JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

On the Hyers-Ulam Stability of n-cocycles

JI Pei-sheng1, QI Wei-qing2, LIU Rong-rong1

J4. 2013, 48(4): 1-4.

Abstract ( 953 )

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Let A be a Banach algebra and M be a Banach A-module. An n-linear mapping f: An→M from An into M is called an n-cocycle if it satisfies that x1f(x1,…,xn+1)+(-1)n+1f(x1,…,xn)xn+1+∑ni=1(-1)if(x1,…,xi-1,xixi+1,xi+2,…,xn+1)=0 for all x1,…,xn+1∈A.It is proved that the n-cocycles from An into M are Hyers-Ulam stable.

Lie higher derivable mappings of triangular algebras at zero points

HU Li-xia, ZHANG Jian-hua

J4. 2013, 48(4): 5-9.

Abstract ( 972 )

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In this note, we study the structure of Lie higher derivable mapping of triangular algebras at zero point, and prove that every Lie higher derivable mapping at zero point is the sum of a higher derivation and a map into its center.

Topological uniform descent and the single valued extension property

YU Wei, CAO Xiao-hong*

J4. 2013, 48(4): 10-14.

Abstract ( 1090 )

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The stability of the property (ω1) for the Helton class operators

ZHAO Hai-yan, CAO Xiao-hong*

J4. 2013, 48(4): 15-19.

Abstract ( 859 )

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Equitable colorings of a special class of Cartesian products of graphs

WU Fang-lan1, ZUO Lian-cui2*

J4. 2013, 48(4): 20-24.

Abstract ( 1101 )

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By using the sort method of vertices, the equitable chromatic number and the equitable chromatic threshold of the Cartesian products of graphs which is extending a path from some point of a circle with a complete bipartite graph are obtained.

On the gracefulness of the (Gr1,Gr2,… ,Gr4h+2)corona of the graph C4h+1⊙K1

WU Yue-sheng, WANG Guang-fu, XU Bao-gen

J4. 2013, 48(4): 25-27.

Abstract ( 985 )

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The definition of the (Gr1,Gr2,…,Gr4h+2)corona of the Graph C4h+1⊙K1 has been given. The gracefulness of the (Gr1,Gr2,…,Gr4h+2)corona of the Graph C4h+1⊙k1 are discussed. The graceful labelings are given.

On L(p,q)-labeling of planar graphs without 4,5,6-cycles and intersecting triangles

ZHU Hai-yang1, CHEN Wei1, L Xin-zhong2, LI Pei-jun3

J4. 2013, 48(4): 28-34.

Abstract ( 1094 )

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Let λp,q(G) denote the L(p,q)-labeling number of a planar graph G. It is showed that if G be a planar graphs without 4,5,6-cycles and intersecting triangles, then λp,q(G)≤(2q-1)Δ(G)+max｛4p+4q-4, 6p+2q-4, 8p-4｝. This result imply that Wagner’s conjecture holds for a planar graph G without 4,5,6-cycles and intersecting triangles.

The construction of Gorenstein-projective modules over some Morita context

ZHANG Yu-lin, YAO Hai-lou

J4. 2013, 48(4): 35-39.

Abstract ( 1047 )

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Let Γ be a Morita context (Λ1,Λ2,N,M,ψ,φ). The properties of some Morita context, and a class of the Gorenstein-projective modules over it are studied.

Hom-Hopf modules for a class of symmetric categories

WANG Sheng-xiang1,2, GUO Shuang-jian2

J4. 2013, 48(4): 40-45.

Abstract ( 1118 )

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Let L be a cotriangular Hopf algebra. By using the definition of Hom-Hopf algebras in LM, the theorem that the dual of a Hom-Hopf algebra in LM is also a Hom-Hopf algebra is proved. Furthermore, the coinvariant subspace of a Hom-Hopf module is defined and the fundamental theorem of Hom-Hopf module in LM is obtained.

On the quotient category and localization of an R-module Category

J4. 2013, 48(4): 46-50.

Abstract ( 1018 )

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The quotient category of an R-module category which is defined by the directed limit and its localization which is given by the equivalent classes of the roofs are proved to be equivalent. For the Abel category and triangulated category,the similar results are obtained.

Composition followed by differentiation from Bloch-type into Zygmund-type space

JIANG Xiao-yu

J4. 2013, 48(4): 51-56.

