Table of Content

  

20 June 2012
Volume 47 Issue 6

Articles

The solution of the time-fractional model of heat transport in complex human tissue

ZHAI Ru-kun, JIANG Xiao-yun

J4. 2012, 47(6):  1-4. 

Abstract ( 1216 )   PDF (816KB) ( 2314 )   Save

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A fractional Pennes bioheat transfer equation is established. By applying the finite Fourier sine transformation, Laplace transformation and their corresponding inverse transforms, the analytic solution of the fractional Pennes bioheat transfer equation is obtained. And the expression in the form of generalized Mittag-Leffler function is given. Finally, the integer-order as a particular case is discussed.

Existence of a solution for anti-periodic boundary value problems of  fractional differential equations

FANG Hai-qin, LIU Xi-ping*, LIN Le-gang

J4. 2012, 47(6):  5-9. 

Abstract ( 1124 )   PDF (641KB) ( 1862 )   Save

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The existence of solutions for anti-periodic boundary value problems of fractional differential equations are studied which include fractional derivatives of unknown function in the nonlinear term. In the case of the nonlinear term bounded and unbounded,  the existence conditions of anti-periodic boundary value problems by means of Schauder fixed point theorem and contraction mapping principle are studied. Some existence results for the anti-periodic boundary value problems are obtained.
 

Existence of a positive solution of singular nonautonomous third-order two-point boundary value problems

YAO Qing-liu

J4. 2012, 47(6):  10-15. 

Abstract ( 1106 )   PDF (603KB) ( 1197 )   Save

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The positive solution of a class of nonautonomous nonlinear third-order two-point boundary value problems is studied, where the nonlinear term is allowed to be singular with respect to the time and space variables. By constructing suitable dominated functions and applying Guo-Krasnosel’skii fixed point theorem on a cone, an existence theorem of a positive solution is established.

Existence of positive solutions of the m-point boundary value problem with p-Laplace operator on time scales

FAN Jin-jun, ZHANG Xue-ling, LIU Yan-sheng

J4. 2012, 47(6):  16-19. 

Abstract ( 1286 )   PDF (616KB) ( 2319 )   Save

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The existence of positive solutions of the m-point boundary value problem with p-Laplace operator on time scales are considered. By using the LeggetWilliams fixed point theorem, the existence of three positive solutions is obtained. As an application, an example verified our results.

Existence and quadratic convergence of solution sequences for functional  differential equations with an impulsive integral condition

HU Bing, QIAO Yuan-hua*

J4. 2012, 47(6):  20-27. 

Abstract ( 1172 )   PDF (647KB) ( 1428 )   Save

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The uniform existence and quadratic convergence of solution sequences for a class of nonlinear first order impulsive functional differential equations under antiperiodic boundary value conditions with an impulsive integral condition is discussed. The main tools are the monotone iterative technique and the method of quasilinearization.

The existence of positive solutions of  a class of fourth-order singular boundary value problems with a p-Laplacian operator

LU Fang, ZHOU Zong-fu*

J4. 2012, 47(6):  28-33. 

Abstract ( 1146 )   PDF (607KB) ( 1480 )   Save

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By using the fixed point index theorem, a class of fourth-order p-Laplacian operator singular boundary value problems is considered in weaker conditions, and two positive solutions are obtained.

An expanded mixed covolume method for Sobolev equations

LI Na, GAO Fu-zheng*, ZHANG Tian-de

J4. 2012, 47(6):  34-39. 

Abstract ( 1093 )   PDF (660KB) ( 2073 )   Save

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Based on the lowest order RaviartThomas mixed element space,  an expanded mixed covolume method forsolving a class of Sobolev equations is presented. Making use of priori error estimate techniques,  the suboptimal L² error estimates for the semidiscrete and fullydiscrete schemes are obtained. Also some numerical results are given to verify our analysis for the schemes.

Finite difference methods for two kinds of fractional convection-diffusion equations

ZHANG Hong-yu， CUI Ming-rong*

J4. 2012, 47(6):  40-48. 

Abstract ( 1335 )   PDF (661KB) ( 1803 )   Save

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Two kinds of fractional partial differential equations are considered. One is a spacefractional convectiondiffusion equation and the other  is a time-space fractional convection-diffusion equation. Based on the shifted Grünwald formula,   the weighted average finite difference method is used to approximate the spatial fractional derivatives in the first equation,  and its stability  is studied by eigenvalue analysis. The error estimate is O(τ+h). A high order approximation for the temporal derivative is used for the second equation. The stability is given by the technique of maximum norm analysis, with the convergence order O(τ^{2-max｛γ1,γ2｝+h}), where γ1,γ2 are the orders of the two Caputo time fractional derivatives, respectively. Numerical examples are presented to demonstrate the theoretical results.

