JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Jordan multiplicative isomorphisms on Spin factors

JI Pei-sheng, SUN Lin, CHEN Jian-hui

J4. 2011, 46(8): 1-3.

Abstract ( 989 )

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Let R be the field of real numbers and H be a real Hilbert space of dimension at least 2. Let A=H十R be the Spin factor corresponding to H. In this note, we prove that if a bijective map Ø from A onto itself satisfies Ø(x。y)=Ø(x)。Ø(y) for all x,y∈A, and Ø(α+β)=Ø(α)+Ø(β) for all α,β∈R, then there is a unitary operator U on H such that Ø(a+α)=Ua+α for every a∈H, α∈R.

Conservative scheme for the general improved KdV equation

ZHANG Tian-de1, ZUO Jin-ming2, DUAN Ling-ji1

J4. 2011, 46(8): 4-7.

Abstract ( 1217 )

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A new conservative finite difference scheme is presented for an initial-boundary value problem of the general improved KdV(GIKdV) equation. It is proved by the discrete energy method that the scheme is unconditionally stable and second-order convergent. Numerical experiments demonstrate that the scheme is accurate efficient.

A subspace accelerated truncated Newton algorithm for solving the extreme eigenvalue of large-scale sparse symmetric matrix

QIAN Xiao-yan

J4. 2011, 46(8): 8-12.

Abstract ( 1316 )

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Based on the classic truncated Newton algorithm for nonlinear optimization, a new subspace accelerated truncated Newton algorithm is presented for large-scale symmetric sparse extreme eigenvalue problems. The convergence properties are proved and numerical experiments are done. The numerical results match the convergence analysis,which showing the new algorithm is effective.

An implicit difference scheme for solving the neutral delay parabolic differential equation

JIN Cheng-ri, YU Zhan-hua, QU Rong-ning

J4. 2011, 46(8): 13-16.

Abstract ( 1088 )

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An implicit difference scheme for solving the neutral delay parabolic differential equation is presented. This scheme is unconditional stable in the sense of discrete L2norm. The local truncation error of this scheme is O(Δt²+Δx²). This scheme leads to a tridiagonal linear system to be solved at each time-step. The Crout factorization algorithm is used to solve this linear system. The numerical results show that the presented implicit difference scheme is effective.

Structure of eigenvalues of multi-point boundary value problems

GAO Jie

J4. 2011, 46(8): 17-22.

Abstract ( 1087 )

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Fundamental solutions of fractional-in-space diffusion equation with Riesz fractional derivative in two and three dimensions

WANG Xue-bin

J4. 2011, 46(8): 23-30.

Abstract ( 1514 )

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The fundamental solutions of fractional-in-space diffusion equation is considered with Riesz fractional derivative (RFDE) in two and three dimensions. The existing definitions of the fractional Laplacian (two dimensions and three dimensions) are investigated and discussed by using eigenfunction expansion, and the relations between fractional Laplacian and Riesz fractional derivative are given. Finally, the fundamental solutions of homogeneous and non-homogeneous RFDE with an initial and boundary condition is derived on a finite domain using a spectral representation.

Higher accuracy analysis for the bilinear element solution of nonlinear viscoelasticity type equations

NIU Yu-qi1, WANG Fen-ling1, SHI Dong-wei2

J4. 2011, 46(8): 31-37.

Abstract ( 1090 )

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In this paper, by use of the integral identities and the mean value technique, approximation of bilinear finite element for the nonlinear viscoelasticity type equations with superclose property of order O(h²) in H¹-norm is obtained. A global superconvergence result is yielded by interpolated post-processing method. Then higher accuracy of order O(h³) for approximation solution is derived through constructing a proper extrapolation scheme.

Approximation method for two-point boundary value problem of differential game based on ridge basis function

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

J4. 2011, 46(8): 38-41.

Abstract ( 1067 )

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The study of differential game has yielded a number of substantial results. However, numerical method for saddle point strategy is still open question. In this paper, a new method with ridge basis function for twopoint boundary value problem of differential game is developed, where the existence and uniqueness of the solution of twopoint boundary value problem is established and discussed.Also, the method is applied to numerical examples to examine its appropriateness. It will be a useful way to solving the numerical solutions of saddle point strategy.

