Table of Content

  

16 June 2008
Volume 43 Issue 6

Articles

The ∑_Γ^－fuzzy truth degree of formula relative to the finite theory in propositional logic system Ln

WU Hong-bo,QIAO Xi-min,

J4. 2008, 43(6):  1-8 .  doi:

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Abstract: The theory of ∑-α-tautologies of fuzzy propositional logic was combined with the theory of truth degree in metrology of logic introduced by professor G.J.Wang, and the theory of ∑_Γ^－fuzzy truth degrees of formula relative to the finite theory in propositional logic system n was introduced. By employing the theory of ∑_Γ^－fuzzy truth degree, the concepts of Γ-pseudometric on F(S) was proposed in the propositional logic system Ln. The results obtained can complement and enhance the original theory of metrology of logic, and can give a new frame for fuzzy reasoning study.

Fractional chromatic number of one class of distance graphs

LIU Xi-kui,ZHAO Bing-qing,WANG Cai-hong,XUE Sheng-wei

J4. 2008, 43(6):  9-11 .  doi:

Abstract ( 1083 )   PDF (175KB) ( 748 )   Save

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The fractional chromatic number of the distance graph G(Z,D_{m,k,k+1,k+2,k+3}) (where D_{m,k,k+1,k+2,k+3}=｛1,2,…,m｝-｛k,k+1,k+2,k+3｝) and its chromatic number for some pairs of integers, when 2k≤m≤2k+5 were discussed.

The contractible edges of the longest cycle in some 5-connected graphs

YANG Zhao-xia

J4. 2008, 43(6):  12-14 .  doi:

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Abstract: The distribution of the contractible edges on some longest cycles of some 5-connected graphs was given. The results show that some of the longest cycles of some 5-connected graphs have at least two contractible edges.

A partition of bipartite graphs with 4-cycle and 8-cycle

LI Feng,GENG Jian-yan,LI Shuo,LIANG Feng

J4. 2008, 43(6):  15-18 .  doi:

Abstract ( 1058 )   PDF (213KB) ( 861 )   Save

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It was proved that if G is a balanced bipartite graph of order 4k satisfying d(x)+d(y)≥2k+1 for any two nonadjacent vertices x∈V₁, y∈V₂, then G contains k-2 4-cycles and one 8-cycle such that all the k-1 cycles are vertex-disjoint.

The heterochromatic girth in edge-colored graphs

LI Shuo,LI Feng,LIANG Feng

J4. 2008, 43(6):  19-20 .  doi:

Abstract ( 992 )   PDF (172KB) ( 577 )   Save

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Let G be an edgecolored graph with order n, n≥3. It is proved that if for each vof G, d^c(v)≥n/(2-α), where α=α=3/(s-3)ln(2+7/3), and s is an integer greater than 3, then g_H(G)≤s.

Equitable coloring of planar graphs without 4,5,6-cycles

XIAO Yu-liang,MA Shuai,WU Jian-liang

J4. 2008, 43(6):  21-24 .  doi:

Abstract ( 1074 )   PDF (197KB) ( 820 )   Save

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A proper vertex-coloring Φ of a graph G is called an equitable coloring of G if the numbers of vertices in any two-color class differ with each other at most one. Then any planar graph G without 4,5,6-cycles and with Δ≥9 is equitable Δ-colorable.

Fuzzy-quotient Lie super-algebras

Chen Wen-juan

J4. 2008, 43(6):  25-27 .  doi:

Abstract ( 999 )   PDF (160KB) ( 612 )   Save

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The fuzzy-quotient Lie superalgebra was defined by using a fuzzy ideal. The result shows the fuzzy-quotient Lie superalgebra is Lie super-algebra. Also, the fuzzy subset of fuzzy-quotient Lie super-algebra was discussed.

