JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Least squares symmetric anti-reflexive solutions of the matrix equation AXA^T=B

ZHAO Lin-lin1, CHEN Guo-liang1, ZHAO Jian-li2

J4. 2010, 45(10): 1-3.

Abstract ( 1589 )

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By applying the canonical correlation decomposition of matrix pairs, the general expression of the least squares symmetric anti-reflexive solution with a given symmetric orthogonal matrix P of the matrix equation AXA^T=B is obtained.

Linear maps preserving inverses of matrices on symmetric matrix modules over principal ideal domains

SHI Xue-ying, CHEN Xiao-ping

J4. 2010, 45(10): 4-8.

Abstract ( 1479 )

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Let R be a principal ideal domain and the characteristic of R be not 3. Assume that 2 is a unit in R. Let n and m be positive integers with n≤m. The linear maps preserving inverses of matrices from n×n symmetric matrix modules S_n(R) onto m×m matrix modules M_m(R) over R are described.

The weighted Moore-Penrose inverse over integral domains

WANG Hong-xing1,2, LIU Xiao-ji3

J4. 2010, 45(10): 9-14.

Abstract ( 1554 )

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The generalized Moore-Penrose inverse is investigated over integral domains. New determinantal representations of the weighted Moore-Penrose inverse are introduced, and necessary and sufficient conditions for its existence over an integral domain are obtained.

On weaker skew-Armendariz rings

WANG Wen-kang

J4. 2010, 45(10): 15-19.

Abstract ( 1361 )

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Some maximal skew-Armendariz subrings of upper triangular matrix rings over reduced rings are described. Weaker skew-Armendariz rings are investigated.

Finitely quasi-injective modules

ZHU Zhan-min

J4. 2010, 45(10): 20-23.

Abstract ( 1551 )

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Let R be a ring. A right R-module M is called finitely quasi-injective if each R-homomorphism from a finitely generated submodule of M to M can be extended to an endomorphism of M. Some characterizations and properties of finitely quasi-injective modules are given, and some finitely generated finitely quasi-injective modules are investigated.

A splitting for the W-weighted Drazin inverse of a linear operator on Banach space

HU Chun-mei，LIU Xiao-ji*

J4. 2010, 45(10): 24-26.

Abstract ( 1526 )

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A splitting and its relative iteration for calculating the W-weighted Drazin inverse of a linear operator on Banach space are presented. A necessary and sufficient condition and the error estimate are given for converging of the iteration to the W-weighted Drazin inverse.

Double edge coloring on two classes of approximate Halin graphs

SHAN Wei1, WU Jian-liang2

J4. 2010, 45(10): 27-30.

Abstract ( 1375 )

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For two classes of approximate Halin graphs,it is proved that the double edge chromatic numbers satisfy χ_e／vf(G)=F_M(G).

Isolated toughness and existence of fractional (g, f)-factors in graphs

LIU Shu-li

J4. 2010, 45(10): 31-34.

Abstract ( 1221 )

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The relationship between isolated toughness and existence of fractional (g, f)-factors is considered. It is proved that a graph G has a fractional (g, f)-factor if δ(G) and I(G) are not less than (a+b)²+2(b-a)/4a when a≠b(mod2)or δ(G) and I(G) are not less than (a+b)²+2(b-a)+1/4a when a≠b(mod2).

Vertex distinguishing total chromatic number of mC₄

XIN Xiao-qing1,2, CHEN Xiang-en1*

J4. 2010, 45(10): 35-39.

Abstract ( 1462 )

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Vertex-distinguishing total chromatic numbers of mC₄(m≥2) are obtained.

Independent domination bicritical graphs

XU Lan1,2, XU Ying 1, ZHANG Li 3

J4. 2010, 45(10): 40-44.

Abstract ( 1369 )

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A graph G is independent domination bicritical if the removal of any pair of vertices decreases the independent domination number. Some particular classes of graphs which are independent domination bicritical are discussed and some properties of independent domination bicritical graphs are studied. Finally, ways of constructing an independent domination bicritical graph from smaller independent domination bicritical graphs are presented.

