JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Algorithms of finite difference domain decomposition for two-heat equation

LI Wan-shan, WANG Wen-qia*

J4. 2011, 46(12): 1-5.

Abstract ( 1398 )

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Considering algorithms of finite difference domain decomposition for twodimensional heat equation, a new kind of explicitimplicit difference schemes which is of unconditional stability is developed. The corresponding schemes consist of one explicit difference schemes at the interface point and fully implicit schemes in the subdomains. The stability and error estimates of the schemes are derived. Finally, the numerical experiment is presented which confirm the results and conclusions.

A new streamline-diffusion mixed finite element method for compressible miscible displacement problem in porous medium

ZHANG Jian-song1, NIU Hai-feng2

J4. 2011, 46(12): 6-12.

Abstract ( 1104 )

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A new streamline-diffusion mixed finite element procedure is constructed for solving compressible miscible displacement problem in porous medium. In this procedure, a splitting positive definite mixed element method, the parabolic-type pressure equation. Using a streamline-diffusion finite element method, the convection-diffusion type concentration equation is solved. The coefficient matrix of the mixed system is symmetric and positive definite. The convergence of the procedure is studied and the corresponding error estimate is also given.

The optimal parameters of PSD method for rank deficient linear systems

LIU Xiao-guang, CHANG Da-wei*

J4. 2011, 46(12): 13-18.

Abstract ( 1082 )

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Combining the geometry and the algebra,the optimal parameters and the optimal spectral radius of PSD method for rank deficient linear systems Ax=b are acquired,where A∈Cm×nr and r<min｛m,n｝, x∈Cn, b∈Cm, then examples are given to illustrate the results.

Conservative linearimplicit scheme for the general Improved KdV equation

ZUO Jin-ming, ZHANG Yao-ming

J4. 2011, 46(12): 19-22.

Abstract ( 1047 )

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A new conservative linear-implicit 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 and efficient.

A linearized finite difference scheme for the generalized regularized long-wave equation with a variable coefficient

MA Wei-yuan, MA Gang

J4. 2011, 46(12): 23-28.

Abstract ( 1056 )

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A linearized finite difference scheme for the damped generalized regularized long-wave equation with a variable coefficient is presented. The existence of the difference scheme is shown by Brouwer fixed-point theorem. Convergence and stability of difference solution are proved. Numerical experiment results demonstrate that the scheme is effective and reliable.

The alternating group method for KuramotoSivashinsky equation

ZUO Jin-ming1, ZHANG Yao-ming1, ZHANG Tian-de2, LI Na2

J4. 2011, 46(12): 29-32.

Abstract ( 1009 )

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A group of asymmetric difference schemes to approximate Kuramoto-Sivashinsky equation are given. Using the schemes, the alternating group method for solving Kuramoto-Sivashinsky equation is constructed. The scheme is linear unconditionally stable by analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show the method has near the fourth order ratio of convergence in space.

The lumped mass nonconforming finite element method of the Crank-Nicolson scheme for nonstationary Stokes problem

ZHANG Fei-ran

J4. 2011, 46(12): 33-38.

Abstract ( 1141 )

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The discrete approximation scheme of the lumped mass nonconforming finite element method are discussed for nonstationary Stokes problem (Crank-Nicolson fulldiscrete scheme).Without using Stokes projection,the optimal error estimations of the velocity and pressure are derived based on interpolation technique.

High order compact scheme combined with extrapolation technique for solving convection-diffusion equations

QIAN Ling-zhi1, GU Hai-bo2

J4. 2011, 46(12): 39-43.

Abstract ( 1105 )

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Compact difference scheme are constructed by means of Padé approximation method, Richardson extrapolation technique and two-grid algorithm combined with compact finite difference scheme for linear convection-diffusion problems. Realization of the scheme,analysis of stability and error estimated are presented. Finally, numerical examples are presented to clarify the method.

Minimal injective cogenerator of principal ideal domain

ZHANG Kui, TANG Yi-li, GE Mao-rong*

J4. 2011, 46(12): 44-45.

Abstract ( 1118 )

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Let R be a Principal Ideal Domain. The concrete structure of minimal injective cogenerator of RM is obtained: R is a minimal injective cogenerator of RM if R is a field; K／R is a minimal injective cogenerator of RM (K is the fractional field of R) if R is not a field.

The Duality of a Hopf π-Comodule Coalgebra

CHEN Hua-xi1, YIN Xiao-bin2

J4. 2011, 46(12): 46-50.

Abstract ( 1108 )

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The definitions of π-H-comodule coalgebras and π-module algebras are given, and it is proved that the duality of a locally finite-dimensional π-H-comodule coalgebra is a π-H*-module algebra.

The influence of the properties of local subgroups on the structure of finite groups

PU Zhao-Nian1, TANG Ju-Ping2, GU Chun-Hua3

J4. 2011, 46(12): 51-54.

Abstract ( 1099 )

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The properties of the subgroups have been localized in order to consider the M-supplementation of NG(P), where P is the Sylow p-subgroup of G, and some results about p-nilpotency and supersolvablity have been obtained.

Weighted Moore-Penrose inverses on rings

YUAN Wan-gui, KONG Xiang-zhi

J4. 2011, 46(12): 55-59.

Abstract ( 1114 )

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Assuming that M, N are arbitrary matrices on rings, it is discussed that the necessary and sufficient conditions of the weighted Moore-Penrose inverses with respect to M,N for existences. In addition, it is found that the all solutions of A｛1,3M｝, A｛1,4N｝, A｛1,2,3M｝, A｛1,3M,4N｝ and A｛1,2,3M,4N｝.