A type of non-overlapping domain decomposition procedure combined with the characteristic method for incompressible miscible displacement in porous media

MA Xiao-pei, SUN Tong-jun

J4. 2012, 47(6):  49-56. 

Abstract ( 1207 )   PDF (792KB) ( 1959 )   Save

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A numerical approximate scheme is considered for incompressible miscible displacement in porous media. This scheme is constructed by two methods. The standard mixed finite element is used for the pressure equation. A parallel non-overlapping domain decomposition procedure combined with the characteristic method is presented for the concentration equation. This parallel procedure uses the implicit Galerkin method in the subdomains and simple explicit flux calculation on the inter-domain boundaries by the integral mean method to predict the inner-boundary conditions. Thus, parallelism can be achieved. Optimal order in L²-norm error estimates are derived for this scheme.
incompressible miscible displacement; non-overlapping domain decomposition procedure; mixed finite element method; characteristic method; integral mean method

Preconditioned NSS methods for non-Hermitian and positive definite linear systems

WANG Yang1, FU Jun1, MA Wei-yuan2

J4. 2012, 47(6):  57-62. 

Abstract ( 1204 )   PDF (609KB) ( 1882 )   Save

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 Based on the normal／skew-Hermitian splitting(NSS) iteration technique for large sparse non-Hermitian and positive definite linear systems, preconditioned normal／skew-Hermitian splitting (PNSS) methods and investigation of their variants are proposed, e.g., the inexact preconditioned normal／skewHermitian splitting (IPNSS) methods. Theoretical analysis shows that the PNSS methods are convergent under some conditions. Also, the computational methods of the optimal choice of the parameter are presented as involved in our iterative schemes and the corresponding minimum values for the upper bound of the iterative spectrums. In the numerical test, we choose incremental unknowns (IUs) and symmetric successive overrelaxation(SSOR) as two types of our precondioners. Numerical results confirm the correctness of the convergence theory and the effectiveness of the proposed methods.

Properly colored paths and cycles in edge colored graphs

SONG Bao-yang, WANG Xiao-zong, REN Yu-ping

J4. 2012, 47(6):  63-66. 

Abstract ( 1414 )   PDF (688KB) ( 1702 )   Save

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Properly colored paths and cycles in edge colored triangle-free graphs are discussed, and the known result is improved in triangle-free graphs. It is proved that in any edge colored triangle-free graph G with color degree at least d(d≥2), there exists either a properly colored path of size at least 4d-2, or a properly colored cycle of size at least 2「2d3.

The set edge chromatic number of a graph

WANG Yan-li, MIAO Lian-ying

J4. 2012, 47(6):  67-70. 

Abstract ( 1195 )   PDF (989KB) ( 1450 )   Save

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The definition of set edge chromatic number is given. By the use of the method of structure graph theory,  the lower bounds of the set edge chromatic numbers of graphs, the relationships among the set edge chromatic numbers of a graph, and its vertexdeleted subgraphs and its edge-deleted subgraphs are given.

The linear 2-arboricity of plane graphs without 4-cycles and 5-cycles

WANG Ran-qun， ZUO Lian-cui

J4. 2012, 47(6):  71-75. 

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Acyclic edge coloring of planar graphs without 4-Cycles

DING Wei

J4. 2012, 47(6):  76-79. 

Abstract ( 1385 )   PDF (587KB) ( 1343 )   Save

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If a proper edge coloring of G contains no bichromatic cycles in G, then it is an acyclic edge coloring of G. The acyclic chromatic number of G is the minimum number of colors among all the acyclic edge colorings of G. By using the properties of planar graphs that have been proposed, it is proved that if G is a 2-connected planar graph without 4-cycles, then its acyclic chromatic number is no more than Δ(G)+11.

Some ［r,s,t］-chromatic number of graphs

YANG Lin1, SUN Lei2*

J4. 2012, 47(6):  80-82. 

Abstract ( 1052 )   PDF (573KB) ( 1259 )   Save

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On signed edge total domination of graphs

LI Zhen-lin, LU Jun-long, L Xin-zhong

J4. 2012, 47(6):  83-86. 

