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    20 October 2015
    Volume 50 Issue 10
    P-augmented matrix and dynamic intelligent discovery-identification of information
    SHI Kai-quan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  1-12.  doi:10.6040/j.issn.1671-9352.7.2015.001
    Abstract ( 409 )   PDF (706KB) ( 429 )   Save
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    By improving ordinary augmented matrix and crossing the concept of ordinary augmented matrix and the dynamic structure of P-sets, P-augmented matrix is proposed,and its structure is also given. P-augmented matrix consists of internal P-augmented matrix and outer P-augmented matrix. Then the attribute theorems of internal P-augmented matrix, outer P-augmented matrix and P-augmented matrix are obtained. The reduction relationships between P-augmented matrix and ordinary augmented matrix are given. By improving P-inference, P-augmented matrix inference is proposed, and its inference structure is given. P-augmented matrix inference consists of internal P-augmented matrix inference and outer P-augmented matrix inference. Then P-augmented conjunctive normal form of attribute is proposed, and the relationships between P-augmented conjunctive normal form of attribute and ordinary conjunctive normal form of attribute are given. The reduction theorems of P-augmented conjunctive normal form of attribute and dynamic intelligent discovery-identification of information that satisfy the antecedent of P-augmented matrix inference are proposed. Finally, an application is shown.
    Surplus-deficiency of cardinal number and inverse P-augmented matrices
    REN Xue-fang, ZHANG Ling, SHI Kai-quan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  13-18.  doi:10.6040/j.issn.1671-9352.7.2015.002
    Abstract ( 491 )   PDF (957KB) ( 357 )   Save
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    By using the dynamic characteristics of inverse P-sets and improving ordinary augmented matrix, internal inverse P-augmented matrix, outer inverse P-augmented matrix and inverse P-augmented matrix are put forward;their structures,generations and relations are given. By crossing the surplus-deficiency of cardinal number with inverse P-augmented matrix, the relationship theorem between surplus value of cardinal number and internal inverse P-augmented matrix, the relationship theorem between deficient value of cardinal number and outer inverse P-augmented matrix, and the relationship theorem between surplus-deficient value of cardinal number and inverse P-augmented matrix are proposed. Finally, an application of these results above is shown.
    The attribute functions of P-sets and attribute conjunctive character-application of P-information fusion
    ZHANG Jing-xiao, XU Feng-sheng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  19-26.  doi:10.6040/j.issn.1671-9352.0.2014.377
    Abstract ( 463 )   PDF (575KB) ( 296 )   Save
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    By using the structure of P-sets, the concepts of element attribute and attribute function in P-sets are defined. The relationship between P-sets and attribute function, the counting problems of injection attribute function and the counting problems of surjection attribute function are discussed. Then the attribute conjunctive expansion-reduction characteristics of P-information fusion, the theorems of attribute conjunctive expansion of internal P-information fusion, the theorems of attribute conjunctive reduction of outer P-information fusion, the discovery theorems of internal P-information fusion possessed attribute conjunctive expansion, and discovery theorems of outer P-information fusion possessed attribute conjunctive reduction are given. Finally, the application instance of generation-discovery of internal P-information fusion possessed attribute conjunctive expansion is provided.
    On the number of contractible edges of longest cycles in k-connected graphs
    WANG Shan-shan, QI En-feng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  27-31.  doi:10.6040/j.issn.1671-9352.0.2015.072
    Abstract ( 381 )   PDF (539KB) ( 335 )   Save
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    The number of contractible edges of longest cycles in k-connected graphs is given. The conclusions are that if every fragment of a k-connected graph has an order at least 「k/2+1,then there exist at least three contractible edges on the longest cycle of this graph. Furthermore, if this graph has a hamiltonian cycle, then there exist at least six contractible edges on the hamiltonian cycle.
    Quantitative approach for linear temporal logic based on DTMC
    SHI Hui-xian, LI Yong-ming
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  32-39.  doi:10.6040/j.issn.1671-9352.0.2014.401
    Abstract ( 410 )   PDF (1022KB) ( 520 )   Save
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    The present paper aims to construct a quantitative approach for linear temporal logic by means of DTMC, a stochastic Kripke structure efficiently used in model checking. Based on a certain kind of probabilistic measure under the frame of DTMC, we compare the set of infinite initial paths satisfying some LTL formula φ with the set of all infinite initial paths, and consider their ratio to be the satisfaction degree of φ with respect to the DTMC D, as defined in this paper. It is pointed out that this satisfaction degree quantitatively extends the notion of Dφ, the classical case in model checking. Furthermore, the concept of similarity degree between LTL formulas is presented, and a corresponding pseudo-metric on the set of all LTL formulas is induced, which enables the LTL logic metric space to be constructed.
    Note on integral group rings of holomorphs of finite metacyclic 2-groups
    LI Zheng-xing, YANG Shu-xian
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  40-42.  doi:10.6040/j.issn.1671-9352.0.2014.374
    Abstract ( 369 )   PDF (504KB) ( 703 )   Save
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    Let G be a finite metacyclic 2-group and let HolG be its holomorph. It is proved that the equality NU(ZHolG)(G)=G·Z(ZHolG) holds in the integral group ring ZHolG.
    Several results on derivations of formal triangular matrix rings
    HUANG Shu-liang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  43-46.  doi:10.6040/j.issn.1671-9352.0.2014.395
    Abstract ( 407 )   PDF (518KB) ( 316 )   Save
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    Let A,B be commutative rings with identity, M a nonzero (A,B)-bimodule and D be a derivation of formal triangular matrix ring
    Tri(A,M,B)={(a0 mb)|aA, mM, bB}.
