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Table of Content

      
    20 February 2014
    Volume 49 Issue 2
    Articles
    On the maximal π-factorable subnormal pairs
    HAI Jin-ke, WANG Sheng-fang, LI Zheng-xing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  1-3.  doi:10.6040/j.issn.1671-9352.0.2013.250
    Abstract ( 408 )   PDF (629KB) ( 435 )   Save
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    Based on existing results in the literature, the π-factorable subnormal pairs of π-separable groups are further discussed. It is proved that the automorphism group has an action on the set of maximal π-factorable subnormal pairs. As a direct result of the action, maximal π-factorable subnormal pairs are conjugate. In particular, Frattini argument of maximal π-factorable subnormal pairs is obtained.

    Characterization of n-left almost regular monoids by flatness property
    QIAO Hu-sheng, LIU Jian-min
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  4-6.  doi:10.6040/j.issn.1671-9352.0.2012.568
    Abstract ( 402 )   PDF (541KB) ( 1085 )   Save
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    Let n be a positive integer and S a monoid. A generalization of left almost regular monoid is investigated, it is called n-left almost regular monoid. Using new flatness property of S-acts, the characterization of these monoids are given.

    Weak σ-skew quasi Armendariz rings
    DING Ting-ting, WU Jun, ZHANG Pei-yu
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  7-11.  doi:10.6040/j.issn.1671-9352.0.2013.176
    Abstract ( 416 )   PDF (583KB) ( 564 )   Save
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    The notion of weak σ-skew quasi Armendariz ring is introduced.Some basic properties of such rings are studied. We show that a ring R is weak σ-skew quasi Armendariz ring if and only if the ring Tn(R) is weak σ-skew quasi Armendariz ring. This generalizes the corresponding results of σ-skew quasi Armendariz rings.

    Rings with weakly symmetric endomorphisms
    WANG Yao1, QIAN Qing1, REN Yan-li2*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  12-17.  doi:10.6040/j.issn.1671-9352.0.2013.407
    Abstract ( 372 )   PDF (809KB) ( 435 )   Save
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    The notion of weakly symmetric α-rings, which is rings with weakly symmetric endomorphismα, is introduced, and the study of weakly symmetric rings is extended. The relationships between weakly symmetric α-rings and related rings are discussed and some extensions of weakly symmetric α-rings are investigated. It is showed that (1) Let α be an endomorphism of a ring R. Then R is α-rigid if and only if R is weakly symmetric α-ring and aRα(a)∈nil(R) implies a=0 for any a∈R; (2) Let R be a semicommutative ring and α an endomorphism of R. Then R is weakly symmetric α-ring if and only if R[x] is weakly symmetric -ring.

    Acyclic list edge coloring of planar graphs with girth #br# ≥ 11 and maximum degree 3
    MA Gang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  18-23.  doi:10.6040/j.issn.1671-9352.0.2013.103
    Abstract ( 423 )   PDF (600KB) ( 431 )   Save
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    Let G be a planar graph with maximum degree 3. It is proved that the acyclic list edge coloring of G is 3 if its girth is at least 11.

    The Gabriel monad and the localization of R-module category
    LIU Yang1, WANG Zheng-ping2, XU Qing-bing2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  24-28.  doi:10.6040/j.issn.1671-9352.0.2013.173
    Abstract ( 459 )   PDF (1515KB) ( 395 )   Save
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    A Gabriel monad is defined as the idempotent monad to characterize the quotient category and localization of R-module category, and prove that the Gabriel monad induces an equivalence between its image and coimage, its image is the localization category which is equivalent to a Kleisli category; its coimage is the quotient category which is equivalent to a Eilengerg-Moore category.

    On the solutions of the distributive equations of #br# logic operators on a finite chain
    HAN Liang, LIU Hua-wen
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  29-35.  doi:10.6040/j.issn.1671-9352.0.2013.532
    Abstract ( 378 )   PDF (596KB) ( 409 )   Save
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    This paper aims at exploring the following distributivity equation on a finite chain: F(G1(x,y),z)=G2(F(x,z),F(y,z)). We characterize all the solutions of the distributivity equation in the following cases: (a) F is a smooth t-norm and G1=G2 are smooth t-conorms(F is a smooth t-conorm and G1=G2 are smooth tnorms); (b) F is an S-implication (or an Rimplication), G1 is a smooth t-norm and G2 is a smooth t-conorm; (c) F is an S-implication (or an R-implication), G1 is a smooth t-conorm and G2 is a smooth t-norm; (d) F is an S-implication (or an R-implication), G1 and G2 are smooth t-norms; (e) F is an S-implication (or an R-implication), G1 and G2 are smooth t-conorms.