Two types of graceful graphs

TANG Bao-xiang1,2, REN Han2

J4. 2010, 45(10): 45-48.

Abstract ( 1200 )

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It is proved that Q²_m×n and u·Q²_m×n are graceful graphs by using the construction methods in the article.

The factorization of adjoint polynomials of graphsH_i ^SS*(1)(q,n(rm+1))

CHEN Gui-xiu1,2

J4. 2010, 45(10): 49-52.

Abstract ( 1403 )

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By studying the factorization of adjoint polynomials of graphs H_i ^SS*(1)(q,n(rm+1)),it is proved that structure characteristics of chromatically equivalent graphs and chromatically non-uniqueness of their complement graphs.

The generalized additivity，transformation theorem and the defect of additivity for fuzzy measures

GONG Zeng-tai, XIE Ting

J4. 2010, 45(10): 53-60.

Abstract ( 1562 )

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Based on the concept of generalized additivity proposed in this paper, the generalized additivity for two popular types of non-additive measures are studied. Simultaneously, the characteristic theorem for generalized additivity fuzzy measures is given, that is, the relationship between generalized additivity and ordinary additivity is presented. Furthermore, the error estimates between generalized additivity and ordinary additivity are discussed.

Fuzzy implicative filters of non-commutative residuated lattices and their properties

HAO Jia-xing, WU Hong-bo

J4. 2010, 45(10): 61-65.

Abstract ( 1464 )

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The structure of non-commutative residuated lattices is further studied.With the help of the thought and method of fuzzy mathematics, the concept of fuzzy filters is introduced, and the relations between fuzzy filters and crisp filters of non-commutative residuated lattices are discussed. On the basis of fuzzy filters, fuzzy implicative filters and fuzzy positive implicative filters of non-commutative residuated lattices are introduced. The basic properties of them are discussed, and then several equivalent characterizations for fuzzy implicative filters and fuzzy positive implicative filters are given.It is proved that fuzzy positive implicative filters must be fuzzy implicative filters. Under certain conditions, the equivalence of fuzzy implicative filters and fuzzy positive implicative filters is proved.

Fuzzy ⊙-ideals in regular residuated lattices

QIN Xue-cheng, LIU Chun-hui*

J4. 2010, 45(10): 66-70.

Abstract ( 1495 )

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Residuated lattices play an important role in studies of fuzzy logic. First, the notions of fuzzy ⊙-ideals in residuated lattices are introduced. Some properties of fuzzy ⊙-ideals in (regular)residuated lattices are discussed and some equivalent characterizations are given. Second, a congruence relation is structured in terms of the notion of fuzzy ⊙-ideal in regular residuated lattices. It is proved that the quotient algebra of a regular residuated lattice under a congruence relation is also a regular residuated lattice.

Strongly ergodic and family F-total sweeping out

LIU Gui-xian, YANG Guo-ying*

J4. 2010, 45(10): 71-72.

Abstract ( 1443 )

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The notion of family F-total ergodic is introduced. The relation of strongly ergodic and family F-total sweeping out is discussed.The connection between special family F-double sweeping out and family F-total sweeping out are shown using the notion of strongly ergodic.

Categorical properties of three kinds of special closure spaces

YU Wen-jing, LI Sheng-gang*

J4. 2010, 45(10): 73-77.

Abstract ( 1535 )

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Properties of the category RCS of reasoning closure spaces, the category NCS of bottomless closure spaces and the category ACS of algebraic closure spaces are studied. It is proved that the categories RCS and NCS have products and coequalizers, but have no coproduct and equalizer, ACS is a topological construct, RCS is a coreflective full subcategory of NCS, and ACS is a coreflective full subcategory of CS.

The local connectedness of L-pretopological spaces: product and L-good extension

HE Xiao-li1, FU Wen-qing2

J4. 2010, 45(10): 78-82.

