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    Volume 48 Issue 10
    Articles
    Characterizations of Jordan isomorphism on standard operator algebras
    ZHAO Jie-ling, ZHANG Jian-hua
    J4. 2013, 48(10):  1-4. 
    Abstract ( 334 )   PDF (650KB) ( 386 )   Save
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    Let A and B be standard operator algebras on an infinite dimensional Banach space X and ψ: A→B be a preserve unit linear bijection. We prove that if ψ(A。B)=ψ(A)。ψ(B) holds for all A,B∈A with AB=0, then for all A,B∈A either ψ(AB)=ψ(A)ψ(B) or ψ(AB)=ψ(B)ψ(A) holds.

    Characterizations of a pair of generalized derivations on nest algebras
    PENG Dong-xia, ZHANG Jian-hua
    J4. 2013, 48(10):  5-8. 
    Abstract ( 383 )   PDF (605KB) ( 449 )   Save
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    Let  τ(N) be any nest algebra on a complex and separable Hilbert space H, and (Φ,ψ)  be a pair of linear mappings of  τ(N).We prove that if  (Φ,ψ)  satisfies Φ(AB)=Φ(A)B+Aψ(B) for all A,B∈τ(N) with AB=0, then (Φ,ψ) is a pair of generalized inner derivations.

    The Hyers-Ulam-Rassias stability of a mixed quintic functional equation of two variables
    JI Pei-sheng, LIU Rong-rong
    J4. 2013, 48(10):  9-13. 
    Abstract ( 359 )   PDF (584KB) ( 584 )   Save
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    Let X be a vector space and Y be a Banach space over the real field, R. A mapping f:X2→Y from X2 into Y is called a mixed quintic functional equation of two variables if it satisfies that f(x1+x2, 2y1+y2)+f(x1+x2,2y1-y2)+f(x1-x2, 2y1+y2)+f(x1-x2, 2y1-y2)=4f(x1,y1+y2)+4f(x2, y1+y2)+4f(x1,y1-y2)+4f(x2, y1-y2)+24f(x1, y1)+24f(x2, y1) for all x1, x2, y1, y2∈X. The general solution of the mixed quintic functional equation of two variables is obtained and the Hyers-Ulam-Rassias stability for it is proved.

    Two parameter C-semigroups and application
    HUANG Cui, WANG Cai-xia, SONG Xiao-qiu*, ZHANG Ming-cui
    J4. 2013, 48(10):  14-17. 
    Abstract ( 348 )   PDF (609KB) ( 497 )   Save
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    According to the C-semigroup and two parameter C0-semigroups, the definition of a more general two-parameter C-semigroup is given.  Total differential of two parameter C-semigroup, partial differential of two parameter C-semigroup, stability and some relations betwwen two parameter C-semigroups with abstract differential equation are obtained.

    The Solutions of initial value problems for integro-differential equations in Banach spaces with discontinuous terms
    WANG Jian-guo, LIU Chun-han
    J4. 2013, 48(10):  18-22. 
    Abstract ( 383 )   PDF (587KB) ( 460 )   Save
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    By use of a new comparison theorem of integro-differential equations on infinite interval, the existence and uniqueness of solutions of the initial value problem for integro-differential equations with discontinuous terms in Banach spaces are investigated, and the error estimate of the iterative sequences of solutions is given.

    Internal P(ρ,σ)-set′s random characteristic-application
    ZHANG Huan-li1,2, LI Yu-ying3*, SHI Kai-quan1
    J4. 2013, 48(10):  23-28. 
    Abstract ( 367 )   PDF (611KB) ( 406 )   Save
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    P(ρ,σ)-sets is the general case of P-sets. Based on the conception of P(ρ,σ)-set (XPρ, XPFσ ), the relation between internal P(ρ,σ)-set and internal P-set is studied. Internal P(ρ,σ)-set and internal P-set relation theorem, internal P(ρ,σ)-set and numerical value ρ relation theorem, internal P(ρ,σ)-set’s range, other characteristics of internal P(ρ,σ)-set, the finiteness theorem of internal P(ρ,σ)-set, the set chain theorem of internal P(ρ,σ)-set, the internal P(ρ,σ)-set probability interval finite partition theorem, and its corollary, generation, reduction, identification theorem of internal P(ρ,σ)-set, filter generation theorem of internal P(ρ,σ)-set are obtained. Finally, internal P(ρ,σ)-set application is given.

