articles | Metrics

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On 2 factors Containing Perfect Matching in Bipartite Graphs WANG Xiao-Li Acta mathematica scientia,Series A. 2004, 24 (4):  475-479.  Abstract ( 1411 )   RICH HTML PDF (365KB) ( 1348 )   Save A bipartite graph G=(X,Y; E) is called  balanced if |X|=|Y|. Let  G=(X,Y; E) be a balanced bipartite  graph of order 2n, suppose  that the minimum degree of G is at least   (2n-1)/3, the author shows that if n≥4k, then for each perfect  matching M, G contains a 2factor with exactly k components  (vertex disjoint cycles) including every edge of M (with one  exception that k=1, n=5 and δ(G)=3). When k=2,  n≥5,  the author has  the same conclusionunder  the condition  4δ≥(n+1)/2,  and  this bound about minimum degree  is the best possible. References | Related Articles | Metrics

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Koppelman Formula with Discrete Holomorphic Kernel and Equation on a Bounded Domain HUANG Yu-Sheng, LIN Liang-Yu Acta mathematica scientia,Series A. 2004, 24 (4):  480-484.  Abstract ( 1423 )   RICH HTML PDF (330KB) ( 1164 )   Save Let D be a bounded domain with piecewise C(1) boundary in C^n,f∈C(1)(0,q)(D and  f∈C(1) (0,q+1)(D  The anthors establish a new integral formula of Koppelman of (0,q) form with discrete holomorphic kernels on D (-1)qf=Lη D f-(RηD+BD)af+R)ηD+BD)f,where LηDf,RηDf,BDf,RηD-fare some corresponding integral operators.If -f=0, then u=(-1)q(RηD+BD)f is a local differentiabl solution of the equation u=f in D, and u has an inner closed uniform estimate in D, i.e. ‖u‖L∞≤C‖f‖L∞.   References | Related Articles | Metrics

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Jones Polynomial of Links HAN You-Fa Acta mathematica scientia,Series A. 2004, 24 (4):  485-490.  Abstract ( 1301 )   RICH HTML PDF (319KB) ( 1278 )   Save In this paper, the author dealts with the properties of derivative of Jones polynomial for links. In particularly, the author discussed the properties of \$υ\-n(K)\$ and \$\-n(L)\$. References | Related Articles | Metrics

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Relation Between Power Lattice and Quotient Lattice  MENG Beng-Hua Acta mathematica scientia,Series A. 2004, 24 (4):  491-495.  Abstract ( 1476 )   RICH HTML PDF (308KB) ( 1297 )   Save Based on ［1］ in which the concept of power lattice is given, thispaper obtains a sufficient and necessary condition of power lattice, introduces the concepts of regular power lattice and relative power lattice, discusses the relations between regular power lattice and quotient lattice as well as those between relative power lattice and quotient lattice. References | Related Articles | Metrics

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Spanning Trees, Basic Cycles and Betti Deficiency of a Graph HUANG Yuan-Qiu, LIU Pan-Pei Acta mathematica scientia,Series A. 2004, 24 (4):  496-500.  Abstract ( 1734 )   RICH HTML PDF (327KB) ( 1214 )   Save Let \$G\$ be a graph and \$T\$ be  a spanning tree of it. The sign \$ξ(G, T)\$ denotes thenumber of components of \$G＼E(T)\$ with  odd number of edges, and it is knownthat  the value \$ξ(G)=min[DD(X]T[DD)]ξ(G, T)\$ is defined as Betti deficiency of \$G\$, where min is taken over all spanning trees of \$G\$. In this paper the authors  study the characteristic structure of a graph  conne ting to  its Betti deficiency, and obtain some new results on the maximum genus of a graph. References | Related Articles | Metrics

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The Approximate Third order Moments and Bispectral Density of LTBL Model WANG Hai-Bin, HUI Bo-Cheng, CHEN Gao-Qiu Acta mathematica scientia,Series A. 2004, 24 (4):  501-512.  Abstract ( 1481 )   RICH HTML PDF (434KB) ( 1269 )   Save Lower triangular bilinear time series, including its special cases, has been studied by several workers.According to the second order structure(i.e., autovariance and spectral density), it is similar to an ARMA model. But the third order structure (the third order moments and bispectral density), which characterizes the model, is rather complicated and tedious and the authors  have not seen the relatedresultsin  literature. In this context, both the approximate third order moments and bispectral density have been obtained. In particular, for the separable lower triangular bilinear time series model, the corresponding results have been significantly simplified. References | Related Articles | Metrics