Table of Content

  

20 December 2013
Volume 48 Issue 12

Articles

On a generalization of quasi GP-injective modules

YIN Xiao-bin, JI Xue-mei

J4. 2013, 48(12):  1-5. 

Abstract ( 814 )   PDF (651KB) ( 598 )   Save

Related Articles | Metrics

The conception of quasi EP-injective module is proposed. An example to explain that quasi EP-injective module is a real generalization of quasi GP-injective module is given. Some properties and characterizations of quasi EP-injective modules are obtained.

On central linear McCoy rings

WANG Wen-kang

J4. 2013, 48(12):  6-13. 

Abstract ( 796 )   PDF (609KB) ( 899 )   Save

Related Articles | Metrics

Central linear McCoy rings are a generalization of linear McCoy rings. It is proved that R is right central linear McCoy if and only if R［x］is right central linear McCoy. If R is right Ore, Q is the classical right quotient ring of R, and R is right central linear McCoy, then Q is right central linear McCoy. Several right central linear McCoy subrings of upper triangular matrix rings over right central linear McCoy rings are given.

The Structure Theorem of weak comodule algebras in
Yetter-Drinfeld module categories

CHEN Hua-xi1, ZHANG Xiao-hui2, XU Qing-bing3

J4. 2013, 48(12):  14-17. 

Abstract ( 863 )   PDF (554KB) ( 1383 )   Save

Related Articles | Metrics

The definitions of weak Hopf algebra and weak comodule algebras in Yetter-Drinfeld module categories are introduced, and the structure theorem of weak comodule algebras in Yetter-Drinfeld module categories is obtained.

Dynamics of the nonautonomous predator system

CHEN Xin-yi

J4. 2013, 48(12):  18-23. 

Abstract ( 689 )   PDF (586KB) ( 633 )   Save

Related Articles | Metrics

In this paper, the dynamics of a nonautonomous predator system are investigated. Some sufficient conditions which guarantee the permanence and the global asymptotic stability of the system are determined by using compare theory and constructing a suitable Lyapunov function. For the periodic case and almost periodic case, by using Brouwer fixed point theorems and constructing Lyapunov function to adjoint system, existence and uniqueness of a positive periodic and almost periodic solution are obtained, which generalizes the known result.

Existence of a solution for the boundary value problem of
fractional differential equation with delay

LI Fan-fan, LIU Xi-ping*, ZHI Er-tao

J4. 2013, 48(12):  24-29. 

Abstract ( 833 )   PDF (575KB) ( 789 )   Save

Related Articles | Metrics

It is studied that the boundary value problem for a class of fractional delay differential equations with Riemann-Liouville fractional derivative. According to the boundary conditions, the definition of upper and lower solutions are given, and the comparison theorem is proved. By using the method of upper and lower solutions, monotone iterative technique and topological degree theory, existence and uniqueness theorems and multiple theorems are obtained.

Existence and uniqueness of almost automorphic mild solutions to
a class of semilinear integro-differential equations

LI Xi-liang1,2, HAN Yu-liang2

J4. 2013, 48(12):  30-34. 

Abstract ( 786 )   PDF (607KB) ( 750 )   Save

Related Articles | Metrics

Sufficient conditions for the existence and uniqueness of almost automorphic mild solution to a class of semilinear integro-differential equations are established. The asymptotic stability property of the uniqueness almost automorphic mild solution is analyzed.

The uniqueness of positive solutions for a predator-prey
model with predator cannibalism

LI Bing-fang1, GUO Gai-hui2, BAI Yun-xiao2

J4. 2013, 48(12):  35-41. 

Abstract ( 920 )   PDF (1024KB) ( 715 )   Save

Related Articles | Metrics

Under homogeneous Dirichlet boundary conditions, a predator-prey model with predator cannibalism is considered. The existence and uniqueness of positive solutions are presented. By maximum principles and lower-upper solution methods, a prior estimate of positive solutions is firstly obtained. Then by Leray-Schauder theory and resorting to calculate fixed point indices of compact maps in cones, sufficient conditions for coexistence are given. Moreover, the uniqueness of positive solutions is derived under some conditions.