Abstract ( 966 )

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The composition followed by differentiation C-D is characterized between the Bloch-type space Bα and the Zygmund-type space Zμ on the unit disk. By the methods of functional analysis and several complex variables, some necessary and sufficient conditions are given for C-D to be a bounded operator or a compact operator from Bα to Zμ.

n-differentiation composition operators between weighted Banach spaces of holomorphic functions

CHEN Cui

J4. 2013, 48(4): 57-59.

Abstract ( 944 )

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Existence and uniqueness results for Caputo fractional differential equations with initial value conditions

LI Jiao

J4. 2013, 48(4): 60-64.

Abstract ( 1153 )

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The Caputo fractional differential equations Dn*0y(x)=f(x,y(x)) with initial value conditions are investigated, where n∈(0,1) and the function f(x,y(x)) meets some integrable conditions. Existence and uniqueness results of solutions are obtained by the method of successive approximations under some weak conditions. An example is given to illustrate the results at last.

Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method

XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1

J4. 2013, 48(4): 65-71.

Abstract ( 1094 )

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The optimal scaling matrix and the estimates of some amounts of M-1N are used to discuss the convergence of the extrapolated Gauss-Seidel iteration methods and the relationship between them and H-matrices. Several equivalent conditions for the Hmatrices based on the extrapolated Gauss-Seidel and the Gauss-Seidel iterative methods are obtained. And the convergence results of the Gauss-Seidel and the extrapolated Gauss-Seidel iterative methods are given for the strictly diagonally dominant matrices, the irreducible diagonally dominant matrices and the Stieltjes matrices.

Dynamical formation and growth of cavity in a heated viscoelastic sphere

CHEN Ya-juan1,2, SHANG Xin-chun1*

J4. 2013, 48(4): 72-76.

Abstract ( 972 )

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Dynamical formation and growth of cavity in a sphere composed of incompressible viscoelastic material subjected to uniform temperature field were studied according to the finite deformation dynamics theory. The nonlinear ordinary differential equation describing cavity movement in a sphere was established by using the finite logarithmic strain measure for geometric large deformation and employing the Kelvin-Voigt differential type constitution equation of thermo-visco-elasticity. By numerical computation, growth curves of cavity radius with temperature and the critical temperature were given, dynamical variation curves of cavity radius increasing with time were obtained, and variation rules of cavity radius increasing with the external temperature, the spherical radius, and the material parameters were also discussed.

The quasi-Wilson nonconforming finite element approximation to pseudo-hyperbolic equations

SHI Yan-hua1, SHI Dong-yang2*

J4. 2013, 48(4): 77-84.

Abstract ( 1062 )

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A quasi-Wilson finite element method is applied to a class of pseudo-hyperbolic equations. Firstly, employing the known high accuracy analysis of the bilinear element, mean-value approach and post-processing technique, the superclose property and the global superconvergence result with the order O(h2) are obtained for semi-discrete scheme. Secondly, combining a special character of the quasi-Wilson element that the consistency error can reach to order O(h3) in broken H1-norm and extrapolation method, the extrapolation solution with the order O(h3) is presented. Finally, the optimal order error estimate is deduced in broken H1-norm for fully-discrete scheme.

Philos-type oscillation criteria for third-order nonlinear functional differential equations with distributed delays and damped terms

GAO Zheng-hui, LUO Li-ping

J4. 2013, 48(4): 85-90.

Abstract ( 911 )

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The oscillation of third-order nonlinear neutral functional differential equations with distributed delays and damped terms is studied. By using a generalized Riccati transformation and H-functions technique, some new sufficient conditions which insure that any solution of this equation Philos-type oscillation or converges to zero are established.

Existence of nontrivial solutions of nonlinear elliptic equation with critical potential

WU Yun1,2, HAN Ya-die1

J4. 2013, 48(4): 91-94.

Abstract ( 881 )

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Through the establishment of a new space H, the existence of nontrivial solutions of fourthorder nonlinear elliptic equation with critical potential in the new Hilbert space are discussed. It proves the existence problem of nontrivial solution in this new space by using the Mountain pass theorem and the (PS) condition.

Global attractivity of a nonlinear discrete Logistic model with feedback control

WU Dai-yong

J4. 2013, 48(4): 114-110.

Abstract ( 842 )

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Global attractivity for a nonlinear discrete logistic model with feedback control is discussed. By using comparison theorem and difference inequation, the sufficient conditions for global attractivity of positive equilibrium of system are obtained.Some examples together with their numerical simulations show the feasibility of the main results.It is obtained that feedback control influences the attractivity of the equilibrium.

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