Convergence theorems for generalized g-expectations

LIN Qian,SHI Yu-feng

J4. 2008, 43(6):  28-30 .  doi:

Abstract ( 1447 )   PDF (196KB) ( 820 )   Save

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Some properties of the generalized g-expectations defined in l1(Ω, F_T, P) were studied. Also, monotonic convergenle theorem, Fatou Lemma, and dominated convergence theorem for the generalized g-expectations were obtained.

A Turan theorem relating to the spectral radius of a graph

FENG Li-hua,YU Gui-hai

J4. 2008, 43(6):  31-33 .  doi:

Abstract ( 1321 )   PDF (152KB) ( 660 )   Save

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Suppose G is a graph on n vertices. If　ρ(G)≤ρ(T_n,t) 　for some t, then e(G)≤e(T_n,t) where Tn,t is the Turan graph with k parts, which partially supports a problem raised by Nikiforov.

Mean value estimate for the greatest divisors of N which is prime to a certain integer(Ⅱ)

GUO Ru-ting

J4. 2008, 43(6):  34-36 .  doi:

Abstract ( 836 )   PDF (167KB) ( 711 )   Save

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For a fixed natural squarefree number k, the mean value of the greatest divisor of N which is prime to k was studied.

Ordering of the largest eigenvalues of trees

ZHANG Sheng-li,PAN Zheng-hua,FENG Shan-zhuang

J4. 2008, 43(6):  37-43 .  doi:

Abstract ( 1351 )   PDF (263KB) ( 674 )   Save

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Let T_n be a set of trees with n vertices. In this ordering, the largest eigenvalues of trees in T_nand their ordering were further investigated, and the fifteenth to thirty-third values and the corresponding trees were obtained.

Computational method for the generalized KdV equation

ZUO Jin-ming

J4. 2008, 43(6):  44-48 .  doi:

Abstract ( 1038 )   PDF (187KB) ( 629 )   Save

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omputational method based on a linearized implicit scheme was proposed for the solution of the generalized Kortewegde Vries (KdV) equation.An important advantage to be gained from the linearized implicit method is unconditional stable.Numerical results portraying a single linesoliton solution and the interaction of two linesolitions were reported for the generalized KdV equation. The results show that this method has good stability and accuracy.

The solutions of boundary value problems for second order integro-differential equations in Banach spaces

DONG Li-li,LIU Yan-sheng

J4. 2008, 43(6):  49-52 .  doi:

Abstract ( 1158 )   PDF (196KB) ( 916 )   Save

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By using a new comparison result and only a lower or an upper solution, the maximal or the minimal solutions of the boundary value problems for second order integro-differential equations in Banach spaces were obtained.

Existence of three solutions for some second-order four-point boundary value problems

HUANG Yu-mei,GAO De-zhi,QIN Wei,DONG Xin

J4. 2008, 43(6):  53-56 .  doi:

Abstract ( 1040 )   PDF (178KB) ( 718 )   Save

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he second-order four-point boundary value problem -x″(t)=f(t,x(t),x′(t)), t∈I=［0,1］;x(0)=ax(ξ), x(1)=bx(η)　was studied, where　0<ξ<η<1,0≤a,b≤1, and f: ［0,1］×［0,∞］→［0,∞］　are non-negative continuous functions. Some degree theory arguments were used to get the multiplicity result.

The fixed point of decreasing operators in Banach space

ZHENG Yan,PANG Xin-qin

J4. 2008, 43(6):  57-60 .  doi:

Abstract ( 1018 )   PDF (187KB) ( 971 )   Save

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In four different ways, in partial ordering Banach space, the existence and uniqueness of solutions for decreasing operators were discussed, and the convergent iterative sequence was also given. Some known results were improved.

Wreath product structure of the left C-wrpp semi-groups

ZHANG Xiao-min

J4. 2008, 43(6):  61-63 .  doi:

Abstract ( 1226 )   PDF (184KB) ( 577 )   Save

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The curler structure of left C-wrpp semi-groups as a generalization of C-wrpp semi-groups has already been established. Another structure of left C-wrpp semi-groups was investigated by means of the wreath product introduced by Nuemann, and the wreath product structure of left C-wrpp semi-groups was obtained. This result further enriches the theory on left C-wrpp semi-groups.

