JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Existence and uniqueness of solutions of a class of singular parabolic equations

YUN Dong-fang, HUANG Shu-xiang

J4. 2012, 47(2): 1-7.

Abstract ( 973 )

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Weak nonlinear singular perturbed boundary value problems with discontinous source terms

DING Hai-yun1,2, NI Ming-kang1,3

J4. 2012, 47(2): 8-13.

Abstract ( 931 )

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A class of weak nonlinear singularly perturbed boundary value problems with discontinuous source terms is examined. Using the method of boundary functions and smooth sewing orbit, the asymptotic solution of this problem is given and shown to be uniformly effective. The existence and uniqueness of the solution for the system is proved. A numerical result illustrats to the theoretical result.

Solutions for asymptotically linear elliptic equations involving Hardy potential and critical parameter

WANG Jiang-chao, ZHANG Yi-min*

J4. 2012, 47(2): 14-18.

Abstract ( 1018 )

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A class of asymptotically linear elliptic equations with Hardy potential and critical parameter is considered. For general bounded domain Ω, there is no nontrivial solution in space H¹₀ (Ω) for this kind of equation (see reference［1］). The existence of non-trivial solutions are proved in a new Sobolev-Hardy space with the technique of Morse theory.

Convergence of the finite element method for two-phase multi-component flow in porous media

YU Jin-biao1,2, XI Kai-hua3*, DAI Tao2, LU Tong-chao3, YANG Yao-zhong2,

J4. 2012, 47(2): 19-25.

Abstract ( 990 )

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The mathematical model for describing two phase incompressible immiscible displacement flow with multi-components in porous media is considered. A global formulation of the governing equations, including pressure, saturation and concentration equations is constructed. For the system, a full-discrete scheme is formulated by the standard Galerkin finite element method and the optimal error estimate in H1 norm is derived.

Explicit blow-up solutions for compressible magneto-hydrodynamic equations

SONG Dan-dan, YUAN Bao-quan*

J4. 2012, 47(2): 26-30.

Abstract ( 900 )

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A family of explicit blow-up solutions in the form of separate variables to the N-dimensional magneto-hydrodynamic equations are constructed by solving ordinary differential equations.

ositive solutions of boundary value problems for systems of nonlinear mixed higher order singular differential equations

ZHANG Hai-yan1,2, LI Yao-hong2

J4. 2012, 47(2): 31-35.

Abstract ( 951 )

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Using fixed point theorems of cone expansion and compression of norm type, the existence and multiplicity of positives solutions to boundary value problems for systems of nonlinear mixed higher order singular differential equations are given under some common limit type conditions. The results presented here improve and generalize many well-known results.

Analysis of the anisotropic R-T element for quasi-linear parabolic problems on anisotropic meshes

MENG Xiao-ran1, SHI Dong-wei2

J4. 2012, 47(2): 36-41.

Abstract ( 1067 )

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The anisotropic property of the R-T element with one order is proved based on the anisotropic interpolation theorem and applied to quasi-linear parabolic problems. The convergence analysis and error estimates are directly given through an interpolation operator without Ritz projection, and by use of integral identity, the supercloseness of flux is derived in H(div,Ω)-norm.

Pseudo almost solutions of difference equations

GUO Ying

J4. 2012, 47(2): 42-46.

Abstract ( 941 )

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Pseudo almost periodic solutions of the linear difference systems and the nonlinear difference systems are investigated by using exponential dichotomy and fixed point theorem, which extend some results of pseudo almost solutions for differential equations.

Quasi-wavelet method for the Stokes problem

WANG Xiao-juan, CHEN Yi-ming, ZHOU Zhi-quan, LI Yu-lian

J4. 2012, 47(2): 47-51.

Abstract ( 847 )

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The second boundary value problem of Stokes equations in the upper half plane is reduced to natural integral equations with hypersingular kernels in the sense of the Hadamard finite part. Consequently, the Galerkin-Quasi-Wavelets method is applied to its equivalent variational problem on the boundary. Simple computational formulae of the entries in stiffness matrix are obtained,and they are diagonally dominant. This greatly reduces the amount of calculation and improves precision.

An upper bound for the adjacent vertex-distinguishing star chromatic number of graphs

LIU Xin-sheng, WEI Zi-ying

J4. 2012, 47(2): 52-55.

Abstract ( 904 )

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The restricted neighbor connectivity of line graphs

WANG Wan-yu, MENG Ji-xiang*, ZHAO Xue-bing

J4. 2012, 47(2): 56-59.

Abstract ( 1013 )

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On the vertex-distinguishing proper edge-coloring of K_3,3∨Kt

GAO Yu-ping1, WANG Zhi-wen2, CHEN Xiang-en1*, YAO Bing1

J4. 2012, 47(2): 60-64.

Abstract ( 1310 )

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A k-proper edge coloring of a simple graph G is called vertex-distinguishing if for two arbitrarily different vertices u and v, the set of colors assigned to the edges incident to u differs from the set of colors assigned to the edges incident to v. The minimum number of colors required for a vertex-distinguishing proper edge-coloring of a simple graph G is called the vertex-distinguishing proper edge chromatic number of G and denoted by χ′s(G). Vertex-distinguishing proper edge colorings of K3,3∨Kt are discussed.

On complete chromatic numbers of cubic Halin graphs

YAO Ming1, YAO Bing2*， CHEN Xiang-en2

J4. 2012, 47(2): 65-70.

Abstract ( 914 )

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On the strong regularity of J-rings

WU Guo-ying, WU Jun

J4. 2012, 47(2): 71-73.

