Table of Content

  

20 August 2013
Volume 48 Issue 8

Articles

An Upper Bound on the Sum of the k Largest Eigenvalues of  the Signless Laplacian Matrix of a Graph

JIN Guang-qing, ZUO Lian-cui*

J4. 2013, 48(8):  1-4. 

Abstract ( 1503 )   PDF (671KB) ( 2801 )   Save

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The sum of the k largest eigenvalues of the signless Laplacian matrix of a simple connected graph is studied and an upper bound is obtained in terms of the degree sequence and the order of the graph.

Coresolution dimensions

YAN Ting-ting, LIU Zhong-kui

J4. 2013, 48(8):  5-14. 

Abstract ( 859 )   PDF (1354KB) ( 1612 )   Save

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Let A be an abelian category, X be a subcategory of A. The X-coresolution dimensions of the objectives of A are introduced, and by using cohomology functor ExtnX, the equivalent characterizations of X-coresolution dimensions are given.

The Zagreb eccentricity indices of Cartesian product of graph

HU Yu-mei, ZHOU Xing-yi, MA Xing-yu*

J4. 2013, 48(8):  15-17. 

Abstract ( 984 )   PDF (618KB) ( 1743 )   Save

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According to some theorems of Cartesian product of graphs, exact expressions for the first and second Zagreb eccentricity indices of Cartesian product of graphs will be presented and also the Zagreb eccentricity indices of arbitrary Cn tube and Cn torus.

Generalized dominating set of digraphs and its algorithm

GUO Yi-hao, XU Shao-ya

J4. 2013, 48(8):  18-20. 

Abstract ( 902 )   PDF (770KB) ( 1825 )   Save

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The generalized dominating set of digraphs is defined, and generalized dominating set of digraphs and its algorithm are determined.

Some remarks on maximum size of bipartite graphs with a given domination number

GAO Chao, HOU Xin-min*

J4. 2013, 48(8):  21-23. 

Abstract ( 1016 )   PDF (868KB) ( 1845 )   Save

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The maximum size of bipartite graphs with a given domination number and a family of extreme graphs are given.

The module algebra structures on M2(k)

ZHAO Shi-yin1,2, ZHOU Ke-yuan1

J4. 2013, 48(8):  24-29. 

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The equivalent classifications of some matrices and pairs of matrices with respect to the weak similarity are studied, respectively. Then by applying these results, the isomorphism classifications of kC2-module algebra structures and kC3module algebra structures on the full matrix algebra M2(k) are described. Finally, kS3module algebra structures on the full matrix algebra M2(k) are given up to isomorphism. When k is an algebraically closed filed, the isomorphism classifications of kS3module algebraic structures on the full matrix algebra M2(k) are obtained.

Estimation on lower bounds for the minimum eigenvalue of the Hadamard  product of inverse matrix of nonsingular M-matrix and M-matrix

WANG Feng

J4. 2013, 48(8):  30-33. 

Abstract ( 1283 )   PDF (594KB) ( 1922 )   Save

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Some new lower bounds for the minimum eigenvalues of the Hadamard product of inverse matrix of nonsingular M-matrix and M-matrix are given. The estimating formulas of the bounds only depend on the entries of matrices, and they are easy to calculate.These bounds improve the related results.

A generalization of infix codes

WANG Shou-feng

J4. 2013, 48(8):  34-35. 

Abstract ( 798 )   PDF (608KB) ( 1459 )   Save

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Strong bifix codes which are generalizations of infix codes in the range of bifix codes are considered and some properties of this class of codes and its subclasses are explored. In particular, it is proved that any subset of a strong bifix code is also a strong bifix code.

Idempotents of semigroup PΓ(Λ×Λ) of binary relations determined by the semilattice Γ on the set Λ

LIN Ping-feng, ZENG Wei, ZENG Chun-yi

J4. 2013, 48(8):  36-40. 