    The prime reverse deductive system of locally finite #br# BL-algebras with properties
    WEN Xian-hong, WU Hong-bo*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  36-41.  doi:10.6040/j.issn.1671-9352.0.2013.294
    Abstract ( 435 )   PDF (581KB) ( 672 )   Save
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    Firstly, the concepts of reverse deductive system and prime reverse deductive system are introduced to BL-algebra. The basic properties of prime reverse deductive system and the relationship between reverse deductive and common ideal in locally finite BL-algebras are investigated. Secondly, the connection between reverse deductive system and congruence relations is discussed. At last, it is proved that the quotient algebra determined by prime reverse deductive system is linear BL-algebra, and that in a locally finite BL-algebra a reverse deductive system is prime reverse deductive system if and only if the quotient algebra determined by itself is a linear BL-algebra.

    Additive maps preserving operator range or kernel inclusion
    LI Rong, JI Guo-xing*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  42-45.  doi:10.6040/j.issn.1671-9352.0.2013.304
    Abstract ( 391 )   PDF (566KB) ( 753 )   Save
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    Let B(X) be the Banach algebra of all bounded linear operators on an infinite dimensional complex Banach space X. We consider additive surjective maps preserving operators range or kernel inclusion in both directions. It is proved that if φ is an additive surjective map on B(X) preserving operators range or kernel inclusion in both directions, then there exist invertible bounded linear or conjugate linear operators U and V on X such that for every T∈B(X), φ(T)=UTV.

    Banach function spaces and weak exponential instability #br# of evolution families
    WANG Shu-li, SONG Xiao-qiu*, YUE Tian
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  46-50.  doi:10.6040/j.issn.1671-9352.0.2013.228
    Abstract ( 399 )   PDF (574KB) ( 412 )   Save
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    The concept of weak exponential instability for evolution families in Banach spaces is presented. Some property of weak exponential expansiveness for evolution families and the necessary and sufficient conditions concerning the weak exponential instability are given in Banach spaces. Variants of Datko result for weak exponential instability of a well-known result from is obtained in the stability theory.

    The algorithms of characteristic polynomial and supersolvability#br#  of a hyperplane arrangement
    GAO Rui-mei1, PEI Dong-he2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  51-57.  doi:10.6040/j.issn.1671-9352.0.2013.416
    Abstract ( 459 )   PDF (584KB) ( 439 )   Save
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    The definitions of coefficient matrix and characteristic matrix for a central arrangement are given. We obtain  the conclusion that the rank of a central arrangement equals to the rank of its coefficient matrix. Calculating characteristic matrix can be changed into calculating the rank of the sub-matrices of the coefficient matrix. The algorithm of characteristic polynomial of a central arrangement is provided. We study some properties of a modular element, and give a equivalent condition of judging a modular element, which simplifies the procedure of looking for a modular element. Based on this result, the algorithm of supersolvability of a central arrangement is offered.

    Soliton solutions for quasilinear Schrdinger equations
    CHEN Zhi-hui, WANG Zhen-zhen, CHENG Yong-kuan*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  58-62.  doi:10.6040/j.issn.1671-9352.0.2013.380
    Abstract ( 429 )   PDF (572KB) ( 780 )   Save
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    We are concerned with the existence result of positive solutions for a quasilinear elliptic equation arising from plasma physics. We convert a quasilinear elliptic equation into a semilinear one and show the existence result for original equation under the suitable conditions on the power of nonlinearity and quasilinearity.

    Fixed points and uniqueness of meromorphic functions#br# of differential polynomials
    SHI Xin-hua
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  63-70.  doi:10.6040/j.issn.1671-9352.0.2013.118
    Abstract ( 320 )   PDF (605KB) ( 753 )   Save
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    Use Nevanlinna′s value distribution theory to study the uniqueness problems of differential polynomials of meromorphic functions concerning fixed points, the results reduced some conditions of the previous theorems, and improvedthe related results.

    Existence of positive solutions for singular fractional #br# differential equations boundary value problems
    SUN Yan-mei
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  71-75.  doi:10.6040/j.issn.1671-9352.1.2012.016
    Abstract ( 429 )   PDF (569KB) ( 753 )   Save
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    The necessary and sufficient conditions for existence of unique solution for Riemann-Liouville fractional differential equations are studied. The results can not only involve the existence and uniqueness of positive solutions for boundary value problems, but also be applied to construct an iterative scheme.

