JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

A survey on a topic of combinatorial semigroups:characterizing and generalizing regular languages by semifilters

GUO Yu-qi 1*, WANG Shou-feng 2, SHUM K. P. 3

J4. 2010, 45(6): 1-7.

Abstract ( 1570 )

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This paper is devoted to a topic of combinatorial semigroups, namely,characterizing and generalizing regular languages by semifilters. Some recent progress and results in this aspect are surveyed. Furthermore, some problems are proposed.

Study of the dynamic characteristics of Rough sets

CUI Yu-quan, ZHANG Li, SHI Kai-quan

J4. 2010, 45(6): 8-14.

Abstract ( 1251 )

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Based on dynamic characteristics of Rough sets, the concepts of two dynamic degrees about Rough sets at different time are proposed. By using transition probability at different time,transition law and two steady-states are researched. Dynamic characteristics of Rough sets and attribute sets are discussed. Finally, an example analysis is given by using these results.

Edge coloring of triangle-free 1-planar graphs

ZHANG Xin, LIU Gui-zhen, WU Jian-liang

J4. 2010, 45(6): 15-17.

Abstract ( 1288 )

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It is shown that each triangle-free 1-planar graph with maximum degree Δ≥7 can be Δ-colorable by Discharging Method.

The adjacent vertex strongly distinguishing EI-total colorings of graphs

CHENG Hui, WANG Zhi-yong

J4. 2010, 45(6): 18-22.

Abstract ( 1040 )

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The concept of adjacent vertex strongly distinguishing EI-total coloring of graph is proposed. Some properties and the adjacent vertex strongly distinguishing EI-total chromatic numbers of some graphs, such as Path, Fan, Wheel, Cycle, Complete bipartite graph, Complete graph,Tree, Petersen graph, are investigated.

Star total colorings of Mycielski’s graphs of the balanced general join of graphs

TIAN Shuang-liang

J4. 2010, 45(6): 23-26.

Abstract ( 1024 )

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The star total colorings of some Mycielski’s graphs of the balanced general join of graphs are studied, and their star total chromatic numbers are obtained.

Characterization of λ_3,q-connected graphs

XIAO Hai-qiang1,2, ZHANG Zhao1*

J4. 2010, 45(6): 27-30.

Abstract ( 1044 )

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A connected graph G is λ_p,q-connected if there is an edge set S such that G-S has two components of order at least p and q, respectively. Some necessary and sufficient conditions for a graph to be λ_3,q-connected are presented.

Endomorphism rings of quasi AP-injective modules

YIN Xiao-bin1, HUANG Xiao-lin1, WANG Kai-yun2

J4. 2010, 45(6): 31-34.

Abstract ( 1032 )

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Let R be a ring, M_R be a quasi AP-injective module, S=End(M_R), N(S) be a set of nilpotents of S. Suppose that S satisfing the special ascending chain conditions, the strong regularity and the semisimplicity of S are investigated, the realationship between S and some special rings are obtained.

Simplification of Θ in the Uq(Sp(2n))-module isomorphism R=Θ。^~f。 P

GONG Ben-xue, LI Sha-sha

J4. 2010, 45(6): 35-38.

Abstract ( 909 )

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On extension of homomorphism of Abelian groups

LIU Jing

J4. 2010, 45(6): 39-42.

Abstract ( 1055 )

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A condition of extension of homomorphism of Abelian groups is given by using pure subgroups, and the uniqueness of extension of homomorphism is discussed. Furthermore, a condition for solvability of the moment problem of Abelian groups is obtained.

Bayesian variable selection based on AIC criteria in linear models

WANG Shu-yun1, SONG Yun-sheng2

J4. 2010, 45(6): 43-45.

Abstract ( 1061 )

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The problem of Bayesian variable selection in linear models is studied. Different with classical method of Bayesian variable selection, AIC criteria is used to construct the posterior distribution of the subset model. Simulation studies are also provided to demonstrate the better performance of the proposed method.

The alternating group method for fifth-order dispersive equation

FU Ji-mei1, ZUO Jin-ming2*, ZHANG Tian-de1

J4. 2010, 45(6): 46-49.

Abstract ( 1060 )

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A group of asymmetric difference schemes to approximate the fifth-order dispersive equation are given. Using the schemes, the alternating group method for solving the fifth-order dispersive equation is constructed. The scheme is unconditionally stable, and is directly used on the parallel computer. The numerical experiments show the method has near the second order ratio of convergence in space.

The finite difference method of miscible displacement problems in deformable porous media

LI Zhi-tao

J4. 2010, 45(6): 50-55.

Abstract ( 953 )

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The generalization for the second type of Feigenbaum’s functional equations

ZHANG Min1, WANG Lian-chi2

J4. 2010, 45(6): 56-59.