A new method of reproducing kernel for periodic
boundary-value problem

ZHANG Rui-min, LIN Ying-zhen

J4. 2013, 48(12):  42-46. 

Abstract ( 741 )   PDF (562KB) ( 932 )   Save

Related Articles | Metrics

Numerical solution for a class of periodic boundary-value problem is studied. A new method of reproducing kernel by using functional analysis is given. The method is valid by means of periodic problem in physics,and it has uniform convergence.

Topological properties of maximal filters in BL algebras

LUO Qing-jun1, 2, WANG Guo-jun1*

J4. 2013, 48(12):  47-51. 

Abstract ( 912 )   PDF (569KB) ( 773 )   Save

Related Articles | Metrics

Two types of topologies J and J* are established on the set MF(L) of all maximal filters in a BL algebra L. It is proved that (MF(L), J) is a compact Hausdorff space, and (MF(L), J*) is a T1 space. Also, we show that J and J* are the same topology if the related universe is either finite or infinite linearly ordered.

Prime fuzzy ⊙ideals and its topological properties of
regular residuated lattices

LIU Chun-hui1,2

J4. 2013, 48(12):  52-56. 

Abstract ( 762 )   PDF (586KB) ( 683 )   Save

Related Articles | Metrics

We deeply study the theory of fuzzy ⊙ideals in regular residuated lattices by using the notion of fuzzy set and its operations which proposed by Zadeh. Firstly, the notion of prime fuzzy ⊙ideals is introduced and its properties are studied. And the prime fuzzy ⊙ideals theorem is established. Secondly, a topology T is constructed on the set of all prime fuzzy ⊙ideals PI⊙(L). It is proved that the topology space (PI⊙(L), T) is T0space.

Lattice of fuzzy filter in a Heyting algebra

LIU Chun-hui1,2

J4. 2013, 48(12):  57-60. 

Abstract ( 861 )   PDF (585KB) ( 927 )   Save

Related Articles | Metrics

Combining fuzzy sets and filters theory, we further studied the concept of fuzzy filters in Heyting algebras. Reviewing the basic results of Heyting algebras and fuzzy filters, the concept of generated fuzzy filter by a fuzzy set in Heyting algebras is  defined and its representation is  obtained. Finally, the lattice operations and implication operation are defined on the set of all fuzzy filters in a Heyting algebra. It is proved that the fuzzy filters set with above operations form a complete Heyting algebra.

MacWilliams identities of the linear codes over ring Fp+vFp

LIU Xiu-sheng, LIU Hua-lu

J4. 2013, 48(12):  61-65. 

Abstract ( 815 )   PDF (568KB) ( 997 )   Save

Related Articles | Metrics

The Lee weight enumerators and the complete weight enumerators for the linear codes over ring Fp+vFp were studied. By using the Gray map φ from (Fp+vFp)n to F2np, it is proved that the Gray images of the self-dual codes over Fp+vFp are the self-dual codes over Fp, and then correctness and application of the two MAcWilliams identities are given.

Counting formulate about partition with the largest part n

PANG Rong-bo

J4. 2013, 48(12):  66-69. 

Abstract ( 816 )   PDF (542KB) ( 1469 )   Save

Related Articles | Metrics

Based on the study the counting formulate about the ‘odd-even’ partition with the largest part n and the ‘even’ partition with the largest part n, some counting formulates are showed by applying the elementary method.

Non-group rank and relative rank of the semigroup W(n,r)

LUO Yong-gui

J4. 2013, 48(12):  70-74. 

Abstract ( 914 )   PDF (609KB) ( 1241 )   Save

Related Articles | Metrics

Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain ［n］. For an arbitrary integer r(2≤r≤n-1), the non-group rank and non-idempotent rank of the semigroup W(n,r)=｛α∈RWn:|Imα|≤r｝ were studied. The semigroup W(n,r) generated by elements of rank r is proved. Furthermore, it is shown that for 1≤l≤r, the relative rank of the semigroup W(n,r) with respect to itself each ideal W(n,l).

