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25 August 2006, Volume 26 Issue 4 Previous Issue    Next Issue

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On the Lie's Theorem for Lie Color Algebras Zhang Shouchuan;Zhang Yaozhong Acta mathematica scientia,Series A. 2006, 26 (4):  481-484.  Abstract ( 1504 )   RICH HTML PDF (252KB) ( 1421 )   Save The authors show that the Lie's Theorem holds for Lie color algebras with a torsion-free abelian group G. The authors give an example to show that the torsion-free condition is necessary. Related Articles | Metrics

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A Generalization of Strassen's Theorem for Brownian Motion Liu Jicheng Acta mathematica scientia,Series A. 2006, 26 (4):  485-492.  Abstract ( 1497 )   RICH HTML PDF (257KB) ( 1369 )   Save In this paper, the author obtains Schilder's theorem in $(p,r)$-capacity and Holder norm case. As an application, the author proves a sharpening of Strassen's law of iterated logarithm in this case. Related Articles | Metrics

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The Iteration of Quasipolynomial Mappings Wu Zhaojun; Sun Daochun Acta mathematica scientia,Series A. 2006, 26 (4):  493-497.  Abstract ( 1451 )   RICH HTML PDF (298KB) ( 1013 )   Save The quasipolynomial mappings are more wider than polynimials. In this paper, the authors discuss the iteration of quasipolynomial mappings, some theorems about the escaping set, filled Julia set and Julia set are proved. Related Articles | Metrics

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Large Time Behavior of the Modified Navier-Stokes Equations Dong Boqing; Li Yongsheng Acta mathematica scientia,Series A. 2006, 26 (4):  498-505.  Abstract ( 1882 )   RICH HTML PDF (293KB) ( 1141 )   Save This paper is concerned with the large time behavior of the modified Navier-Stokes equations in Rn . By improving the Fourier splitting methods, it is proved that the weak solution decays in L2 norm at the rate (1+t)n/4 when the initial data u0∈ L2∩L1. Moreover, the error estimate between modified Navier-Stokes equations and classic Navier-Stokes equations is studied. Related Articles | Metrics

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Generalized Game and System of Generalized Vector Quasi-equilibrium Problems in G -convex Spaces Ding Xieping Acta mathematica scientia,Series A. 2006, 26 (4):  506-515.  Abstract ( 1456 )   RICH HTML PDF (297KB) ( 1064 )   Save A new class of system of generalized vector quasi-equilibrium problems (SGVQEP) is introduced and studied in generalized convex spaces. By using an existence theorem of maximal elements for a family of set-valued mappings due to the author, a new equilibriu existence theorem for generalized games is proved. As applications, some new existence theorems of solutions for the SGVQEP are established in noncompact product G-convex spaces. Related Articles | Metrics

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The Impact of Regulation on Modern Commerclal Bank's Decision Wang Yan Acta mathematica scientia,Series A. 2006, 26 (4):  516-521.  Abstract ( 1531 )   RICH HTML PDF (361KB) ( 1223 )   Save By making use of Montin-Klein model induced liquidity risk, this paper analyses commercial bank's optimal strategy when central bank gives reserves and deposit and loan rates regulations. When the central bank imposes a regulation on reserves, the ceiling on the reserves decreases the loan and deposit rates. When regulating on the loan and deposit rate, the commercial bank will make optimal strategies in different cases. Both the penalty rate rp and interest rate r impact the strategy of the commercial bank. Because of the large management cost in many developing countries, the central bank usually can't obtain its object, and the commercial bank also can't realize its optimal strategy. The commercial bank must do some internal adjustment to adapt the international environment. With the Chinese financial reform, these analyses propose some useful advices for the central bank to increase the efficiency of regulatory policies. Related Articles | Metrics

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Apollonian Isometries and Mobius Transformations Chu Yuming Acta mathematica scientia,Series A. 2006, 26 (4):  522-526.  Abstract ( 1369 )   RICH HTML PDF (234KB) ( 1289 )   Save et DoverlineR2 be a simply connected domain with boundary containing at least three points, and for any x, y∈ D, aD(x, y) denote theApollonian metric in D with respect to x and y. A. F. Beardon gave the following conjecture in 1998: If f: D →D be an Apollonian isometry,then f is a M"obius transformation.In this paper, the author affirms and proves the conjecture when D is a disk. Related Articles | Metrics

