Loading...

- 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 ( 658 ) PDF (816KB) ( 1468 ) Save
- Related Articles | Metrics
- 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 ( 616 ) PDF (641KB) ( 1265 ) Save
- Related Articles | Metrics
- 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 ( 601 ) PDF (603KB) ( 911 ) Save
- Related Articles | Metrics
- 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 ( 623 ) PDF (616KB) ( 2105 ) Save
- Related Articles | Metrics
- 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 ( 562 ) PDF (647KB) ( 1062 ) Save
- Related Articles | Metrics
- 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 ( 640 ) PDF (607KB) ( 1225 ) Save
- Related Articles | Metrics
- An expanded mixed covolume method for Sobolev equations
- LI Na, GAO Fu-zheng*, ZHANG Tian-de
- J4. 2012, 47(6): 34-39.
- Abstract ( 571 ) PDF (660KB) ( 1434 ) Save
- Related Articles | Metrics
- Finite difference methods for two kinds of fractional convection-diffusion equations
- ZHANG Hong-yu， CUI Ming-rong*
- J4. 2012, 47(6): 40-48.
- Abstract ( 742 ) PDF (661KB) ( 1309 ) Save
- Related Articles | Metrics
- 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 ( 594 ) PDF (792KB) ( 1455 ) Save
- Related Articles | Metrics
- 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 ( 612 ) PDF (609KB) ( 1576 ) Save
- Related Articles | Metrics
- 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 ( 694 ) PDF (688KB) ( 1459 ) Save
- Related Articles | Metrics
- The set edge chromatic number of a graph
- WANG Yan-li, MIAO Lian-ying
- J4. 2012, 47(6): 67-70.
- Abstract ( 603 ) PDF (989KB) ( 903 ) Save
- Related Articles | Metrics
- 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.
- Abstract ( 657 ) PDF (588KB) ( 1386 ) Save
- Related Articles | Metrics
- Acyclic edge coloring of planar graphs without 4-Cycles
- DING Wei
- J4. 2012, 47(6): 76-79.
- Abstract ( 671 ) PDF (587KB) ( 1176 ) Save
- Related Articles | Metrics
- Some ［r,s,t］-chromatic number of graphs
- YANG Lin1, SUN Lei2*
- J4. 2012, 47(6): 80-82.
- Abstract ( 555 ) PDF (573KB) ( 1109 ) Save
- Related Articles | Metrics
- On signed edge total domination of graphs
- LI Zhen-lin, LU Jun-long, L Xin-zhong
- J4. 2012, 47(6): 83-86.
- Abstract ( 586 ) PDF (585KB) ( 1053 ) Save
- Related Articles | Metrics
- 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 ( 889 ) PDF (606KB) ( 1179 ) Save
- Related Articles | Metrics
- An identity in terms of 2-Motzkin paths and its applications
- SUN Yi1, SU Gui-fu2
- J4. 2012, 47(6): 90-94.
- Abstract ( 617 ) PDF (753KB) ( 1514 ) Save
- Related Articles | Metrics
- Two Lie algebras and their applications
- Two Lie algebras and their applications
- J4. 2012, 47(6): 95-101.
- Abstract ( 613 ) PDF (611KB) ( 1166 ) Save
- Related Articles | Metrics
- Research on the commutative properties of codes
- WANG Jiong, WANG Zhi-xi, HE Yong
- J4. 2012, 47(6): 102-106.
- Abstract ( 907 ) PDF (636KB) ( 1312 ) Save
- Related Articles | Metrics
- 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 ( 534 ) PDF (583KB) ( 1219 ) Save
- Related Articles | Metrics
- 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 ( 552 ) PDF (708KB) ( 1429 ) Save
- Related Articles | Metrics
- Borel-Cantelli lemma for capacities
- SONG Li
- J4. 2012, 47(6): 117-120.
- Abstract ( 552 ) PDF (639KB) ( 999 ) Save
- Related Articles | Metrics
- The conditional randomized truth degree of formulas in the fuzzy logic system L*
- ZUO Wei-bing
- J4. 2012, 47(6): 121-126.
- Abstract ( 627 ) PDF (620KB) ( 1217 ) Save
- Related Articles | Metrics

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.

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.

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.

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

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

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.

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 L^{2 }error estimates for the semidiscrete and fullydiscrete schemes are obtained. Also some numerical results are given to verify our analysis for the schemes.

Two kinds of fractional partial differential equations are considered. One is a spacefractional convectiondiffusion 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 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 subdomains 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 L^{2}-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

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／skewHermitian 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 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 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 vertexdeleted subgraphs and its edge-deleted subgraphs are given.

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.

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 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.

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 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.

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.

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.

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.

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

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 pseudometric between formulas are presented and conditional randomized logic metric space is built. Several properties of conditional pseudometric 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.