Table of Content

  

16 October 2009
Volume 44 Issue 10

Articles

On stochastic generalized porous media and fast diffusion equations

WANG Feng-Yu

J4. 2009, 44(10):  1-13. 

Abstract ( 882 )   PDF (329KB) ( 491 )   Save

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In terms of some recent work of the author and collaborators, this paper provides a selfcontained account for the study of stochastic generalized porous media and fastdiffusion equations. We start from the corresponding deterministic equations in PDEs to explain the framework of the study, then introduce, respectively, results on the existence and uniqueness of solutions, the Harnack inequality for the associated transition semigroups and applications, the L² solutions and Large deviation principles with small noise.

An upper bound on the vertex distinguishing IE total chromatic number of graphs

LIU Shen-Sheng, SHU Zhi-Jiang

J4. 2009, 44(10):  14-16. 

Abstract ( 1393 )   PDF (129KB) ( 607 )   Save

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The upper bound for the vertex distinguishing IE-total chromatic number by the probability method is studied. If δ≥7 and 16Δ≤n≤Δ⁷/[32×10⁵(Δ+1)] +1 则χ^ie_vt(G)≤16Δ,thenχ^ie_vt(G)≤16Δis proved, where n is the order of G and δ is the minimum degree of G and  Δ is the maximum degree of G

List edge and list total colorings of planar graphs with adjacent triangles

DONG Ai-Jun, LI Guo-Jun, JU Jing-Song

J4. 2009, 44(10):  17-20. 

Abstract ( 1386 )   PDF (197KB) ( 1059 )   Save

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Given a planar graph G，let G,χ´_l(G)andχ"_l(G)denote the list edge chromatic number and list total chromatic number of  G respectively. It is proved that if a planar graph G withΔ(G)≥7 such that a triangle is adjacent to at most one triangle,then χ´_l(G)≤Δ(G)+1and χ"_l(G)≤Δ(G)+2

A degree condition for graphs to have Hamiltonian (g,f)-factors

WANG Chao

J4. 2009, 44(10):  21-25. 

Abstract ( 1600 )   PDF (201KB) ( 722 )   Save

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Let G be a 2 connected graph of order n, and let a and b be integers such that 2≤a＜b, and let g(x) and f(x) be two nonnegative integer valued  functions defined on V(G) such that a≤g(x)＜f(x)≤b for each x∈V(G). It is proved that G has a Hamiltonian (g,f) factor if the minimum degree of G satisfies the following conditions,δ(G)≥[(b-1)²-(a-1)(b-a)]/(a-1)〖SX)〗,[n＞(a+b-3)(a+b-2)]/(a-1), and max｛d_G(x) ,d_G(y) ｝≥(b-1)n/(a+b-2) for any two nonadjacent vertices x and y in G.

A finite difference method for the two sided space fractional advection diffusion equation

SU Li-Juan, Wang-Wen-He

J4. 2009, 44(10):  26-29. 

Abstract ( 1614 )   PDF (306KB) ( 1251 )   Save

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An implicit finite difference method for solving the two sided space fractional advectiondiffusion equation is given. Consistency, unconditional stability, and  convergence of the method are analyzed. Finally a numerical example is provided, and a comparison between the exact analytical solution and the merical prediction is made. 

Preconditioned simultaneous displacement(PSD) method for rank deficient  linear systems

YUE Jiang, CHANG Da-Wei

J4. 2009, 44(10):  30-35. 

Abstract ( 1383 )   PDF (229KB) ( 1157 )   Save

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The rank deficient linear systemÂx=b  is augmented to a block 4×4 linear system Âη=b´, where A is a square matrix, then A is split with PSD subproper splitting. The necessary and sufficient condition for the PSD method being semiconvergent is obtained. Finally a method is provided to compute the least square solution of minimal norm to ]Ax=b and exmamples are given to illustrate the process, whereA∈C^m×nb∈C^m,b´∈C ^m+n

A class of singular sublinear Sturm-Liouville boundary value problems

TAO Qiang-Liu

J4. 2009, 44(10):  36-38. 

Abstract ( 1241 )   PDF (185KB) ( 876 )   Save

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The positive solution is studied for a class of sublinear Sturm-Liouville boundary value problems, where the nonlinear term f(t,u) is allowed to be singular at t=0, t=1and u=0.The main tools are the Green function of the related linear problem and the corresponding Hammerstein integral equation. By nsidering the growth features of the nonlinear term at u=0 and u=+∞,and applying the Guo-Krasnosel'skii fixed point theorem on a cone, a new existence theorem is proved

Multiplicity results for a class of quasi-linear Neumann problems

HU Mo-Yin

J4. 2009, 44(10):  39-42. 

Abstract ( 1398 )   PDF (213KB) ( 944 )   Save

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Using a variational method and an improved three critical point theorem duo to B Ricceri, sufficient condition of the existence of at least three weak solutions for a class of quasilinear Neumann problem involving p-Laplacian are established. Also,  results in the literature are generalized.

Periodic solution of the higher order nonlinear differential equation

CHEN Xin-Yi

J4. 2009, 44(10):  43-47. 