Maximal regular subsemigroups of orientation-preserving or orientation-reserving transformation semigroups I(n，r)

ZHAO Ping1, HU hua-bi1, XU Bo2

J4. 2011, 46(12): 60-65.

Abstract ( 1051 )

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Let Pn be the orientation-preserving or orientation-reserving transformation semigroup on ［n］, and let I(n,r)=｛α∈Pn:|im(α)|≤r｝(3≤r≤n-1). The classification of maximal regular subsemigroup of semigroup is obtained completely.

The companion semi-rings of IS-algebras

YANG Wen-qi

J4. 2011, 46(12): 66-69.

Abstract ( 1426 )

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The companion semi-rings and the ring parts of IS-algebras are introduced. By discussing their properties, the relations between the general IS-algebras and the semi-rings or rings are shown, and some IS-algebras are characterized.

A generalization of principle of inclusion-exclusion and its application(Ⅱ)

TANG Shan-gang

J4. 2011, 46(12): 70-75.

Abstract ( 1285 )

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The principle of inclusion-exclusion is extended to the general restricted conditions on a weighted finite set, a weighted generalization of principle of inclusion-exclusion is given. Some applications of generalized principle of inclusion-exclusion are given on the combinatorial enumeration.

Mean value of D.H.Lehmer problem in short interval

GUO Xiao-yan

J4. 2011, 46(12): 76-82.

Abstract ( 1093 )

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The mean value of D.H.Lehmer problem in short interval is investigated. Some asymptotic formula is obtained by using the Fourier expansion for character sums and the estimates for exponential sums.

Complete spacelike submanifolds in de Sitter spaces with parallel normalized mean curvature vector

QI Bang-jiao

J4. 2011, 46(12): 83-87.

Abstract ( 1005 )

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By using Yau’s general maximal principle, sufficient conditions for complete space-like submanifolds with parallel normalized mean curvature vector in a de Sitter spaces Sn+pp(c) are obtained.

Weighted boundedness of commutators of the fractional integral on λ-central Morrey spaces

ZHAO Kai, DONG Peng-juan, SHAO Shuai

J4. 2011, 46(12): 88-92.

Abstract ( 1197 )

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The weighted λ-central Morrey spaces and weighted CBMO functions are introduced. Then by the properties of Ap weighted functions and the real-variable methods of harmonic analysis, the weighted boundedness of commutators of the fractional integral with CBMO function on weighted λ-central Morrey spaces is obtained. This result enriches the certain theory of commutators.

Oscillation of solutions of some non-homogeneous differential equations

RONG Chang1, CAI Hui-ping2, WANG Jun3

J4. 2011, 46(12): 93-95.

Abstract ( 1052 )

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Fast algorithm for solving the first plus last circulant linear system

TIAN Zhi-ping

J4. 2011, 46(12): 96-103.

Abstract ( 1091 )

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A fast algorithm for solving the first plus last circulant linear system is presented by the fast algorithm for computing polynomials. When the first plus last circulant matrix is nonsingular, we compute its unique solution. When the first plus last circulant matrix is singular, we compute its special solution and general solution. Finally, a fast algorithm for solving the first plus last retrocirculant linear system is proposed by using the relationship between the first plus last circulant matrix and the first plus last retrocirculant matrix.

Analytical blow-up solutions to the Euler equations

YAN Xiao-li, YUAN Bao-quan*

J4. 2011, 46(12): 104-107.

Abstract ( 1154 )

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A family of analytical solutions to the N dimensional isothermal Euler equations and the pressureless Euler equations with frictional damping are constructed by solving a second order ordinary differential equation. Especially, the solutions may blow up at a finite time T.

Positive solutions of three-point boundary value problems for third-order impulsive differential equations with p-Laplacian operator

GUI Wang-sheng

J4. 2011, 46(12): 108-113.

Abstract ( 1032 )

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The positive solution of three-point boundary value problem for third-order impulsive differential equations with p-Laplacian operator is considered. This problem is transformed into an equivalent integral equation by applying the Green’s function of threepoint boundary value problem for secondorder impulsive differential equations. The existence of the positive solution is discussed by applying Avery-Peteron fixed point theorem on a suitable cone. Thus a sufficient condition is obtained for the existence of three positive solutions.

Two-direction S-probability rough sets and its application

LI Zhi-yi, LIU Ji-qin*

J4. 2011, 46(12): 114-119.

Abstract ( 974 )

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Considering two-direction dynamic property of the set X and statistical informational in knowledge base, two-direction S-probability rough sets is presented. Dynamic properties of two-direction Sprobability rough sets are discussed, and its application is proposed.

(λ,μ)-anti-fuzzy normal subgroup

XIAO Bing-feng, YAO Bing-xue

J4. 2011, 46(12): 120-123.

Abstract ( 1168 )

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Abstract: Based on the theory of (λ,μ)-fuzzy normal subgroup,the definitions of the (λ,μ)-anti-fuzzy normal subgroup, (λ,μ)-anti-fuzzy normalizer and (λ,μ)-anti-fuzzy centralizer are introduced. Some conditions of equivalence and properties are discussed. Also,some corresponding theorems of (λ,μ)-anti-fuzzy normal subgroup in homomorphic mapping are established.

The I_r-functor on L-Top

JIN Qiu, LI Ling-qiang*, SUN Shou-bin, MENG Guang-wu

J4. 2011, 46(12): 124-126.

Abstract ( 1266 )

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For a prime element r of a frame L, a concrete functor Ir on the category L-Top is introduced. The composition of the stratifiorm Lowen functors ωrL and ιrL is proved, and its some applications are given. Finally, the relationship between it and Rodabaugh′s stratification functor GLk is studied.

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