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    20 February 2019
    Volume 54 Issue 2
    Big data structure-logic characteristics and big data law
    SHI Kai-quan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  1-29.  doi:10.6040/j.issn.1671-9352.0.2018.698
    Abstract ( 379 )   PDF (1304KB) ( 154 )   Save
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    P-sets, inverse P-sets are two models obtained by introducing dynamic features into a finite ordinary set X and improving the set X. By using P-sets, inverse P-sets and their dynamic and logical features, ∧-type big data structure and its generation with attribute conjunction extension-contraction feature, ∨-type big data structure and its generation with attribute disjunctive extension-contraction feature, and∧-∨type big data structure and its generation of the mixture of ∧-type big data and ∨-type big data are given respectively. The fusion and its generation of big data and the intelligent mining theorems of big data fusion are given. Granulation characteristics and granulation filtration theorems of big data are given. The heredity and its generation of big data, and heredity intelligence separation and separation theorem of big data are given. Big data hiding-camouflage and intelligent generation under the inference condition of P-augmented matrix, and big data hiding-camouflage theorems are given. The model and method of big data law generation, and the state of big data law are given. By using the state of big data law, the risk estimation of investment-profit big data is given.
    Multi-scale theory in formal concept analysis
    LI Jin-hai, WU Wei-zhi, DENG Shuo
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  30-40.  doi:10.6040/j.issn.1671-9352.9.2018.002
    Abstract ( 460 )   PDF (791KB) ( 165 )   Save
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    By using forward and backward scaling approaches, the transformation relationship between information systems and formal contexts was clarified, and the notion of a multi-scale formal context was formally defined. It was verified that multi-scale formal contexts and multi-scale information systems could semantically be equivalent to each other. As for a multi-scale formal context, implication rules obtained from different scales were induced by each other. The obtained results could provide a theoretical reference for the further research of multi-scale approaches in formal concept analysis.
    Research on collaborative filtering algorithm based on rough set
    ZHENG Li-ping, HU Min-jie, YANG Hong-he, LIN Yao-jin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  41-50.  doi:10.6040/j.issn.1671-9352.0.2018.037
    Abstract ( 337 )   PDF (1293KB) ( 95 )   Save
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    In collaborative filtering, the recommendation performance is limited by the data sparsity of rating matrix. To alleviate this problem, a rough set based collaborative filtering method is proposed, which is helpful to reduce the influence of the data sparsity to some extent. First, the procedure of data pre-processing is executed. As the eigenvalue for user classification, users ratings with the rating number are employed. Then, an attribute reduction approach of rough set is introduced to eliminate the item which has little effect with respect to user classification, and a smaller scale user-item rating matrix is generated to lower the data sparsity. Finally, the similarity between users is calculated based on the reducing attributes to obtain real neighbors of active users. The experimental results demonstrate that the proposed algorithm in MAE, COVERAGE, PRECISION and RECALL are significantly better than the ones of COS, PCC, ADCOS, NHSM.
    RL-fuzzy topology and the related fuzzy compactness
    LI Hong-yan, LI Qing-hua
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  51-56.  doi:10.6040/j.issn.1671-9352.0.2018.372
    Abstract ( 338 )   PDF (390KB) ( 115 )   Save
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    The concept of pseudo-complement on an L-subset A is defined and studied, where L is a completely distributive De Morgan algebra. Based on this new concept, the definition of RL-fuzzy topology on A is introduced. The L-fuzzy topology in sense of Kubiak and Šostak and the RL-topology on A are special cases of this kind of topology. The RL-fuzzy compactness of RL-fuzzy topological spaces is further studied. The union of two RL-fuzzy compact sets is RL-fuzzy compact. The intersection of an RL-fuzzy compact set and an RL-fuzzy closed set is RL-fuzzy compact. The RL-fuzzy compactness is an invariant under RL-fuzzy continuous maps.
    Expand fuzzy filters in Heyting algebras
    LIU Chun-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  57-65.  doi:10.6040/j.issn.1671-9352.0.2018.228
    Abstract ( 307 )   Save
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    The theory of fuzzy filters is studied in Heyting algebras by using the methods and principles of algebra and fuzzy sets. The notions of expand fuzzy filter and invariant fuzzy filter of a fuzzy filter f associated to a fuzzy subset μ in a Heyting algebra(H,≤,→)are introduced. Some properties of expand and invariant fuzzy filters are obtained. The relation between expand fuzzy filters and generated fuzzy filters is built, and the application of expand fuzzy filters in study of lattice structures is given by using this relation. We proved that three subsets of the set FFil(H)of containing all fuzzy filters in a Heyting algebra(H,≤,→), under fuzzy set-inclusion order, are form complete Heyting algebras.
    Simple-root bases for the deformations of extended Shi arrangements
    GAO Rui-mei, GAO Jia-ying, CHU Ying
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  66-70.  doi:10.6040/j.issn.1671-9352.0.2018.127
    Abstract ( 245 )   PDF (350KB) ( 143 )   Save
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    The cone of an extended Shi arrangement is used S k to denote. The existence of the simple-root bases of the derivation modules for S k and the freeness of B +Γ and B -Γ are proved. They are formed by adding and deleting some reflection hyperplanes of S k, which are corresponding to simple roots. B +Γ and B -Γ are called the deformations of extended Shi arrangements. According to Saitos criterion, the explicit constructions of the bases of the derivation modules are given for B +Γ and B -Γ, and the exponents of them are calculated.
