Table of Content

    20 December 2013
    Volume 48 Issue 12
    On a generalization of quasi GP-injective modules
    YIN Xiao-bin, JI Xue-mei
    J4. 2013, 48(12):  1-5. 
    Abstract ( 276 )   PDF (651KB) ( 442 )   Save
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    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 ( 333 )   PDF (609KB) ( 491 )   Save
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    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 ( 371 )   PDF (554KB) ( 1037 )   Save
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    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 ( 270 )   PDF (586KB) ( 381 )   Save
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    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 ( 352 )   PDF (575KB) ( 394 )   Save
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    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 ( 281 )   PDF (607KB) ( 503 )   Save
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    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 ( 272 )   PDF (1024KB) ( 392 )   Save
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    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 ( 280 )   PDF (562KB) ( 400 )   Save
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    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 ( 349 )   PDF (569KB) ( 476 )   Save
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    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 ( 270 )   PDF (586KB) ( 519 )   Save
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    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 ( 387 )   PDF (585KB) ( 533 )   Save
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    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 ( 304 )   PDF (568KB) ( 479 )   Save
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    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 ( 286 )   PDF (542KB) ( 466 )   Save
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    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 ( 323 )   PDF (609KB) ( 563 )   Save
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    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 ( 286 )   PDF (580KB) ( 366 )   Save
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    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 ( 287 )   PDF (573KB) ( 411 )   Save
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    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 ( 312 )   PDF (602KB) ( 351 )   Save
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    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 ( 300 )   PDF (579KB) ( 420 )   Save
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    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 ( 377 )   PDF (567KB) ( 413 )   Save
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    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 ( 286 )   PDF (823KB) ( 418 )   Save
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    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 ( 305 )   PDF (556KB) ( 377 )   Save
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    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.