Abstract ( 951 )   PDF (614KB) ( 1748 )   Save

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Let Λ be an arbitrary nonempty set, and Γ be a semilattice on the set Λ, semigroup PΓ(Λ×Λ) is a semigroup of binary relations determined by the semilattice Γ on the set Λ. Use of the nature of the semilattice,characteristics of idempotents of the semigroup PΓ(Λ×Λ) are obtained,and a class of idempotents is constructed; Finally, left units of the semigroup PΓ(Λ×Λ) are characterized.

Characterizations of ξ-Lie derivations of B(X)

LIU Dan, ZHANG Jian-hua*

J4. 2013, 48(8):  41-44. 

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Let X be a Banach space with dim X>1, and  ξ≠±1。 In this paper, we show that if a linear map φ:B(X)→B(X) satisfies φ(［A,B］ξ)=［φ(A),B］ξ+［A,φ(B)］ξ for all A,B∈B(X) with ABA=A, then φ is a derivation.

Existence of solution for the  boundary value problem of a class of fractional differential equation

ZHOU Wen-xue1,2, LIU Hai-zhong1

J4. 2013, 48(8):  45-49. 

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 A class of boundary value problem of fractional differential equation is studied. By the means of the Green′s function, the boundary value problem of fractional differential equation can be reduced to the equivalent integral equation, and some sufficient conditions on the existence of solution for the boundary value problem are obtained by using Schaefer′s fixed point theorem and Leray-Schauder fixed point theorem. Some known results are extended and improved.

Cauchy problem for doubly nonlinear parabolic equations with time-dependent source

CHENG Jun-xiang, SHANG Hai-feng

J4. 2013, 48(8):  50-55. 

Abstract ( 900 )   PDF (622KB) ( 1721 )   Save

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The Cauchy problem of the equation ut-div(|Dum|p-2Dum)=t-σuq,is studied, where m>0, p>1. This equation is called doubly nonlinear parabolic equation, since the principal part may be doubly degenerate or doubly singular related to the parameters m, p. By a priori estimates and compactness methods, and fine classifications to parameters m, p, we obtain the optimal existence of solutions of the equation with initial data measures are obtained.

Soft Boolean algebra

LIU Wei-feng

J4. 2013, 48(8):  56-62. 

Abstract ( 1289 )   PDF (626KB) ( 2018 )   Save

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The soft set theory is applied to the Boolean algebra. The concepts of soft Boolean algebra, soft Boolean subalgebra, soft ideal of soft Boolean algebra and idealistic soft Boolean algebra are presented and some related algebraic properties are discussed. The relations between soft Boolean algebra and several kinds of fuzzy subalgebras of Boolean algebra are preliminarily investigated.

A Dugdale-Barenblatt model for a finite width  strip with single edge crack

YANG Lin

J4. 2013, 48(8):  63-67. 

Abstract ( 1217 )   PDF (739KB) ( 2214 )   Save

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The present study aims at determining the solutions of the well-known problem of a finite width strip with single edge crack, which is transformed a mathematically daunting problem. Cohesive forces are incorporated into a plastic strip in the elastic body. By superposing the two linear elastic fields, one evaluated with internal loadings and the other with cohesive forces, the problem is treated in Dugdale-Barenblatt′s manner. A simple but yet rigorous version of the complex analysis theory is employed here, which involves transcendental function conformal mapping technique. The analytical approach leads to establish a few equations, which allows the exact calculation of the corresponding stress intensity factors and the size of cohesive force zone.

The analysis of stock index sequence based on timing series model

CUI Yu-quan, LI Pei-pei, LI Lin-lin

J4. 2013, 48(8):  68-77. 

Abstract ( 1224 )   PDF (1320KB) ( 3635 )   Save

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According to econometric time series model, the paper creatively proposed combing econometric model and fractal dimension based on Shanghai and Shenzhen stock market data system of great wisdom and statistical software EVIEWS during 2005-2009.It uses a high-dimensional chaotic characteristics of the stock index, using LP algorithm to determine the fractal dimension, using vector autoregressive VAR model to test unit root on the two stock markets in Shanghai and Shenzhen. According to AIC and SC information criterion, it determine the number of lags, predict the future trend of the stock market in dynamic and static state and obtain more reasonable results.

