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Table of Content

      
    16 December 2008
    Volume 43 Issue 12
    Articles
    On Hermitian solutions to general linear quaternionic matrix equations
    LING Si-Chao, CHENG Wue-Han, WEI Mu-Sheng
    J4. 2008, 43(12):  1-4. 
    Abstract ( 985 )   PDF (195KB) ( 741 )   Save
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    On the basis of vector function and Kronecker product of matrixes, the partial vector function  was defined, and a translational method was given for  studying Hermitian solutions to general linear quaternionic matrix equations.

    Viscosity solutions of multidimensional quasilinear parabolic PDEs
    HUANG Zong-Yuan, ZHANG Feng
    J4. 2008, 43(12):  5-9. 
    Abstract ( 1192 )   PDF (240KB) ( 611 )   Save
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    It was proved with two different methods, that a function expressed in terms of the solution of a multidimensionalbackward stochastic equation is indeed a unique viscosity solutionof a certain qusilinear parabolic partial differential equation.

    The PC1 ([0,1],R+) positive solutions of singular boundary value problems of impulsive Emden-Fowler equations with a positive exponent
    DAI Li-Mei
    J4. 2008, 43(12):  10-14. 
    Abstract ( 942 )   PDF (191KB) ( 907 )   Save
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    A necessary and sufficient condition for the existence of the PC1([0,1],R+) positive solutions to the sub-linear singular mixed boundary value problems of Emden-Fowler equations with impulse was obtained by the method of lower and upper solutions to impulsive singular mixed boundary value problems.

    Computation of the integral of lifetime distribution in the δ-shock model and the properties of the M function
    MA Ming
    J4. 2008, 43(12):  15-19. 
    Abstract ( 843 )   PDF (221KB) ( 718 )   Save
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    The shock models play an important role in reliability theory, and the δ-shock model is  particular. The computation of the multiple integral of lifetime distribution in the δ-shock model was discussed, and  the properties of the M function, which is defined by the multiple integral were obtained.

    Asymptotic bifurcation points of nonlinear operators
    ZOU Yu-Mei, TAO Chang-Li, CUI Yu-Jun
    J4. 2008, 43(12):  20-23. 
    Abstract ( 1050 )   PDF (179KB) ( 953 )   Save
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    The existence and nonexistence of asymptotic bifurcation points of nonlinear operators in Banach space was investigated by use of a positively homogeneous operator under the conditions that the asymptotic Fréchet differentiability is not assumed.

    Elimination of the not minimal covering of preserving binary regularly separable relations in partial four-valued logic
    ZHOU Xiao-qiang, LIU Ren-ren
    J4. 2008, 43(12):  24-27. 
    Abstract ( 853 )   PDF (204KB) ( 914 )   Save
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    To determine the minimal covering in partial four-valued logic, according to the completeness theory in partial K-valued logic, regularly separable relation and the similar relationship theory among precomplete sets, the minimal covering in partial four-valued logic was analyzed, and 222 sets of 270 preserving quaternary regularly separable relations function sets were proved not to belong to the minimal covering members in partial four-valued logic.

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    LIU Xiao-Yan
    J4. 2008, 43(12):  28-30. 
    Abstract ( 828 )   PDF (176KB) ( 741 )   Save
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    A graph G is called an [s,t]-graph, if there are at least t edges in every induced subgraph of s vertices. Let G be a 2-connected [4,2]-graph and the order of G be not less than 7, then G is a pancyclicity graph.

    Three types of fuzzy modal logics about K
    DUAN Jing-Yao, WANG Guo-Jun
    J4. 2008, 43(12):  31-39. 
    Abstract ( 1125 )   PDF (287KB) ( 737 )   Save
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    The concept of MR0 algebra was introduced, and some major properties were discussed. Then the isomorphism theorems of MR0 algebra were given. Additionally, the modal logic system K1 was formed, which can be proved to be a complete system under MR0 semantics. Finally, the modal logic system K2 that proved to be soundness was formed through fuzzifying of the evaluation V in the Kripke model, and the modal logic system K3 was formed and proved to be complete through the fuzzifying of the binary relationship R in the Kripke model.