(Strongly)Relative semi-compactness in L-topological spaces

HAN Hong-xia

J4. 2008, 43(6):  64-67 .  doi:

Abstract ( 984 )   PDF (164KB) ( 486 )   Save

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The notions of relative semi-compactness and strongly relative semi-compactness were introduced in L-topological spaces, and some of their properties were studied.

A modified super-memory gradient method with angle property

SUN Min

J4. 2008, 43(6):  68-70 .  doi:

Abstract ( 875 )   PDF (199KB) ( 726 )   Save

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A modified super-memory gradient method was proposed. The method has the following two attractive properties, one is that the iterative direction is always a sufficiently descent direction without utilizing the line search, the other is that the iterative direction always satisfies the angle property. Under mild conditions, the global convergence of the method was proved. The preliminary numerical results show the efficiency of this method.

The reverse order law for (T,S,2)-inverse of a matrix semi-tensor product

SONG Cai-qin,ZHAO Jian-li,LI Dong-fang

J4. 2008, 43(6):  71-76 .  doi:

Abstract ( 910 )   PDF (204KB) ( 753 )   Save

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The necessary and sufficient condition for the validity of the reverse order law for (T, S, 2)-inverse of a matrix semitensor product was given. In addition, the equality (A⊙B)⁺_MP=(A⁺_MN(A⊙B))⁺_NP((A⊙B)(B⁺_NPIp))⁺_MN was proved.

The Gnedenko system attended by a repairman with simple vacations

CAO Jing,YUE De-quan

J4. 2008, 43(6):  77-82 .  doi:

Abstract ( 1219 )   PDF (241KB) ( 980 )   Save

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The Gnedenko system attended by a repairman with simple vacations was studied. It was assumed that the life of the operating unit and the standby, and the vacation time of the repairman were all exponential distributions, while the repair time of the unit had a general continuous distribution. By using the supplementary variables approach and generalized Markov process method, the Laplace transform of the reliability and the mean time to the first failure were attained. Meanwhile, the availability and the failure frequency of the system were obtained.

Free product of left quasi-normal bands

BI Xiao-dong

J4. 2008, 43(6):  83-86 .  doi:

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It is proved that the maximal left quasi-normal band homomorphic image of the free product of right quasi-normal bands in the semi-group categrory is isomorphic to their free product in the left quasi-normal band category. Then, the existence of the free product in left quasinormal band was proved. Finally, the concept of commutative free product was given, and the relationship between semi-lattice free product and commutative free product was examined.

Complete convergence of weighted sums for arrays of row-wise ρ^--mixing random variables

TAN Cheng-liang,WU Qun-ying,TIAN Guo-hua

J4. 2008, 43(6):  87-91 .  doi:

Abstract ( 1018 )   PDF (206KB) ( 587 )   Save

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Using a Rosenthaltype inequality of partial sums for ρ^-mixing random variables, the complete convergence of weighted sums for arrays of rowwise ρ^--mixing random variables was studied. The results obtained can extend the corresponding results of arrays of row-wise independent random variables, and some complete convergence corollaries for weighted sums for arrays of row-wise NA and ρ*-mixing random variables.

An economic growth model of optimization and allocation with endogenous utility index of lands

JI Rong-fang,GUO Zhong-jin

J4. 2008, 43(6):  92-96 .  doi:

Abstract ( 977 )   PDF (228KB) ( 757 )   Save

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By integrating both population growths with environmental factor, utility index of land resources, and production amounts of society, and introducing a utility function with both consumption and utility index of land resources was introduced, and the optimization problem with infinite level was also presented. A three-dimension dynamic system was obtained by solving the optimization problem. It is proved that this system has unique non-zero positive equilibrium, which is a saddle.