    Existence of positive solutions for fractional differential system with coupled integral boundary conditions
    QI Ting-ting, ZHANG Zhen-fu, LIU Yan-sheng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  71-78.  doi:10.6040/j.issn.1671-9352.0.2017.464
    Abstract ( 376 )   PDF (386KB) ( 270 )   Save
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    By defining appropriate Banach space and norm, giving the appropriate operators, using fixed-point theorem on cone and fractional calculus, the existence of positive solutions for fractional differential system with coupled integral boundary conditions is investigagted. An example is given to illustrate the application of the main result.
    Linear maps on triangular algebras for which the space of all inner derivations is Lie invariant
    FEI Xiu-hai, ZHANG Jian-hua
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  79-83.  doi:10.6040/j.issn.1671-9352.0.2018.017
    Abstract ( 353 )   PDF (329KB) ( 200 )   Save
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    Let U be a triangular algebra with πA(Z(U))=Z(A)and πB(Z(U))=Z(B ), φ be a R-linear mapping from U into itself. If ID(U)is a Lie invariant subspace for φ, then there exists a Lie derivation δ on U and a center element λ such that φ(x)=δ(x)+λx for all x∈U.
    Infinitely many nontrival solutions for a class of Schrödinger equations
    WU Yi-jia, CHENG Rong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  84-88.  doi:10.6040/j.issn.1671-9352.0.2018.155
    Abstract ( 388 )   PDF (379KB) ( 132 )   Save
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    This paper considers the existence of infinitely many nontrival solutions for a class of Schrödinger equation with sign-changing potentials. Under the condition that the nonlinearity has superquadratic growth, the existent result is established, which generalizes the existing results.
    Finitely presented dimensions on recollements of Abelian categories
    FENG Yao-yao, YAO Hai-lou
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  89-94.  doi:10.6040/j.issn.1671-9352.0.2018.145
    Abstract ( 248 )   PDF (415KB) ( 104 )   Save
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    The concepts of finitely presented dimensions in Abelian categories are introduced, and the relations of finitely presented dimensions of objects in a short exact sequence are studied. Let Rab(A,B,C )be a recollement of Abelian categories where A,B and C are abelian categories, it is proved that finitely presented dimension of B is finite if and only if the finitely presented dimensions of A and C are finite under some conditions.
    (J,M)-Quasi Armendariz rings
    HUANG Wen-qiang, WU Jun, CUI Jian
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  95-100.  doi:10.6040/j.issn.1671-9352.0.2018.034
    Abstract ( 266 )   PDF (360KB) ( 120 )   Save
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    The notion of (J,M)-quasi Armendariz ring which relatives to its Jacobson root and a monoid M is introduced. Some basic properties of such rings are studied. And the equivalent characterization of the (J,M)-quasi Armendariz ring are given.
    T.Asai and T.Yoshida problem of group homomorphism
    ZHAO Yan-wei, HAI Jin-ke
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  101-105.  doi:10.6040/j.issn.1671-9352.0.2018.048
    Abstract ( 287 )   PDF (357KB) ( 158 )   Save
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    Let A and G be finite groups, A=A1×A2. Suppose that A1/A'1, A2/A'2 meet certain conditions, where A'1, A'2 are the derived group A1, A2 respectively. The number of homomorphisms from A to G is divisible by the greatest common divisor of |A/A'| and |G| is proved, the conjecture of Asai and Yohsida is true.
    Gröbner-Shirshov basis of degenerate affine Hecke algebras of type A
    Munayim Dilxat, Abdukadir Obul
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  106-110.  doi:10.6040/j.issn.1671-9352.0.2018.363
    Abstract ( 294 )   PDF (339KB) ( 97 )   Save
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    A Gröbner-Shirshov basis of degenerate affine Hecke algebra of type A is given. By using this Gröbner-Shirshov basis and the composition-diamond lemma of associative algebras, a linear basis of the degenerate affine Hecke algebra of type A is constructed.
    Exact solution of GKP equation with variable coefficients
    YANG Fei, LIU Xi-qiang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  111-120.  doi:10.6040/j.issn.1671-9352.0.2017.565
    Abstract ( 353 )   PDF (1128KB) ( 110 )   Save
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    In order to solve a kind of GKP equation with variable coefficients, the form of the solution is first constructed then combined with the new solutions of different auxiliary equations and corresponding Bäcklund transformations. With the help of mathematical calculation software, the new exact solutions of infinite sequence soliton-like of the equation are obtained. The types of these solutions include Jacobi elliptic function type, trigonometric function type, exponential function type, hyperbolic function type, etc. Using the hypothetical solitary wave method, this kind of GKP equation with variable coefficients is studied. Then alternative solitary wave solutions are obtained.
    Related properties of rotation operator in quantum computing
    HAN Qi, YIN Shi-de, CHEN Zhi-he
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(2):  121-126.  doi:10.6040/j.issn.1671-9352.0.2018.299
    Abstract ( 465 )   PDF (372KB) ( 287 )   Save
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