Super-convergence analysis of Adini′s finite element for a kind of nonlinear generalized nerve conductive equations

QIAO Bao-min, LIANG Hong-liang

J4. 2011, 46(8): 42-46.

Abstract ( 1161 )

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The convergence analysis is studied for a kind of nonlinear generalized nerve conductive equations by Adini′s finite element. Error estimates and result of superclose are obtained by using some novel approaches and techniques. Finally, the corresponding global superconvergence is obtained by taking the advantage of the post-processing technique.

Existence of periodic solutions for higher order nonlinear neutral delay equations

CHEN Xin-yi

J4. 2011, 46(8): 47-51.

Abstract ( 1064 )

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The following nonlinear neutral delay equations ［x(t)+cx(t-τ)］⁽ⁿ⁾ +g(t,x(t-σ))=p(t) is discussed. By using the coincidence degree theory, a sufficient condition for the existence of periodic solution of the equation is given, which generalizes the known results.

Some new integral inequalities in two independent variables and their applications

ZHANG Hong-xia1, KONG Xiang-zhi2

J4. 2011, 46(8): 52-58.

Abstract ( 1326 )

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Some new nonlinear delay integral inequalities in two independent variables are established. The boundedness of the solution of more general delay integral equations of two variables are carried out.

Oscillation of second order difference equations with positive and negative coefficients

YANG Jia-shan, SUN Wen-bing

J4. 2011, 46(8): 59-62.

Abstract ( 1173 )

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The oscillation of a class of second order nonlinear neutral variable delay difference equation with positive and negative coefficients is discussed. Using the fixed point theorem in Banach space, a new nonoscillation criteria for the equation is obtained by introducing parameter function and the generalized Riccati transformation. Also, a sufficient condition for oscillation of the equation is proposed. These criteria can improve the restriction of the conditions for the equation, which promote some existed results.

A note normal criterion about share values

QI Jian-ming1, DING Jie2, ZHU Tai-ying1

J4. 2011, 46(8): 63-67.

Abstract ( 1046 )

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By the ideas of sharing values, and using the Zaclman lemma, a generaliztiona of the original result is improved.

Stabilizer of N(2,2,0) algebras

LI Xu-dong

J4. 2011, 46(8): 68-72.

Abstract ( 1113 )

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The stabilizer of N(2,2,0) algebras is studied. By using the stabilizer, congruence decomposition on N(2,2,0) algebras is given. The algebraic structure of the quotient algebra is obtained and also algebraic structure and some properties of a class of converse images under the natural homomorphism are obtained.

The lattice of fuzzy ⊙-ideals in regular residuated lattices

QIN Xue-cheng, LIU Chun-hui*

J4. 2011, 46(8): 73-76.

Abstract ( 1151 )

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The lattice operations and the adjoint pair on the set of all fuzzy ⊙-ideals in regular residuated lattices are defined. It is obtained that the fuzzy ⊙-ideals lattice defined in our sense is a distributive residuated lattice.

Quasi-elastic spaces

MIAO Cheng-dong, XU Yu-ming, CAO Zhen-bo

J4. 2011, 46(8): 77-79.

Abstract ( 1056 )

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The definition of quasi-elastic spaces and network-elastic spaces are defined. Quasi-elastic spaces are well-ordered (F) spaces and network-elastic spaces are equivalent to T1 spaces.

Quasi-uniformities and topologies on a finite set

WANG Yi-rui1, LI Sheng-gang2

J4. 2011, 46(8): 80-83.

Abstract ( 1117 )

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Star edge coloring of tree

DENG Kai1, LIU Xin-sheng2, TIAN Shuang-liang1

J4. 2011, 46(8): 84-88.

Abstract ( 1478 )

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The star edge coloring of tree is studied, the star chromatic index of two kinds of special trees are obtained, and an attainable upper bound of star chromatic index of tree is proved.

Adjacent vertex distinguishing incidence coloring of the join of some special graphs

WANG Qian, TIAN Shuang-liang

J4. 2011, 46(8): 89-91.