    General solutions to two pairs of quaternion matrix equations
    XIE Zhong-Zhou, LIU Xiao-Ji
    J4. 2008, 43(12):  40-47. 
    Abstract ( 815 )   PDF (208KB) ( 912 )   Save
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    The purpose was to discuss the general solution to the systems of quaternion matrix equations X1A1=C1, X2A2=C2,A3X1B1+A4X2B2=Cb and A1X1=C1, X2A2=C2,A3X1B1+A4X2B2=Cb.Then the necessary and sufficient conditions for the existence and the expressions of the general solution to the systems mentioned above were obtained.

    Incidence chromatic number of several generalized Petersen graphs
    LIU Da-Kun, Wang Shu-Dong
    J4. 2008, 43(12):  48-51. 
    Abstract ( 786 )   PDF (199KB) ( 1184 )   Save
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    When n≡0(mod 4),if k be odd, k=2,and k=4,the incidence chromatic number of generalized Peterson graph P(n,k) was obtained.

    An optimal integral differential solution for a two-person interaction programming problem
    XU Xin-Sheng, SUN Jian-Wu
    J4. 2008, 43(12):  52-55. 
    Abstract ( 765 )   PDF (221KB) ( 882 )   Save
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    A new concept called the t*-optimal integral differential solution for a two-person interaction programming problem(IPP) was introduced, where t* is a non-negative constant. It can be shown that the t*-optimal integral differential solution is equivalent to the optimal solution for another mathematical programming problem. In addition,  the t*-optimal integral differential solution that the giving-up value of each decision maker is different was discussed, the relation between the t*-optimal integral differential solution and the s-optimal joint solution was also presented. A numerical example illustrated that the method presented here is efficient for solving a two-person interaction programming problem.

    Function one-direction SPF-rough sets and their probability characteristic
    SU Fen-Xiao, ZHANG Ling
    J4. 2008, 43(12):  56-60. 
    Abstract ( 946 )   PDF (204KB) ( 769 )   Save
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    Based on function S-rough sets and the randomness of function transfer, the concept of function one-direction SPF-rough sets was put forth, and their mathematical structure was given. The probability characteristic of function one-direction SPF-rough sets was also discussed. It was proved that a function one-direction SPF-rough set was the generalization of function one-direction SPF-rough sets, and the function one-direction S-rough sets was a special case of function one-direction SPF-rough sets according to the probability.

    The β-Rough integral
    SU Fen-Xiao, CHEN Bao-Hui
    J4. 2008, 43(12):  61-65. 
    Abstract ( 1013 )   PDF (215KB) ( 474 )   Save
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    Based on the concept of the F-rough integral proposed by Yu[1], the concept of the β-rough integral was given by employing the transfer credibility degree β, the relation between the F-rough integral and the β-rough integral was discussed. It was proved that the β-rough integral is a generalization of the F-rough integral, while the F-rough integral is a special case of the β-rough integral.

    F-rough law and its attribute control
    XIU Ming, CHEN Bao-Hui, SHI Kai-Quan
    J4. 2008, 43(12):  66-72. 
    Abstract ( 1009 )   Save
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    Function one direction S-rough sets (function one direction singular rough sets) was defined by the R-function equivalent class [u], which has dynamic characteristic, and the function one direction S-rough sets has law (function) characteristic. By using function one direction S-rough sets, the  concepts of the structure of F-rough law (w-(x)F,w-(x)F), the attribute characteristic of rough law (w-(x),w-(x)), attribute distance, and status coefficient were presented, and F-rough law and its attribute control, the principle of attribute control, attribute control theorem and applications were proposed. F-rough law and its attribute control is a new application research direction of function S-rough sets (function singular rough sets).