Abstract ( 1646 )

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It is mainly proved that the local connectedness is multiplicative with respect to product operation and the L-good extension.

Essential spectrum of the products of operators

ZHAO Ling-ling, ZHANG He-jia, CAO Xiao-hong*

J4. 2010, 45(10): 83-88.

Abstract ( 1702 )

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Let A be a bounded linear operator on a Hilbert space H. A∈B(H) is called a consistent in Fredholm (briefly CF operator) or A has property CF if σ_e(AB)=σ_e(BA) for every B∈B(H), where σ_e(·) denotes the essential spectrum. In this note, sufficient and necessary conditions for property CF are given, and the property CF for compact perturbation of A is considered. Finally, the properties CF of operator matrices are studied.

Uniform convergence of high-dimensional wavelet expansions

ZHAO Shu-gai 1, CAO Huai-xin2*

J4. 2010, 45(10): 89-92.

Abstract ( 1413 )

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Uniform convergence of high-dimensional wavelet expansions is discussed. First, a uniform convergence theorem on high-dimensional wavelet expansion is established when m→-∞.Then, by introducing the concept of a quasi-positive δ sequence, a uniformly convergent sequence is constructed and its pointwise convergence is obtained. Finally, it is proved that the reproducing kernel sequence ｛q_m｝_m∈Z of a multiresolution analysis on certain conditions is a quasi-positive δ sequence, and a uniform convergence theorem on high-dimensional wavelet expansion is given when m→+∞.

Solvability of singular third-order m-point boundary value problems

ZHOU Shao-lin

J4. 2010, 45(10): 93-97.

Abstract ( 1226 )

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Existence of multiple positive solutions for singular second order Neumann boundary value problems

LIU Shu-kuan

J4. 2010, 45(10): 98-103.

Abstract ( 1233 )

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Using the fixed point index in cones, the existences of multiple positive solutions for singular second order Neumann boundary value problems are studied under some conditions concerning the first eigenvalue corresponding to the relevant linear problems. It improves and extends some results.

The semi-infinite problems of the solutions for a system of nonlocal wave equations

LU Qiu-ci1, ZENG You-dong2

J4. 2010, 45(10): 104-108.

Abstract ( 1381 )

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Reduction in general consistent approximate representation space

LI Jin-jin1, ZHANG Yan-lan2, XU Qing-yuan2

J4. 2010, 45(10): 109-115.

Abstract ( 1658 )

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The inclusion relation of topologies is used to recognize the theory of reduction in consistent approximate representation space. And then the equivalent relations of consistent approximate representation space are extend to general binary relations. The general consistent approximate representation space is defined. In general consistent approximate representation space, the theory of relational reduction is given, and an extension for the theory of reduction in consistent covering decision systems is introduced. Finally, the model shows an application of the theory of reduction.

Alternating segment explicit-implicit scheme for the fifth-order dispersive KdV equation

ZUO Jin-ming1, ZHANG Tian-de2

J4. 2010, 45(10): 116-121.

Abstract ( 1499 )

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A group of asymmetric difference schemes to approach the fifth-order dispersive KdV equation are given. Using the schemes and the full explicit difference scheme and the full implicit difference scheme, the alternating difference scheme for solving the fifthorder dispersive KdV equation is constructed. The scheme is linear unconditionally stable by analysis of linearization procedure, and is used directly on the parallel computer. Numerical experiments show that the method has high accuracy.

Properties of ruin probability for a risk model based on the policy entrance process under heavily-tailed claims

XIAO Hong-min1, BAI Jian-ming2*

J4. 2010, 45(10): 122-126.

Abstract ( 1360 )

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An insurance risk model based on the policy entrance process, called as LIG model, was constructed. This model allows a policy to claim more than once during its validity-term. Under the basic assumptions of the entrance process is a non-homogeneous Poisson, and the claim size belongs to S, the family of subexponential distributions, an asymptotical equality expression of the finite time ruin probability was obtained.

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