Abstract ( 1080 )

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An adjacent vertex distinguishing incidence coloring of graph G is an incidence coloring of G such that no pair of adjacent vertices meets the same set of colors. The adjacent vertex distinguishing incidence chromatic number of G∨C_m, G∨S_m and G∨T_m are obtained, where G is a star, wheel, or fan of order n+1 and C_m is a cycle of order m, S_m is a star of order m+1, T_m is a tree of order m.

The application of some special hyper-graphs in the perfect graphs

SUN Lin

J4. 2011, 46(8): 92-94.

Abstract ( 1414 )

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It is proved that the representative graphs of unimodular hyper-graph, balanced hypergraph and tree hypergraph are perfect. The definition of the kperfect hypergraph is given, which is an extention of the perfect graph. Finally, the properties of normal hyper-graph and quasi-regularizable hypergraph are discussed, and some results are obtained.

The L(p,q)-labeling of planar graphs with girth g(G)≥5

ZHU Hai-yang1, HOU Li-feng1, CHEN Wei1, Lü Xin-zhong2

J4. 2011, 46(8): 95-103.

Abstract ( 1088 )

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Let p and q be two positive integers with p≥q, and let λ_p,q(G) be the L(p,q)-labeling number of a planar graph G. It is proved that λ_p,q(G)≤(2q-1)Δ(G)+6p+10q-8 if G is a planar graphs with girth g(G)≥5, which implies Wegner’s conjecture holds for a planar graph G with girth g(G)≥5 and Δ(G)≥16.

Properties of interval-valued intuitionistic fuzzy rough sets with implicators

LIN Meng-lei1, YANG Wei-ping2

J4. 2011, 46(8): 104-109.

Abstract ( 1123 )

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By employing two interval-valued intuitionistic fuzzy implicators I and J, interval-valued intuitionistic fuzzy rough sets with implicators are first defined in the intervalvalued intuitionistic fuzzy approximation space. Properties of interval-valued intuitionistic fuzzy rough sets with implicators are proved. Finally, the reflexivity, symmetry and transitivity of interval-valued intuitionistic fuzzy relations are characterized.

A one-direction S-fuzzy rough set and its application

LU Xiao-yun1, YANG Yong 2

J4. 2011, 46(8): 110-113.

Abstract ( 997 )

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A one-direction fuzzy rough set is proposed, and its general structure and the concept are given by the theory of Dubois fuzzy rough set and the concept of the dynamic fuzzy set. Then, the relationships between a one-direction S-fuzzy rough set and fuzzy rough set are analyzed, and properties and its application of one-direction S-fuzzy rough set are presented.

Remarks on axiomatizations of generalized rough sets theory

MA Zhou-ming1,2, LI Jin-jin1,2*

J4. 2011, 46(8): 114-117.

Abstract ( 937 )

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Generalized rough sets theory is a development of rough sets theory based on equivalence relation. The axiomatizations of generalized rough sets is discussed based on binary relations, and the necessary axiom condition of a binary relations are analyzed by the actual examples.The sufficient conditions of every axiom set are given.

P-sets and dynamic data outer access-applications

XIE Wei-qi1,2, LIU Dao-guang1

J4. 2011, 46(8): 118-121.

Abstract ( 951 )

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P-sets can be obtained from the improved finite general sets based on the dynamic characteristics. P-sets are a pair of set. Using outer P-sets, the process and characteristic of dynamic data outer access are given, and the metric and dependence relation of dynamic data outer access are obtained. Then, the iterative algorithm and criterion of dynamic data outer access are proposed. Finally the applications are given.

P-set and it′s measure space

ZHAO Zhan-ping, ZHOU Hou-yong, XIE Li-ming

J4. 2011, 46(8): 122-126.

Abstract ( 1054 )

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The P-set is generalized from finite sets to arbitrary set. The dynamic σ-algebra of P-set and P-measure space are proposed according to the knowledge about measure theory based on the given measure space. The P-set based on the arbitrary ordinary sets is studied,which is provided reliable theory support for the information safety.

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