    On the exact solution of a diffusion equation with boundary conditions by the homotopy analysis method
    ZHANG Xin-Dong, HU Yu-Hong
    J4. 2008, 43(12):  73-76. 
    Abstract ( 1305 )   PDF (201KB) ( 855 )   Save
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    The homotopy analysis method was presented (short: HAM) for obtaining numerical solutions of a diffusion equation with boundary conditions. The series solution was developed and the recurrence relations were explicitly given. The initial approximation can be freely chosen with possible unknown constants, which can be determined by imposing the boundary and initial conditions. The HAM contains the auxiliary parameter h, which can provide a simple way to adjust and control the convergence region of solution series. Comparisons were made between the HAM, the exact solution and the other method. The results revealed that the HAM is  effective and simple.

    Characterizations of the stability of generalized Jordan-derivations and Jordan-homomorphisms
    SUN Liang-Ji
    J4. 2008, 43(12):  77-79. 
    Abstract ( 827 )   PDF (160KB) ( 779 )   Save
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    Let A be a unital Banach algebra, the generalized Hyers-Ulam-Rassias stability of generalized Jordan-derivations on unital Banach algebras, and the generalized Hyers-Ulam-Rassias stability of Jordanhomomorphisms on unital Banach algebras were discussed.

    The existence of equilibrium in the multi-dimension Bertrand game
    XU Jin, CHEN Bo-Xiao
    J4. 2008, 43(12):  80-83. 
    Abstract ( 829 )   PDF (219KB) ( 806 )   Save
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    According to the phenomena of games among the corporations in economic activities, the multi-dimension Bertrand model was developed through the introduction of the condition that the firms were limited by capacity constrains. It was shownthat if the value of the capacity is different,  the game possesses pure-strategy or mixed-strategy equilibria.

    The existence and uniqueness of a monotone decreasing positive solution of a third-order two-point boundary value problem
    XU Xiao-Xin, LIANG Yue-Liang, SANG Yan-Bin
    J4. 2008, 43(12):  84-87. 
    Abstract ( 998 )   PDF (187KB) ( 695 )   Save
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    By using Banach fixed point theorem in cone, one sufficient condition of the existence and uniqueness of a monotone decreasing positive solution was established to the nonlinear third-order two-point boundary value problem:u″+q(u′)f(t,u)=0, a.e. t∈[0,1],u′(0)=A, u(1)=B, u″(0)=C, where A≤0, B≥0, C≤0 were constants。

    F-rough integrals and their covered area-boundary thickness characteristics
    FANG Wen-Qing, XU Xiu-Qing, SHI Kai-Quan
    J4. 2008, 43(12):  88-92. 
    Abstract ( 714 )   PDF (211KB) ( 647 )   Save
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     F-rough integrals were composed with one pair of the integrals, which was used to  introduce the concepts of the degree of covered area and boundary thickness. The characteristics of the area were discussed and  the dynamic law was given. The degree of covered area and boundary thickness turns the discussion about F-rough integrals from quality to quantity.

    Design and realization of a hyperchaotic system based FPGA
    WANG Zhong-Lin, YAO Fu-An, LI Xiang-Feng
    J4. 2008, 43(12):  93-96. 
    Abstract ( 945 )   PDF (2310KB) ( 957 )   Save
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    A novel method was adopted to design a hyperchaotic system Generator, based on a hyperchaotic system and implemented in FPGA. This method was based on the Matlab/Simulink, Altera Quartus II and DSP Builder. The hyperchaotic system was built by Altera DSP Builder, which is embedded into the Matlab/Simulink as a toolbox. After successful simulation of this model, the VHDL code was generated automatically. Then this code could be complied, simulated, configured and download by the Altera Quartus II. The research results indicated that this new method is not only simple and convenient but also effective to precisely produce a hyperchaotic system. It showed good agreement between system simulations and experimental results.