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ermanence and Global Stability for Single-species Model with Three Life Stages and Time Delay Gao Shujing ;Chen Lansun Acta mathematica scientia,Series A. 2006, 26 (4):  527-533.  Abstract ( 2050 )   RICH HTML PDF (308KB) ( 1223 )   Save In this paper, a single-species model with distributed time delay in which individuals exhibit three life stages is considered. Sufficient conditions are obtained for the permanence of the system. Moreover, by using Lyapunov function, some conditions for global asymptotic stability of the system are investigated. An example satisfying the conditions of the main resuilts is given. Related Articles | Metrics

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Weighted Hardy Theory on a Domain in Rn Lan Jiacheng ;Yan Dunyan Acta mathematica scientia,Series A. 2006, 26 (4):  534-546.  Abstract ( 1509 )   RICH HTML PDF (341KB) ( 1080 )   Save In this paper, let Ω С Rn be a domain.The authors define some weighted Hardy spaces on Ω and get atomic decompositions for these spaces. This paper is preliminary for them to study in the field about weighted Hardy theory on a smooth domain in Rn and elliptic boundary value problems. Related Articles | Metrics

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Confidence Regions in Nonlinear Reproductive Dispersion Mixed Models in Terms of Curvatures Zhang Wenzhuan;Tang Niansheng ; Wang Xueren Acta mathematica scientia,Series A. 2006, 26 (4):  547-558.  Abstract ( 2146 )   RICH HTML PDF (430KB) ( 1160 )   Save A modified geometric framework is proposed for nonlinear reproductive dispersion mixed models (NRDMMs) based on the Laplace approximate marginal likelihood. Three improved approximate confidence regions of parameters and subset paramters are investigated for NRDMMs based on the proposed curvatures. The results for nonlinear regression models and exponential family nonlinear models are extended to the complicated nonlinear reproductive dispersion mixed models including exponential family nonlinear models and nonlinear reproductive dispersion models as their special cases. Related Articles | Metrics

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Standing Waves for a Class of Coupled Nonlinear Klein-Gordon Equations Gan Zaihui ;Zhang Jian Acta mathematica scientia,Series A. 2006, 26 (4):  559-569.  Abstract ( 2009 )   RICH HTML PDF (318KB) ( 1323 )   Save This paper is concerned with the initial value problem of a class of coupled nonlinear Klein-Gordon equations in two space dimensions. The authors first establish the existence of the standing wave with the ground state by using variational calculus, next the authors derive out the sharp conditions for blowing-up and global existence in terms of the result, at last the authors show the instability of the standing wave with the ground state. Related Articles | Metrics

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Graphs with Strong Endomorphism Monoid being the Union of Groups Li Weimin Acta mathematica scientia,Series A. 2006, 26 (4):  570-577.  Abstract ( 2055 )   RICH HTML PDF (269KB) ( 1123 )   Save In this paper, the author gives a characterization for a graph G such that s End(G), the monoid of the strong endomorphisms of G, is the union of groups. In particular, if this is the case, the author explicitly finds the identity element of each group in s End(G). Related Articles | Metrics

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Real Representiations of Quaternion Matrices and Quaternion Matrix Equations Jiang Tongsong;Wei Musheng Acta mathematica scientia,Series A. 2006, 26 (4):  578-584.  Abstract ( 2169 )   RICH HTML PDF (251KB) ( 1406 )   Save Quaternion matrices and quaternion matrix equations play important roles in quantum mechanics. By introducing real representations of quaternion matrices, this paper studies the solution of the general quaternion matrix equation AXB-CYD=E, and gives a prectical technique of finding the solution of the quaternion matrix equation. This paper also obtains a Roth's theorem over the quaternion field. Related Articles | Metrics

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The Growth of Random Dirichlet Series on the Right Half-plane Wang Zhigang;Ou Yigui Acta mathematica scientia,Series A. 2006, 26 (4):  585-590.  Abstract ( 2012 )   RICH HTML PDF (272KB) ( 1106 )   Save This paper proves a theorem about the growth of the Dirichcet series on the right half-plane under weak conditions of coefficients, and obtains that Dirichlet series and some random Dirichlet series a.s. have the same order under certain conditions, which extend and improve a series of known theorems. Related Articles | Metrics

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The Satisfactory Improvements of the Modified Gauss-Seidel Method for H -matrices Sun Liying Acta mathematica scientia,Series A. 2006, 26 (4):  591-594.  Abstract ( 1680 )   RICH HTML PDF (232KB) ( 939 )   Save In this paper, the author presents the convergent theorems of the improving modified Gauss-Seidel method, referred to as the IMGS method, for H-matrices as well as compare the range of parameters aiwith the parameter ω of the SOR iterative method. The methods and results appeared in this paper are superior to those in recent results. The corresponding results in this paper also show that the IMGS method is effective to H-matrices. Related Articles | Metrics

