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- 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 ( 730 ) PDF (671KB) ( 2216 ) Save
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- Coresolution dimensions
- YAN Ting-ting, LIU Zhong-kui
- J4. 2013, 48(8): 5-14.
- Abstract ( 399 ) PDF (1354KB) ( 1296 ) Save
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- 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 ( 435 ) PDF (618KB) ( 1487 ) Save
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- Generalized dominating set of digraphs and its algorithm
- GUO Yi-hao, XU Shao-ya
- J4. 2013, 48(8): 18-20.
- Abstract ( 406 ) PDF (770KB) ( 1468 ) Save
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- 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 ( 460 ) PDF (868KB) ( 1352 ) Save
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- The module algebra structures on M2(k)
- ZHAO Shi-yin1,2, ZHOU Ke-yuan1
- J4. 2013, 48(8): 24-29.
- Abstract ( 421 ) PDF (614KB) ( 1286 ) Save
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- 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 ( 615 ) PDF (594KB) ( 1587 ) Save
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- A generalization of infix codes
- WANG Shou-feng
- J4. 2013, 48(8): 34-35.
- Abstract ( 388 ) PDF (608KB) ( 1272 ) Save
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- 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 ( 410 ) PDF (614KB) ( 1480 ) Save
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- Characterizations of ξ-Lie derivations of B(X)
- LIU Dan, ZHANG Jian-hua*
- J4. 2013, 48(8): 41-44.
- Abstract ( 344 ) PDF (595KB) ( 1189 ) Save
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- 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.
- Abstract ( 360 ) PDF (610KB) ( 1432 ) Save
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- Cauchy problem for doubly nonlinear parabolic equations with time-dependent source
- CHENG Jun-xiang, SHANG Hai-feng
- J4. 2013, 48(8): 50-55.
- Abstract ( 363 ) PDF (622KB) ( 1477 ) Save
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- Soft Boolean algebra
- LIU Wei-feng
- J4. 2013, 48(8): 56-62.
- Abstract ( 566 ) PDF (626KB) ( 1717 ) Save
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- A Dugdale-Barenblatt model for a finite width strip with single edge crack
- YANG Lin
- J4. 2013, 48(8): 63-67.
- Abstract ( 420 ) PDF (739KB) ( 1486 ) Save
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- 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 ( 603 ) PDF (1320KB) ( 3061 ) Save
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- 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 ( 414 ) PDF (952KB) ( 1591 ) Save
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- 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 ( 346 ) PDF (599KB) ( 1196 ) Save
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- Outer P-information and its anti-dynamic characteristic
- ZHANG Huan-li1,3, FAN Cheng-xian2
- J4. 2013, 48(8): 88-91.
- Abstract ( 327 ) PDF (630KB) ( 1499 ) Save
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- 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 ( 481 ) PDF (1106KB) ( 1239 ) Save
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- 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 ( 366 ) PDF (728KB) ( 1110 ) 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.

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.

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.

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

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

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 kC3module algebra structures on the full matrix algebra M2(k) are described. Finally, kS3module 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 kS3module algebraic structures on the full matrix algebra M2(k) are obtained.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 IonChannel modeling theory. Finally, a numerical example is given to illustrate these results obtained in the paper.

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.

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 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.

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.