Abstract ( 1100 )   PDF (585KB) ( 1228 )   Save

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 Let γ′_st(G) be the signed edge total domination number of a graph G. The bounds of the signed edge total domination number of a graph G and hypercube are given, and the signed edge total domination number of Kn,n is determined.

A kind of d-Koszul algebra with normal-regular elements

CHENG Zhi1,2, WANG Xiu-jian1, DU Xian-neng1

J4. 2012, 47(6):  87-89. 

Abstract ( 1435 )   PDF (606KB) ( 1408 )   Save

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A kind of d-Koszul algebra with normal-regular elements is studied. With the knowledge of homological algebra, some quotient algebras of this kind of d-Koszul algebra are also a d-Koszul algebra. The conclusion generalizes the result of Schelton.

An identity in terms of 2-Motzkin paths and its applications

SUN Yi1, SU Gui-fu2

J4. 2012, 47(6):  90-94. 

Abstract ( 1186 )   PDF (753KB) ( 2217 )   Save

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One of the identities of Coker is generalized, which is proved by an algebraic method. Some useful identities related to Narayana number and Catalan number are also presented.

Two Lie algebras and their applications

Two Lie algebras and their applications

J4. 2012, 47(6):  95-101. 

Abstract ( 1241 )   PDF (611KB) ( 1632 )   Save

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Two high-dimensional Lie algebras Hand E and the corresponding loop algebras  and are introduced. By taking advantage of  and , two types of coupling integrable couplings of the new hierarchy are obtained.  The coupling integrable couplings of the new hierarchy obtained can be reduced to two types of the coupling integrable couplings of the dispersive long wave DLW equation.

Research on the commutative properties of codes

WANG Jiong, WANG Zhi-xi, HE Yong

J4. 2012, 47(6):  102-106. 

Abstract ( 1370 )   PDF (636KB) ( 1570 )   Save

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The relations between commutative codes, unambiguous products, maximal codes and primitive roots are studied. Several results of commutation and partial commutation with codes are given, and the relevant results about maximal codes are generated. Also, an equivalent proposition of a conjecture about the roots of codes is given.

Bi-continuous n-times integrated C-semigroups and C-wellposedness of an abstract Cauchy problem

CHANG Sheng-wei, LIU Rui

J4. 2012, 47(6):  107-110. 

Abstract ( 1068 )   PDF (583KB) ( 1532 )   Save

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The relations of bi-continuous n-times integrated C-semigroups and C-wellposedness of an Abstract Cauchy Problem(ACP) are discussed. A closed linear operator A(sub) generating bi-continuous n-times integrated C-semigroups is equivalent to (ACP) owing C-wellposedness.

Ideal statistical convergence and ideal lacunary statistical convergence for a sequence of fuzzy numbers

GONG Zeng-tai, LIU Xiao-xia

J4. 2012, 47(6):  111-116. 

Abstract ( 1001 )   PDF (708KB) ( 1738 )   Save

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The concepts of the ideal statistical convergence and ideal lacunary statistical convergence for a sequence of fuzzy numbers are defined, and their relationship is also investigated. In addition, the relationship between statistical convergence (lacunary statistical convergence) and ideal statistical convergence (ideal lacunary statistical convergence) for a sequence of fuzzy numbers is discussed.

Borel-Cantelli lemma for capacities

SONG Li

J4. 2012, 47(6):  117-120. 

Abstract ( 1208 )   PDF (639KB) ( 1633 )   Save

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Under the framework of sublinear expectations, the Borel-Cantelli lemma for capacities induced by sublinear expectations is proved.

The conditional randomized truth degree of formulas in the fuzzy logic system L*

ZUO Wei-bing

J4. 2012, 47(6):  121-126. 

Abstract ( 1061 )   PDF (620KB) ( 1457 )   Save

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In the fuzzy logic system L* with valuation lattice ［0,1］, based on conditional probability and using the randomization method of valuation set, the concept of conditional randomized truth degree of formulas is introduced. The MP rule and HS rule of conditional randomized truth degrees are proved. The concepts of conditional randomized similarity and conditional pseudometric between formulas are presented and conditional randomized logic metric space is built. Several properties of conditional pseudometric are deduced and it is proved that the logical operations are continuous on conditional randomized logic metric space. Then the theory of approximate reasoning under certain information is studied.