Some equivalent conditions of supercyclicity of bounded linear operators

LIU Yang

J4. 2013, 48(12):  75-79. 

Abstract ( 809 )   PDF (580KB) ( 1006 )   Save

Related Articles | Metrics

Using the property of the topological uniform descent,  the judgement for an operator A∈SC(H) is given, which SC(H) denoted the norm-closure of the class of all the supercyclic operators on an infinite dimensional separable complex Hilbert space.

On nonuniform polynomial trichotomy of 
evolution operators in Banach space

LI Zhi-gang, SONG Xiao-qiu*, YUE Tian

J4. 2013, 48(12):  80-85. 

Abstract ( 741 )   PDF (573KB) ( 881 )   Save

Related Articles | Metrics

The integral properties of nonuniform polynomial trichotomy of evolution operators are discussed in Banach space, and  an example is  illustrated the relationship between the two polynomial trichotomies which shows the evolution operator is nonuniform polynomial trichotomy but not uniform polynomial trichotomy.

Linear maps between operator algebras preserving the ascent and descent

CHEN Shi-zhao, CAO Xiao-hong*

J4. 2013, 48(12):  86-89. 

Abstract ( 900 )   PDF (602KB) ( 642 )   Save

Related Articles | Metrics

Let B(H) be the algebra of all bounded linear operators on infinite dimensional complex Hilbert space H, and let :B(H)→B(H) be a surjective linear map. If  preserves the upper semi-Browder spectrum or descent spectrum and the set of isolated points, then  is an automorphism on B(H).  If  preserves the Drazin spectrum and the set of isolated points, the  two probable structures are given.

Properties of a new kind of exact augmented Lagrangian function

LI Mei-xia1,2， LIU Qian3

J4. 2013, 48(12):  90-95. 

Abstract ( 793 )   PDF (579KB) ( 766 )   Save

Related Articles | Metrics

new kind of augmented Lagrangian function for constrained optimization problem with both equality and inequality contraints is introduced. The elementary properties of this kind of function are given. Furthermore, the equivalence between its slationary point of uncontrained minimization and the KKT point of the original constrained problem is proved.

Boundedness of the Littlewood-Paley function g*λ, μ  on the generalized
Morrey spaces with non-doubling measures

SUN Ai-wen, WANG Xiao-shan, SHU Li-sheng

J4. 2013, 48(12):  96-99. 

Abstract ( 962 )   PDF (567KB) ( 756 )   Save

Related Articles | Metrics

Assuming the non-doubling  μ  satisfies some conditions,  its boundedness on the generalized Morrey spaces is discussed according to the boundedness of the Littlewood-Paley function g*λ, μ on the Lp(μ).

Discovery and application of function P-reasoning
under the information law state

XU Feng-sheng, YU Xiu-qing

J4. 2013, 48(12):  100-103. 

Abstract ( 857 )   PDF (823KB) ( 591 )   Save

Related Articles | Metrics

Based on the function P-sets, the concept of P-information law generation is proposed. Also, the concepts of information law deficit state, information law surplus state and the corresponding attribute theorem are given. By using the function P-reasoning, P-information law state discovery and discovery theorem are proposed. Finally, applications of information law state to economic system and economic information are given.

Interval estimation under median ranked set sampling

ZHANG Liang-yong1,2, XU Xing-zhong2, DONG Xiao-fang1

J4. 2013, 48(12):  107-110. 

Abstract ( 824 )   PDF (556KB) ( 1009 )   Save

Related Articles | Metrics

The interval estimation for the infinite population median was constructed by using the order statistics of the median ranked set sample, and the new estimator was shown to be distribution-free. In addition, it was proofed analytically the precision of the new interval estimator is higher than the interval estimator of the population median under ranked set sampling. Finally, a practical application was carried out for a real data set related to conifer trees.