    P-sets and the dominant-recessive characteristics of internal P-information
    ZHANG Huan-li1,2, FAN Cheng-xian3, SHI Kai-quan1*
    J4. 2013, 48(10):  29-34. 
    Abstract ( 420 )   PDF (596KB) ( 534 )   Save
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    P-sets(packet sets) is proposed by embedding the dynamic characteristic into the finite cantor set X and improving it. P-sets is a set-pair composed of internal P-set X(internal packet set X) and outer P-set XF(outer packet set XF), or (X, XF) is P-sets. Using the structure of P-sets and the concept intersection of dominant gene and recessive gene, the dominant and recessive concepts, the dominant and recessive characteristics and measurement, the dominant and recessive theorems, the attribute characteristic generated by the dominant and recessive of internal P-information are given. The dominant and recessive is one of the important characteristics of P-sets.

    Outer P-reasoning information recovery and its attribute hiding characteristic
    WU Song-li1,2, FAN Cheng-xian3
    J4. 2013, 48(10):  35-40. 
    Abstract ( 365 )   PDF (604KB) ( 377 )   Save
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    Using outer P-set and outer P-reasoning, outer P-reasoning generation and its attribute hiding, information element deleted theorem, dependence theorem, attribute hiding and attribute hiding discovery theorems of outer P-information recovery as well as outer P-information recovery concept and its recovery characteristic are given.

    Dependence-reduction and application of outward-recursion data
    LI Yu-ying1,2, ZHANG Zhi-ling1, LIN Hong-kang1,2, RUAN Qun-sheng1, ZHANG Shi-liang1
    J4. 2013, 48(10):  41-46. 
    Abstract ( 376 )   PDF (601KB) ( 412 )   Save
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    By using the structure and dynamic characteristic of outer P-set based on a class of data which has a characteristic of recurrence amplification, the concept of outward-recursion data is proposed. Also, the paper gives the structure, the generation principle and the criterion as well as the interrelated theorems of dependence and reduction for the outward recursion data. Finally, the application of the outward-recursion information is presented.

    The solvable condition researched on a pair of matrix equations
    JIANG Jing1, LI Ning2, WANG Ting1
    J4. 2013, 48(10):  47-50. 
    Abstract ( 409 )   PDF (607KB) ( 498 )   Save
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    The matrix equations A1XA*1+B1YB*1=C1
    A2XA*2+B2YB*2=C2 are studied, where Ci=C*i, i=1, 2. By the rank of matrix, a necessary and sufficient condition is given for the matrix equations to have a pair of common Hermitian solutions X and Y. As a consequence, we have derived the conditions for the matrix equations to have Hermitian solution X or Y respectively by ranks.

    Multiplicative properties and connectedness in interval-valued metric spaces
    CHEN Gui-xiu1,2, LI Sheng-gang1*, SUONAN Ren-qian1,2
    J4. 2013, 48(10):  51-55. 
    Abstract ( 360 )   PDF (594KB) ( 441 )   Save
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    The definition of interval-valued metric spaces are given; then according to the definition of general topological space, the fact that the countable number of interval-valued metric spaces satisfied multiplicative properties are proved; Finally, the connectedness of interval-valued metric spaces are discussed in the paper.

    Disconnectednesses of bi-pre-topological spaces
    SHEN Wen-xia, LI Sheng-gang
    J4. 2013, 48(10):  56-61. 
    Abstract ( 363 )   PDF (609KB) ( 429 )   Save
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     Connectednesses and disconnectednesses of topological spaces are extended to bi-pre-topological spaces. Some properties of disconnectednesses of bi-pre-topological spaces are given. Also, the structure of a disconnectednesses of bi-pre-topological spaces which including two-element spaces is discussed.

    Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative
    QIN Xiao-na, JIA Mei*, LIU Shuai
    J4. 2013, 48(10):  62-67. 
    Abstract ( 457 )   PDF (617KB) ( 475 )   Save
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    The paper is concerned with the existence of solutions for a class of fractional differential equations boundary value problems with Caputo derivative, where there exist fractional derivative in the boundary conditions and the nonlinear term  f:[0,1]×[0,∞)→[0,∞) satisfies Caratheodory conditions.By using the Krasnosel’skii fixed theorem on a cone, the sufficient conditions for the problem at least one and two positive solutions are obtained.

    Persistence and extinction in stochastic SIS epidemic model with nonlinear incidence rate
    ZHOU Yan-li1,2, ZHANG Wei-guo1
    J4. 2013, 48(10):  68-77. 
    Abstract ( 326 )   PDF (615KB) ( 446 )   Save
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    A stochastic SIS epidemic model with nonlinear incidence is investigated. First, the existence of global positive solution is obtained; Next, the asymptotic behaviors of the model are studied that is if R0≤1, the disease-free equilibrium is stochastically asymptotical stability, and if R0>1 the solution is oscillating around the endemic equilibrium of the deterministic model. Furthermore, the sufficient conditions of persistence in the mean and stochastic extinction are obtained. Finally, the theoretical results are illustrated by numerical simulations.