Abstract ( 814 )

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The strong regularity of J-rings is studied. By using some properties of SF-rings, GP-V-rings, and GP-V′-rings, we obtain some conditions for a ring to be a strongly regular ring.These extend some corresponding results.

On quadratic P-Hermitian matrix equations

YUAN Hui-ping, LI Qin-yu

J4. 2012, 47(2): 74-77.

Abstract ( 982 )

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A matrix equation XAX=A is considered where A is a P-Hermitian matrix. Some necessary and sufficient conditions to this equation in some special cases are given. Specific forms of these solutions are also presented.

On the idempotent ranks of the semigroup V(n,r)

ZHAO Ping

J4. 2012, 47(2): 78-81.

Abstract ( 860 )

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The conditional truth degree of theory in proposition logic

ZHANG Le, PEI Dao-wu

J4. 2012, 47(2): 82-85.

Abstract ( 901 )

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The properties of truth degree of theory are discussed. Then, the conditional truth degree of theory in proposition logic is proposed on the ideal of conditional probability. Based on the conditional truth degree of theory, a new approximate reasoning mode between formula sets is proposed, which can be used to search for the best reasoning conclusion and premise. Finally, the harmonious degree of theory is proposed for characterizing the extent of the internal harmony of the theory.

The regularness of WBR₀-algebras and relationship with other logic algebras

ZHOU Jian-ren, WU Hong-bo*

J4. 2012, 47(2): 86-92.

Abstract ( 1041 )

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Regular residuated lattices and WBR₀-algebras are investigated in depth. The relationship between WBR₀-algebras and other logic algebras is made clearer and more definite than before. The main results of this paper are as follows: (1) It is proved that regular residuated lattices and WBR0algebras are the same algebraic structure. (2) The connection among WBR₀-algebras with other classical logic algebras is given by the network, through which the roles of WBR₀-algebras are explained. (3) The difference between WBR₀-algebras and other logic algebras is revealed by constructing a special WBR₀-algebra.

BR₀-distributivity and its generalization

LI Ling-ling, WU Hong-bo*

J4. 2012, 47(2): 93-97.

Abstract ( 991 )

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BR₀-distributivity has an important position in the structure of BR0algebras which says a→b∨c=(a→b)∨(a→c). It is proved that residuated lattices with BR0-distributivity also have good properties. BR₀-distributivity is introduced in residuated lattices, and its equivalent form is given. Then the BR0-distributivity is generalized in complete residuated lattices, and BR₀-first infinite distributivity and BR₀-second infinite distributivity are obtained. Finally, the properties and relationship between two kinds of BR₀-infinite distributivity are discussed in regular complete residuated lattices and the unite interval ［0,1］, respectively.

TL-filters and TL-congruences of residuated lattices

LIU Yi1,2, XU Yang2, QIN Xiao-yan 2, QIN Ya3

J4. 2012, 47(2): 98-103.

Abstract ( 839 )

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t-norm T of bounded lattices is applied to filters and congruences in residuated lattices, and the concept of TL-filters and TL-congruences of a residuated lattice are introduced. Their properties and some equivalent characterizations are derived.We prove that there is a correspondent bijection between the set of all TL-filters of a residuated lattice and the set of all TL-congruences in that residuated lattice. Finally, quotient residuated lattices and homomorphism theorem are derived. These results and methods still hold in other logical algebraic structures.

Consistently quasi-semicontinuous Domains and consistently meet-semicontinuous Domains

GUO Zhi-lian1,2, YANG Hai-long1*

J4. 2012, 47(2): 104-108.

Abstract ( 925 )

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The concepts of consistently quasi-semicontinuous Domains and consistently meet-semicontinuous Domains are introduced, and some properties are given. The relations of consistently semicontinuous Domains and consistently quasi-semicontinuous Domains and consistently meet-semicontinuous Domains are discussed. Also, the equivalences of consistently meet-semicontinuous Domains are given.

λ-resolution for medium predicate logic based on an improved form of infinite-valued semantic interpretation

ZHANG Sheng-li1, PAN Zheng-hua2

J4. 2012, 47(2): 109-114.

Abstract ( 956 )

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On a kind of S-closed spaces

ZHANG Xia-wei1， KONG Qing-zhao2*， CHEN Hai-yan3

J4. 2012, 47(2): 115-118.

Abstract ( 947 )

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The properties extending S-closed spaces are discussed. It is shown that (1) every semi-open regular subspace of a locally S-closed space is locally S-closed. (2)If A is a regular open subset of X, then A is locally S-closed if and only if A is locally S-closed relative to X. (3) Every T2 minimal-locally-S-closed space is Sclosed.

Intuitionistic fuzzy fully invariant subgroups and characteristic subgroups

LI Xiao-ping1， SUN Gang2

J4. 2012, 47(2): 119-122.

Abstract ( 1265 )

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The cut-sets of an intuitionistic fuzzy set are introduced, and an intuitionistic fuzzy fully invariant subgroup and an intuitionstic fuzzy characteristic subgroup are defined. The relationship between the intuitionistic fuzzy fully invariant subgroups and intuitionstic fuzzy characteristic subgroups is investigated. Finally, the structure and characteristic of the intuitionistic fuzzy subgroup of a circulating group are discussed.

The hierarchy internal P-relation and internal P-cluster algorithms

XIE Wei-qi1,2, LI Xiao-xin1

J4. 2012, 47(2): 123-126.

Abstract ( 941 )

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By using the dynamic characteristics of the P-set, the concept of the hierarchy internal P-sets is proposed. The relationship among the P-sets, the metric characteristics, the cluster analysis algorithm and application of P-sets based on the similarity relationship are studied, and the internal P-cluster algorithms is tested.

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