    Synchronization and control of a novel fractional-order chaotic system
    YANG Ye-hong, XIAO Jian*, MA Zhen-zhen
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  76-83.  doi:10.6040/j.issn.1671-9352.0.2013.225
    Abstract ( 409 )   PDF (1457KB) ( 503 )   Save
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    A novel fractional-order chaotic system with three non-linearity quadratic terms was constructed and its basic chaotic dynamical behavior was analyzed. The control of the new chaotic system was realized by Laplace transform. Based on Lyapunov stability theory and fractional-order chaotic system stability theory, the sufficient condition of synchronization of the new fractional-order chaotic system was obtained. Further, adaptive control laws were derived to achieve chaos synchronization of the new chaotic systems with unknown parameters. Numerical simulation demonstrates the correctness of the method.

    Precise large deviations of claim process in a time-dependent #br# compound renewal risk model
    TANG Feng-qin1, BAI Jian-ming2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  84-88.  doi:10.6040/j.issn.1671-9352.0.2013.348
    Abstract ( 478 )   PDF (564KB) ( 755 )   Save
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    The precise large deviations for a compound renewal risk process were considened. The claim sizes related to one accident are heavy-tailed distributed random variables with extend negatively upper orthant dependence (ENUOD) structure. The aggregate amount of claims and the inter-accident times correspondingly obeys a dependence structure.

    Intelligent fusion of internal inverse packet information and #br# expansion relationship of attribute disjunction
    TANG Ji-hua, CHEN Bao-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  89-92.  doi:10.6040/j.issn.1671-9352.0.2013.473
    Abstract ( 392 )   PDF (682KB) ( 454 )   Save
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    Inverse packet sets is a dynamic model composed of internal and outer inverse packet set. Inverse packet reasoning is a dynamic reasoning generated by inverse packet set, and it is composed of internal and outer inverse packet reasoning. Based on internal inverse packet set theory and internal inverse packet reasoning, the intelligent fusion generating of internal inverse packet information and their attribute feature are proposed. The concepts of intelligent fusion degree and coefficient are given. Intelligent fusion circle theorem of outer information and fusion degree-coefficient theorem are put forward. Intelligent fusion of internal inverse packet information and their structure and theorem of attribute disjunction expansion are also shown.

    The fusion of internal packet information and its feature of #br# attribute conjunction
    ZHANG Ling1, TANG Ji-hua1, SHI Kai-quan2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  93-97.  doi:10.6040/j.issn.1671-9352.0.2013.488
    Abstract ( 427 )   PDF (575KB) ( 528 )   Save
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    Packet sets is a set pair composed of internal and outer packet set X and XF, i.e., (X,XF) is a packet sets. It has dynamic characteristics. Based on internal packet set theory, several concepts are proposed, such as the fusion generating, the fusion redundancy generating and the fusion measure of internal packet information. Then the fusion generating theorem, the fusion dependence and fusion reduction theorem of internal packet information are given. The attribute conjunction and their extending theorems of internal packet information fusion are put forward. The principle of discovering internal packet information by attribute conjunction expansion is given. Using those results, application is shown.

    Attribute conjunctive expansion-reduction characteristics and #br# intelligent discovery of P-information
    YAN Li-mei, XU Feng-sheng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  98-103.  doi:10.6040/j.issn.1671-9352.0.2013.486
    Abstract ( 325 )   PDF (629KB) ( 789 )   Save
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    Based on P-sets and P-reasoning, notion of attribute conjunctive expansion-reduction of P-information (packet information), attribute conjunctive expansion-reduction characteristics and theorems of attribute conjunctive expansion-reduction are given. On the basis of internal P-reasoning and attribute conjunctive expansion, theorems of intelligent discovery of internal P-information are given.  According to P-reasoning and attribute conjunctive reduction, theorems of intelligent discovery and criterion of out P-information are given. To illustrate the theoretical result, applications of intelligent discovery of internal P-information possessed attribute conjunctive expansion are provided in information identification.

    Interval soft Boolean algebras
    LIU Wei-feng, DU Ying-xue, XU Hong-wei
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(2):  104-110.  doi:10.6040/j.issn.1671-9352.0.2013.444
    Abstract ( 389 )   PDF (596KB) ( 416 )   Save
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    The interval soft set is applied to the Boolean algebras. The concepts of interval soft Boolean algebras, interval soft Boolean subalgebras,  interval idealistic soft Boolean algebras and interval soft homomorphism between interval soft Boolean algebras are defined and some related properties are discussed. Soft Boolean algebras and related results are generalized.