Abstract ( 1347 )   PDF (196KB) ( 852 )   Save

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By employing the coincidence degree, a kind of higher order differential equations with delay  and the equation x⁽ⁿ⁾(t)+h(x´(t))+f(x(t))x´(t)+g(x(t-τ(t)))=p(t) are studied. Some new results on the existence of  T(T>0) periodic solutions are obtained, which generalizes the known results.

Linear maps preserving zeros of a polynominal on  factor von Neumann algebras

CUI Yun-Li, ZHANG Jian-Hua

J4. 2009, 44(10):  48-50. 

Abstract ( 1378 )   PDF (191KB) ( 917 )   Save

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Let M be a factor von Neumann algebra acting on a complex separable Hilbert spaceM with dim M>2, and Φ be a linear bijective map from M onto itself.  We prove that  Φ satisfies Φ(A)Φ(B)=Φ(B)Φ(A)* whenever AB=BA* for all A,B∈M if and only if  Φ(A)=λΨ(A) for all A∈M, where λ is a nonzero real number and Ψ is an atomorphism of  M

An equivalent characterization of Ω-filter

LI Lian-Jiang, JIN Qiu

J4. 2009, 44(10):  51-53. 

Abstract ( 1171 )   PDF (167KB) ( 531 )   Save

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We reinterpret the axioms of filters, and give an equivalent characterization of Ω-filters investigated in reference ［1］

Theory of truth degrees in Lukasiewicz three valued propositional logic

MA Li-Na, WANG Guo-Dun

J4. 2009, 44(10):  54-59. 

Abstract ( 1477 )   PDF (260KB) ( 1002 )   Save

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Based on the infinite product of unevenly distributed probability space, the theory of truth degrees in Lukasiewicz three valued propositional logicis introduced and inference rules with truth degrees are given. Moreover, it is proved that the set of truth degrees of propositions in the three valued (a/5,b/5,c/5)logic measure isdense in ［0,1］,and expressions of truth degrees are obtained. This paves the way for further study on approximate reasoning.

An exact solution of unsteady Couette flow of generalized Oldroyd-B fluid

GUO Xiao-Yi, XU Meng-Yu

J4. 2009, 44(10):  60-63. 

Abstract ( 1385 )   PDF (196KB) ( 924 )   Save

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The unsteady Couette flow of generalized Oldroyd-B fluid with a fractional derivative is studied. The exact solution is obtained by using the Laplace transform, the Weber transform and the generalized Mittag-Leffler function

Some results on linearly D-spaces

GUO Hong-Feng, SUN Wei-Hua, Zhang-Xin

J4. 2009, 44(10):  64-66. 

Abstract ( 1313 )   PDF (183KB) ( 743 )   Save

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The following results are proved: if a space X=∪｛X_α:α<λ｝, where each subspace X_α is linearly D- and for any β<λ,the set∪｛Xα:α<β｝is closed in X, then X is linearly D-; Every D_σ-spaceis linearly D-

Mixed type guaranteed cost controller design for neutral systems with nonlinearity

ZHANG Jia-Cheng, TUN Bao-Wei

J4. 2009, 44(10):  67-74. 

Abstract ( 1318 )   PDF (296KB) ( 654 )   Save

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The mixed memory and memoryless guaranteed cost controller design problems for a class of uncertain neutral systems with time-varying delays and nonlinearity are  discussed. A sufficient condition for the existence of unperturbed systems is given in terms of linear matrix inequalitis(LMIs). Based on this  sufficient condition,the corresponding results of systems with uncertainties are obtained. All the results can be handled by Matlab／LMI toolbox. Finally, a numerical example is illustrated to show the feasiblity of the obtained results.

Martingale transforms between the martingale spaces Q₁ and Q_Φ

MENG Wei-Wei, XU Lin

J4. 2009, 44(10):  75-79. 

Abstract ( 1295 )   PDF (296KB) ( 977 )   Save

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The relationship between Hardy space Q₁ and Hardy-OrliczQ_Φspace of martingales is characterized, and some results in the literature are extended.

Reverse order law for the weighted Moore-Penrose inverse of a triple left matrix semitensor product

SONG Cai-Qin, DIAO Jian-Li, WANG Xiao-Dong

J4. 2009, 44(10):  80-86. 

Abstract ( 1576 )   PDF (214KB) ( 915 )   Save

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The reverse order law for the weighted Moore-Penrose inverse of a triple matrix left semitensor product is investigated, and a necessary and sufficient condition for it is given.

q-supplement in finite groups and its applications

LIU Xiao-Lei, WANG Yan-Ming

J4. 2009, 44(10):  87-90. 

Abstract ( 1400 )   PDF (198KB) ( 991 )   Save

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Finite groups are investigated in terms of q-supplement, some sufficient conditions on supersolubility and p-nilpotence of finite groups are obtained.

A special generalized self-shrinking sequence on GF(q)

WANG Jin-Ling, LAN Juan-Li

J4. 2009, 44(10):  91-96. 

Abstract ( 1342 )   PDF (258KB) ( 984 )   Save

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A new sequence generator on GF(q) is presented.The novel generalized self-shrinking sequence family B(a) on GF(q) has a group and linear structure. Any two sequences of the family have a perfect crosscorrelation feature,and all sequences in the family are balanced except several special sequences.　If n≥2, no less than(q-1)/q of the family B(a) have their least periods 2×q^n-1. Finally,the upper bounds of linear complexity in every case are given.