The reliability analysis for aggregated Markov repairable system with fatigue time omission

WEN Yan-qing, MENG Xian-qing, CHANG Ke-liang

J4. 2013, 48(8):  78-82. 

Abstract ( 960 )   PDF (952KB) ( 2188 )   Save

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Based on the classical Markov repairable system, the state space of the system is divided into the set of working states and the set of failure states. Further, the set of the working states is divided into the set of the fully working states and the set of the fatigue working states based on the different working levels. If the sojourn time that the system is in the fatigue working states is less than a given constant τ, then this fatigue working time can be omitted, i.e. the system is thought of as excellent working during this fatigue working time. Otherwise, If the sojourn time that the system is in the fatigue working states is more than the given constant τ, then this fatigue working time can’t be omitted. Based on this assumption, aggregated Markov repairable system with fatigue time omission is modeled. Some reliability indexes of the original model and the new model are derived by using Laplace transform and the IonChannel modeling theory. Finally, a numerical example is given to illustrate these results obtained in the paper.

Dominant-recessive separation of internal P-information and the dominant-recessive separation theorem

WU Song-li1,3, WU Yu-qin2, SHI Kai-quan1*

J4. 2013, 48(8):  83-87. 

Abstract ( 975 )   PDF (599KB) ( 1579 )   Save

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 Using the characteristic of internal P-set, the concepts of dominant separation and recessive separation and the dominant-recessive separation theorem about internal P-information, the attribute characteristic generated by the dominant-recessive separation are given.

Outer P-information and its anti-dynamic characteristic

ZHANG Huan-li1,3, FAN Cheng-xian2

J4. 2013, 48(8):  88-91. 

Abstract ( 1079 )   PDF (630KB) ( 1867 )   Save

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P-sets(packet sets) is an element set pair composed of internal P-set X(internal packet set X) and outer P-set XF(outer packet set XF), or (X,XF) is P-sets, and it has the dynamic characteristic. Using the structure and dynamic characteristic of outer P-set XF and studying its anti-dynamic characteristic,  the concepts of basis information, outer P-information, F-supplemented information, outer P-anti-dynamic information are given. Based on the concepts, a few of theory results are proposed, by which the application of outer P-anti-dynamic information in the information system is given.

Inverse P-sets and intelligent fusion mining-discovery of information

GUO Hua-long, CHEN Bao-hui*, TANG Ji-hua

J4. 2013, 48(8):  97-103. 

Abstract ( 941 )   PDF (1106KB) ( 1565 )   Save

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Inverse packet sets is a new dynamic mathematical model, which is presented by introducing dynamic characteristics into Cantor set and improving Cantor set theory. Inverse packet sets is composed of internal inverse P-sets and outer inverse P-sets, and it is a set pair, i.e., (F,) a inverse packet sets, which has dynamic characteristic. In certain conditions, the inverse packet sets can be reduced into a finite general set. It has opposite dynamic characteristics to packet sets. Inverse packet reasoning is a dynamic reasoning generated by inverse packet sets. Based on inverse packet sets and inverse packet reasoning, the concepts of intelligent fusion generation of information and the intelligent fusion degree of information are put forward. The mining-discovery theorem of intelligent fusion of information and the mining-discovery criterion are given. Using those results, the application to intelligent fusion mining-discovery of information is proposed.

Function inverse P-sets and the dynamic separationof  inverse P-sets information laws

TANG Ji-hua1, CHEN Bao-hui1*, ZHANG Ling1, BAI Xing-rui2

J4. 2013, 48(8):  104-110. 

Abstract ( 813 )   PDF (728KB) ( 1346 )   Save

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Based on function inverse P-sets theory, the generation of inverse P-sets information law and its generating theorems the concept of dynamic separation of inverse P-sets information law,its separate characteristics and dynamic separating criterion are proposed. Using these results, the application of dynamic separation of inverse P-sets information law to information image hiding is given.