    If D(Xm)=(D(X))n or D((XY)n)=D(Xn)D(Yn) for all X,Y∈Tri(A,M,B),where m,n≥1 are fixed integers, then D=0.
    Constructions of bent-negabent Boolean functions
    ZHUO Ze-peng, CHONG Jin-feng, WEI Shi-min
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  47-51.  doi:10.6040/j.issn.1671-9352.0.2014.409
    Abstract ( 388 )   PDF (992KB) ( 268 )   Save
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    A new method to construct negabent function was provided. Based on it, a construction of bent-negabent function was obtained. And then, the special Boolean function by concatenation was investigated. A necessary conditions for this Boolean function to be a negabent function was presented. Finally, the direct sum construction of bent-negabent function is given.
    Ore extensions of G-cograded multiplier Hopf algebras
    LU Dao-wei, ZHANG Xiao-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  52-58.  doi:10.6040/j.issn.1671-9352.0.2014.457
    Abstract ( 429 )   PDF (561KB) ( 334 )   Save
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    The Ore extensions of G-cograded multiplier Hopf algebras are constructed, and some sufficient and necessary conditons for the Ore extensons to be G-cograded multiplier Hopf algebras are given. As an application, an example will be given at the end.
    Generalized Hom-Smash products over monoidal Hom-bialgebras
    ZHAO Xiao-fan, ZHANG Xiao-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  59-63.  doi:10.6040/j.issn.1671-9352.0.2014.426
    Abstract ( 411 )   PDF (552KB) ( 265 )   Save
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    The generalized Hom-smash products over monoidal Hom-bialgebras are investigated, and a generalized Hom-smash product is proved to be a left Radford's Hom-biproduct-Hom-comodule algebra.
    On pseudo-umbilical timelike submanifold in a de Sitter space
    LI Ying, SONG Wei-dong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  64-67.  doi:10.6040/j.issn.1671-9352.0.2014.391
    Abstract ( 416 )   PDF (518KB) ( 334 )   Save
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    Based on the moving frames, the pseudo-umbilical timelike submanifold in a de Sitter space was studied. Also, an integral inequality about the squared norm of the second fundamental form for the submanifold and some rigidity theorems are obtained.
    Gorenstein weak flat modules
    RAO Yan-ping, YANG Gang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  68-75.  doi:10.6040/j.issn.1671-9352.0.2014.449
    Abstract ( 462 )   PDF (1497KB) ( 470 )   Save
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    Gorenstein weak flat modules are introduced and some properties of such modules are given. It is proved that the class of Gorenstein weak flat modules is closed under direct products, and that the class of Gorenstein weak flat modules is projectively resolving if and only if it is closed under extensions. Moreover, it is proved that every module has a Gorenstein weak flat precover.
    Dual module Jordan derivations and dual module generalized derivations of triangular Banach algebra
    LI Jun, ZHANG Jian-hua, CHEN Lin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  76-80.  doi:10.6040/j.issn.1671-9352.0.2015.148
    Abstract ( 533 )   PDF (528KB) ( 310 )   Save
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    Let A and B be unital Banach algebras, and let M be a Banach A, B-bimodule. Then T=(A MB) becomes a triangular Banach algebra when equipped with the usual matrix operation and a Banach space norm ‖(a mb)‖=‖a‖A+‖m‖M+‖b‖B. T*=(A* M*B*) is the dual space of T by the action (f hg)(a mb)=f(a)+h(m)+g(b). T* becomes a dual Banach T- bimodule with the module action defined by am (a mb)·(f hg)=(a·f+m·h b·hb·g), (f hg)·(a mb)=(f·a h·ah·m+g·b). The map from T into T* is called dual module map. We investigate the dual module Jordan derivations and dual module generalized derivations on T, giving a condition under which a dual module Jordan derivation is a dual module derivation and a characterization of dual module generalized derivation.
    Existence of positive periodic solutions for second order singular coupled systems
    WU Cheng-ming
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  81-88.  doi:10.6040/j.issn.1671-9352.0.2014.578
    Abstract ( 403 )   PDF (560KB) ( 335 )   Save
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    Using Schauder's fixed point theorem, we study the existence of positive periodic solutions for second order non-autonomous singular coupled systems
                                                                 
    where ai, eiL1(R/TZ, R), fi∈Car(R/TZ×(0,∞), R), that is, fi|[0,T]:[0,T]×(0,∞)→R are L1-Carathéodory functions(i=1, 2), and f1, f2 may be singular at y=0, x=0, respectively. The existence of positive periodic solutions for the singular coupled systems are obtained under the conditions that the signs of integral disturbance terms are positive, or negative, or different.
    Analytical solutions for the multi-term time-space Caputo-Riesz fractional diffusion equations in 2-D and 3-D
    WANG Xue-bin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(10):  89-94.  doi:10.6040/j.issn.1671-9352.0.2014.371
    Abstract ( 475 )   PDF (551KB) ( 311 )   Save
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    In this paper, the multi-term time-space Caputo-Riesz fractional Diffusion equations (MT-TSCR-FDE) in 2-D and 3-D with Dirichlet nonhomogeneous boundary conditions are considered. By using a spectral representation we propose some new technique that enable the derivation of the analytical solutions for the MT-TSCR-FDE.