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 ( 1585 )   PDF (195KB) ( 914 )   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 ( 1762 )   PDF (240KB) ( 991 )   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 ( 1509 )   PDF (191KB) ( 1220 )   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 ( 1466 )   PDF (221KB) ( 950 )   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 ( 1672 )   PDF (179KB) ( 1128 )   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 ( 1327 )   PDF (204KB) ( 1116 )   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 ( 1259 )   PDF (176KB) ( 906 )   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 ( 1780 )   PDF (287KB) ( 978 )   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 ( 1444 )   PDF (208KB) ( 1115 )   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=C_b and A₁X₁=C₁, X₂A₂=C₂,A₃X₁B₁+A₄X₂B₂=C_b.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 ( 1510 )   PDF (199KB) ( 1408 )   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 ( 1322 )   PDF (221KB) ( 1126 )   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 S_PF-rough sets and their probability characteristic

SU Fen-Xiao, ZHANG Ling

J4. 2008, 43(12):  56-60. 

Abstract ( 1500 )   PDF (204KB) ( 936 )   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 S_PF-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 S_PF^-rough sets according to the probability.

The β-Rough integral

SU Fen-Xiao, CHEN Bao-Hui

J4. 2008, 43(12):  61-65. 

Abstract ( 1530 )   PDF (215KB) ( 647 )   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 ( 1514 )   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 ( 1993 )   PDF (201KB) ( 1049 )   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 ( 1440 )   PDF (160KB) ( 910 )   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 ( 1444 )   PDF (219KB) ( 1400 )   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 ( 1619 )   PDF (187KB) ( 814 )   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 ( 1245 )   PDF (211KB) ( 776 )   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 ( 1467 )   PDF (2310KB) ( 1274 )   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.