    Boundedness of Littlewood-Paley operators with non-doubling measures
    GENG Su-li, ZHAO Kai*, ZHANG Li-ping
    J4. 2013, 48(10):  78-81. 
    Abstract ( 380 )   PDF (604KB) ( 413 )   Save
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    Let μ be a positive Radon measure on Rd which may be non-doubling. The only condition that μ must satisfy is μ(B(x,r))≤C0rn, for x∈Rd,r>0 and some fixed constants C0>0 and 0<n≤d. Supposing  Littlewood-Paley g is bounded on L2(μ), by using the Calderón-Zygmund decompsition under non-doubling measure, the boundedness of g from L1(μ) to L1,∞(μ) is obtaind. And then the boundedness of g from Hardy space H1(μ) to L1(μ) is established.

    Uniqueness of meromorphic functions and differential polynomials sharing two values IM
    SHI Xin-hua
    J4. 2013, 48(10):  82-85. 
    Abstract ( 364 )   PDF (570KB) ( 973 )   Save
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    Use Nevanlinna′s value distribution theory to study the uniqueness problems of differential polynomials of meromorphic functions that share two values, the results reduced some conditions of the previous theorems, and improved the related results.

    Value distribution of q-difference polynomials of meromorphic functions
    ZHANG Ke-yu1,2, YI Hong-xun2
    J4. 2013, 48(10):  86-89. 
    Abstract ( 377 )   PDF (567KB) ( 763 )   Save
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    Applying the theory of Nevanlinna, investigate the value distribution of q-difference polynomials of meromorphic functions fn(z)(fm(z)-1)∏di=1 f(qiz)(k) and fn(z)(fm(z)-1)∏di=1qi f(z)(k),  where n,m,k,d are positive integers, and obtained some results which improved some existing results.

    A note on a result due to Yang Le and Schwick
    CHEN Wei1, YUAN Wen-jun2, TIAN Hong-gen1*
    J4. 2013, 48(10):  90-93. 
    Abstract ( 330 )   PDF (581KB) ( 416 )   Save
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    Let F be a family of meromorphic functions defined in a domain D, ψ(z)≠0 be a holomorphic function in D and k be a positive integer. If for each f∈F with f≠0, for each pair of functions f and g in F, f(k)and g(k) share ψ(z) in D, then F is normal in D, which improves a result obtained by Xu Yan in 2010.

    Interval valued (∈,∈∨ q)fuzzy subalgebras of Boolean algebras
    LIU Chun-hui1,2
    J4. 2013, 48(10):  94-98. 
    Abstract ( 348 )   PDF (596KB) ( 405 )   Save
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    The concept of interval valued (∈,∈∨ q)fuzzy subalgebras is introduced in Boolean algebras and some equivalent characterizations of this concept are given. The properties of homomorphism image and direct product of interval valued (∈,∈∨ q)fuzzy subalgebras in Boolean algebras are discussed. It is proved that the surjective homomorphism image and direct product of interval valued (∈,∈∨ q)fuzzy subalgebras are also interval valued (∈,∈∨ q)fuzzy subalgebras of Boolean algebras, respectively.

    Fuzzy ideals in Quantic lattices
    ZHOU Xin, ZHAO Bin*
    J4. 2013, 48(10):  99-104. 
    Abstract ( 326 )   PDF (605KB) ( 719 )   Save
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    The concepts of fuzzy subquantic lattices, fuzzy ideals and prime fuzzy ideals of a quantic lattice are given. Then  the relationships between fuzzy ideals and fuzzy subquantic lattices are discussed and   the characterizations of fuzzy ideals and prime fuzzy ideals are studied.  It is proved that  every ideal of a quantic lattice can be regarded as a cutset of a fuzzy ideal.

    Block Pulse functions method for solving nonlinear Volterra-Fredholm-Hammerstein integral equations
    CHEN Yi-ming, XIE Jia-quan, YUAN Run-hao, HAO Xiao-guang
    J4. 2013, 48(10):  105-110. 
    Abstract ( 547 )   PDF (590KB) ( 991 )   Save
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    In order to obtain a numerical solution for nonlinear Volterra-Fredholm-Hammerstein integral equation,the nonlinear Volterra-Fredholm-Hammerstein integral equations are transformed into a nonlinear system of algebraic equations by using BPFs as basis functionand combined with its orthogonally properties,and numerical solution of the original equation are obtained after discreting type of unknown variables. The numerical results show that the method is feasible and effective.