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- On the Hyers-Ulam Stability of n-cocycles
- JI Pei-sheng1, QI Wei-qing2, LIU Rong-rong1
- J4. 2013, 48(4): 1-4.
- Abstract ( 529 ) PDF (659KB) ( 1066 ) Save
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- Lie higher derivable mappings of triangular algebras at zero points
- HU Li-xia, ZHANG Jian-hua
- J4. 2013, 48(4): 5-9.
- Abstract ( 495 ) PDF (547KB) ( 1062 ) Save
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- Topological uniform descent and the single valued extension property
- YU Wei, CAO Xiao-hong*
- J4. 2013, 48(4): 10-14.
- Abstract ( 488 ) PDF (557KB) ( 1294 ) Save
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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 ( 444 ) PDF (551KB) ( 1201 ) Save
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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 ( 491 ) PDF (541KB) ( 1445 ) Save
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- 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 ( 438 ) PDF (963KB) ( 834 ) Save
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- 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 ( 525 ) PDF (578KB) ( 1317 ) Save
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- The construction of Gorenstein-projective modules over some Morita context
- ZHANG Yu-lin, YAO Hai-lou
- J4. 2013, 48(4): 35-39.
- Abstract ( 513 ) PDF (1061KB) ( 1039 ) Save
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- Hom-Hopf modules for a class of symmetric categories
- WANG Sheng-xiang1,2, GUO Shuang-jian2
- J4. 2013, 48(4): 40-45.
- Abstract ( 546 ) PDF (556KB) ( 947 ) Save
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- On the quotient category and localization of an R-module Category
- On the quotient category and localization of an R-module Category
- J4. 2013, 48(4): 46-50.
- Abstract ( 498 ) PDF (1856KB) ( 1228 ) Save
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- Composition followed by differentiation from Bloch-type into Zygmund-type space
- JIANG Xiao-yu
- J4. 2013, 48(4): 51-56.
- Abstract ( 481 ) PDF (560KB) ( 973 ) Save
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- n-differentiation composition operators between weighted Banach spaces of holomorphic functions
- CHEN Cui
- J4. 2013, 48(4): 57-59.
- Abstract ( 496 ) PDF (551KB) ( 1035 ) Save
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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 ( 473 ) PDF (543KB) ( 1348 ) Save
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- Several equivalent conditions for H-matrix based on the extrapolated GaussSeidel iterative method
- XUE Qiu-fang1,2, GAO Xing-bao1*, LIU Xiao-guang1
- J4. 2013, 48(4): 65-71.
- Abstract ( 532 ) PDF (567KB) ( 961 ) Save
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- Dynamical formation and growth of cavity in a heated viscoelastic sphere
- CHEN Ya-juan1,2, SHANG Xin-chun1*
- J4. 2013, 48(4): 72-76.
- Abstract ( 426 ) PDF (1223KB) ( 1105 ) Save
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- The quasi-Wilson nonconforming finite element approximation to pseudo-hyperbolic equations
- SHI Yan-hua1, SHI Dong-yang2*
- J4. 2013, 48(4): 77-84.
- Abstract ( 474 ) PDF (578KB) ( 1146 ) Save
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- 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 ( 413 ) PDF (554KB) ( 1093 ) Save
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- Existence of nontrivial solutions of nonlinear elliptic equation with critical potential
- WU Yun1,2, HAN Ya-die1
- J4. 2013, 48(4): 91-94.
- Abstract ( 393 ) PDF (566KB) ( 1376 ) Save
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- Global attractivity of a nonlinear discrete Logistic model with feedback control
- WU Dai-yong
- J4. 2013, 48(4): 114-110.
- Abstract ( 433 ) PDF (801KB) ( 1168 ) Save
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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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 Hmatrices 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 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.

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.

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.

Through the establishment of a new space H, the existence of nontrivial solutions of fourthorder 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 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.