Abstract ( 916 )

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Global exponential stability of almost periodic solution for competitive neural networks with distributed delays and different time-scales

ZHAO Yong-chang1, WANG Lin-shan1,2

J4. 2010, 45(6): 60-64.

Abstract ( 1024 )

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The global exponential stability of almost periodic solutions for competitive neural networks with distributed delays and different time-scales are studied by using the fixed point theory, Lyapunov function and differential inequality technique. Sufficient conditions are established for the global exponential stability of it.

The existence and uniqueness of the solution of parabolic equations with wavelet collocation

FANG Bao-yan1, WANG Zhi-gang2, TIAN Shuang-liang1*, SU Li-jun2

J4. 2010, 45(6): 65-69.

Abstract ( 962 )

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The study of the numerical solutions of PDEs with wavelet collocation has yielded a number of substantial results. However, the existence and uniqueness of the solution has not been discussed. The existence and uniqueness of the solution of parabolic equations with wavelet collocation are established and discussed, where its explicit scheme and implicit scheme are given. Also, wavelet collocation is applied to parabolic equations to examine its appropriateness.

The initial and Neumann boundary value problem for a class parabolic Monge-Ampère equations

WANG Juan1, LIU Hui-zhao2

J4. 2010, 45(6): 70-73.

Abstract ( 1010 )

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It is proved that a classical solution to the initial and Neumann boundary value problem for parabolic-type Monge-Ampère equation is existent and unique. Using compare principle, it is shown the uniqueness of the classical solution. By employing proper auxiliary functions and barrier functions, the priori estimations are obtained. The existence of the strict convex classical solution is obtained by the continuous method.

Solutions to the operator equation AXB=C

TIAN Xue-gang, WANG Shao-ying

J4. 2010, 45(6): 74-80.

Abstract ( 1063 )

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Using the block operator matrix technique and the generalized inverse of operator,the solutions to the operator equation AXB=C are studied in infinite Hilbert space. The sufficient and necessary condition for the existence of solutions to the equation AXB=C and the representation of the solutions are established. Especially when R(A*)R(B) or R(B)R(A*), the sufficient and necessary condition for the existence of positive solutions of the equation AXB=C and the general form of the positive solutions are also derived.

A new hybrid conjugate gradient method

CHENG Li-qing1,2, SHI Qiao-lian2

J4. 2010, 45(6): 81-85.

Abstract ( 927 )

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A new hybrid conjugate gradient formula for solving unconstrained optimization problem is proposed. The corresponding method can guarantee that the search directions are descent directions without any line search, and this algorithm with Wolfe-Powell line search is proved to be globally convergent. Preliminary numerical results show that the new hybrid conjugate gradient method is very efficient.

Topological properties of three-valued logic metric space

HU Ming-Di, SHE Yan-Hong, WANG Min

J4. 2010, 45(6): 86-90.

Abstract ( 1023 )

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On the growth of the meromorphic solutions of complex algebraic differential equations

XU Jun-feng

J4. 2010, 45(6): 91-93.

Abstract ( 1044 )

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By Zalcman Lemama, estimating the growth order of the solution of a type of systems of higher order algbraic differential equations are obtained. Many results concerning the solutions of differential equation are generalized and improved.

A proof of the necessity of Tb-theorem

ZHAO Kai, XU Yi,WANG Yong-gang

J4. 2010, 45(6): 94-98.

Abstract ( 962 )

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The bilinear forms of Calderón-Zygmund operator T with Tb-theorem on non-homogeneous spaces which is defined on smooth functions are introduced. Under such condition, the necessity of Tb-theorem has been proved and the two BMO spaces are equivalent to the Tb-theorem on non-homogeneous spaces have been shown.

Passive sliding mode control for uncertain time-delay systems subjected to input nonlinearity

LI Ya-nan1, LIU Lei-po2, WANG Yu-guang3

J4. 2010, 45(6): 99-104.

Abstract ( 985 )

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The problem of passive sliding mode control for uncertain timedelay systems subjected to input nonlinearity is investigated. Using the sliding mode control, a robust law is established such that the reachability of the sliding surface in the state space is guaranteed in a finite time, and the sufficient condition for the passivity and asymptotic stability of sliding mode dynamics is derived via linear matrix inequality(LMI). Finally, a simulation example is presented to verify the validity of the proposed method.

Synchronization analysis of oscillatory activities in a biological cell system

HUO Yu-hong, JI Quan-bao

J4. 2010, 45(6): 105-110.

Abstract ( 1024 )

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The synchronizations in chain and ring connections repectively related to three coupled systems are investigated. It is concluded that the criteria value in chain connection is bigger than that in ring connection to obtain synchronization in our analysis and simulations.

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