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The Persistence of Nonoscillatory Solutions of Difference Equations Under Impulsive Perturbations Wei Gengping; Shen Jianhua Acta mathematica scientia,Series A. 2006, 26 (4):  595-600.  Abstract ( 1788 )   RICH HTML PDF (247KB) ( 1044 )   Save The authors obtain a sufficient condition for the persistence of nonoscillatory solutions of the difference equation with continuous variable x(t+τ)-x(t)+p(t)x(t-rτ)=0 under the impulsive perturbations x(tk+τ)-x(tk)=b_kx(tk), k∈N(1) Related Articles | Metrics

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Weak Skew Paired Bialgebras and Weak Relative Long Bialgebras Zhang Liangyun Acta mathematica scientia,Series A. 2006, 26 (4):  601-611.  Abstract ( 1646 )   RICH HTML PDF (318KB) ( 1132 )   Save This paper gives a sufficient and necessary condition for given twisted product $(H^\sigma,\cdot_\sigma)$ to be a weak bialgebra. If $[B, H, \tau]$ are weak skew paired bialgebras and $\tau$ is invertible, then, under some condition, the weak bicrossed product $B\bowtie_\tau H$ is a weak bialgebra. If $(B, H, \sigma)$ is a weak relative Long bialgebra and $\sigma$ invertible, then the weak bicrossed product $B^{OP}\bowtie_\sigma H$ can be constructed. Espically, for the Sweedler 4-dimensional Hopf algebra $H_4$, the author gives an example to show that $(B^{OP}\bowtie_\sigma H_4, \beta)$ is not only a Long bialgebra but also a non-commutative and non-cocommutative 8-dimensional Hopf algebra, where $B$ is a sub-Hopf algebra of $H_4$. If $B$ and $H$ are weak bialgebras, and $\sigma: B\otimes H\rightarrow k$ is a linear map, then a sufficient and necessary condition for $(B,\sigma,\leftharpoonup, \Delta_B)$ to be a weak right relative $(H, B)$-dimodule algebra is given. Related Articles | Metrics

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On the Hermitian Generalized Anti-Hamiltonian Semi-definite Solutions of Linear Matrix Equations Zhang Zhongzhi;Hu Xiyan; Zhang Lei Acta mathematica scientia,Series A. 2006, 26 (4):  612-620.  Abstract ( 2210 )   RICH HTML PDF (310KB) ( 1245 )   Save By means of the properties of Hermitian generalized anti-Hamiltonian semi-definite matrices, the authors give some necessary and sufficient conditions for the solvability of the linear matrix equation in Hermitian generalized anti-Hamiltonian semi-definite matrix set, and obtain a general expression of the solution for a solvable case. The authors also give some necessary and sufficient conditions of the solvability for inverse enginvalume problem of Hermitian generalized anti-Hamiltonian semi-definite matrices. For any n× n complex matrix, the authors derive the representation of its unique optimal approximation. Related Articles | Metrics

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Influence Analysis of Covariance Matrix Disturbance in Linear Model with Respect to a Restricted Condition Zhang Shangli;Qin Hong Acta mathematica scientia,Series A. 2006, 26 (4):  621-628.  Abstract ( 1785 )   RICH HTML PDF (298KB) ( 1038 )   Save In this paper, the authors study the issue of the influence of Best Linear Unbiased Estimate (BLUE) with covariance matrix disturbing or data missing. The relationship of the BLUE of regression parameter β among some linear models with respect to restricted condition β=0, such as Gauss-Markov model, generalized linear model and linear model with delected data, is made explicitly. In addition, the authors also propose the generalized Cook distance DV to asses the disturbing influence, and obtain two computational formulae of DV. Related Articles | Metrics

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Existence of Solutions for the Boundary Value Problem of First Order Differential Difference Equations of Mixed Type Yang Dianwu;Han Zhenlai Acta mathematica scientia,Series A. 2006, 26 (4):  629-633.  Abstract ( 1717 )   RICH HTML PDF (243KB) ( 1123 )   Save In this paper, by estimates of spectral of an integral operator, the authors give a theorem on the existence of solutions for first order differential difference equations with boundary condition. Related Articles | Metrics

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Stability of Periodic Solution for a Discrete Leslie Predator-prey System Liang Zhiqing;Chen Lansun Acta mathematica scientia,Series A. 2006, 26 (4):  634-640.  Abstract ( 2050 )   RICH HTML PDF (259KB) ( 1125 )   Save The paper discusses a class of discrete Leslie predator-prey system. The authors obtain the persistence of the system, assuming that the coefficients in the system are periodic and the existence of a periodic solution. Under some additional conditions, the periodic solution is globally stable. Related Articles | Metrics