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    20 June 2014
    Volume 49 Issue 06
    Outer-disturbances and attributes conjunctive shrink#br# law mining and separating
    WU Song-li1,2, CHEN Gui-you3*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  1-5.  doi:10.6040/j.issn.1671-9352.0.2013.615
    Abstract ( 381 )   PDF (700KB) ( 391 )   Save
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    Using function P-sets model,  its dynamic characters and law feature, the law disturbance concept, recovery of disturbances and disturbance scale are presented. Using these concepts, the outer-disturbances and attributes conjunctive shink theorem, attributes conjunctive shrink and outer-disturbances law mining-separating theorem, outer-disturbances and law mining-identification theorem and outer-disturbances and law mining attributes constancy theorem are proposed.
    Granulation degree of P-sets and discernibility-discovery of P-knowledge
    LIU Ji-qin, ZHANG Tong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  6-10.  doi:10.6040/j.issn.1671-9352.0.2014.058
    Abstract ( 428 )   PDF (569KB) ( 360 )   Save
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    By using P-sets, the concept and properties of granulation degree in P-sets is presented. The relation theorems between the granulation degree and packet degree, the decomposition theorems and the monotonicity theorem of the granulation degree are proposed. P-knowledge and its discernibility degree are defined. P-sets and the properties of the granulation degree are applied to discernibility-discovery of P-knowledge, and the discernibility-discovery theorems of P-knowledge are obtained. Finally, the discernibility-discovery theorems are applied to system state detectionrecognition, and the criterion of system state detection-recognition and its application are given.
    Attribute inner fusion and data fusion mining#br#
    QIU Yu-feng, TANG Ji-hua*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  11-17.  doi:10.6040/j.issn.1671-9352.0.2014.136
    Abstract ( 342 )   PDF (594KB) ( 319 )   Save
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    Attribute fusion is an important applied characteristic hidden in packet sets, whose dynamic features come from its attribute fusion. By using internal packet sets structure and their dynamic features, the concept and structure of attribute inner fusion are proposed, and attribute inner fusion theorem is given. Then data fusion mining under the condition of attribute inner fusion is put forward. Moreover, the application of mining criterion with miningscreening of data fusion is shown.
    Irregular assignments of the union of several vertex-disjoint #br# paths with order n
    GUO Jing1, CHEN Xiang-en1, WANG Zhi-wen2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  18-25.  doi:10.6040/j.issn.1671-9352.0.2013.493
    Abstract ( 498 )   PDF (2268KB) ( 305 )   Save
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    The m-weighting w of G is a mapping from E(G) to {1,2,…,m}. The image w(e) of each edge e of G is called the weight of e. An mweighting of G is called an m-irregular assignment if, for any two distinct vertices u and v, the sum of the weights of the edges incident with u is different from the sum of the weights of the edges incident with v. The minimum integer m such that G has an mirregular assignment is called the irregularity strength of G. Based on the conception, it is investigated the irregularity strengths of the vertex-disjoint union of t paths with order n(n≡2(mod 4) and n≡3 (mod 4)).
    The linear 2-arboricity of planar graphs without 5-, 6-cycles with chord
    CHEN Hong-yu1, ZHANG Li2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  26-30.  doi:10.6040/j.issn.1671-9352.0.2013.077
    Abstract ( 392 )   PDF (575KB) ( 334 )   Save
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    Let G be a planar graph without 5-,6-cycles with chord. It is proved that if G is connected and  δ(G)≥2, than G contains an edge xy with d(x)+d(y)≤9 or a 2alternating cycle. By this result, we obtain that G-s linear 2-arboricity la2(G)≤Δ(G)2+6.
    Vertex-distinguishing edge coloring of the generalized lexicographic product of some graphs#br#
    TIAN Shuang-liang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  31-34.  doi:10.6040/j.issn.1671-9352.0.2013.649
    Abstract ( 365 )   PDF (613KB) ( 333 )   Save
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    For the generalized lexicographic product G[hn] of a graph G and a sequence of vertex disjoint graphs hn=(Hi)i∈{0,1,…,n-1}, if HiH for i=0,1,…,n-1, then G[hn]=G[H], where G[H] is the lexicographic product of two graphs. The minimum number of colors required for a vertexdistinguishing edge coloring of G is called the vertexdistinguishing edge chromatic number of G and denoted by  χ′vd(G). For any graph G with  χ′vd (G)=Δ(G), two upper bounds on the parameter χ′vd (G[hn]) are provided in this paper and those are proved to be attainable precisely, where every Hi is a simply graph of order m. It is also proved that if χ′vd(G)=Δ(G), χ′vd(H)=Δ(H) and Δ(G[H])=Δ(H[G]), then χ′vd (G[H])=χ′vd (H[G]), where G and H are simply graphs of order n and m, respectively.
    WGP-injectivity of rings#br#
    LU Qi1, BAO Hong-wei1, LIANG Liang2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  35-39.  doi:10.6040/j.issn.1671-9352.0.2013.474
    Abstract ( 409 )   PDF (576KB) ( 483 )   Save
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    Some equivalent definitions of WGP-injective rings are introduced. And the properties of WGP-injective rings are studied. It is proved that if R is a left nonsingular left WGP-injective ring, and the ascending chain l(a1)l(a1a2)l(a1a2a3)… terminates for every infinite sequence a1,a2,a3…, then R is semisimple.
    Some properties of skew polynomial rings#br#
    WANG Yao1, JIANG Mei-mei1, REN Yan-li2*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  40-45.  doi:10.6040/j.issn.1671-9352.0.2014.153
    Abstract ( 436 )   PDF (607KB) ( 316 )   Save
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    Some properties of skew polynomial rings are studied. It is proved that (1) If R is an αArmendariz ring, then J(R[x;α])∩R is nil; (2) If R is an αArmendariz ring, then R is an α-Baer ring if and only if R[x;α-is an -Baer ring; (3) If R is an α-Armendariz ring and satisfies Cα condition, then R is an α-quasi-Baer ring (resp., right α-p.q.-Baer ring, right zip ring) if and only if R[x;α] is an -quasi-Baer ring (resp.,  a right -p.q.-Baer ring, a right zip ring).
    A note on class-preserving automorphisms#br#
    GUO Ji-dong1, HAI Jin-ke2*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  46-49.  doi:10.6040/j.issn.1671-9352.0.2013.593
    Abstract ( 338 )   PDF (564KB) ( 350 )   Save
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    Let G be a semidirect product of a cyclic group C and a 2-group P of maximal class. If a Sylow 2-subgroup of G has an abelian subgroup of index 2. It is shown that every class-preserving automorphism of G is an inner automorphism. In particular, the normalizer property holds for G.
    On f derivations and g derivations of MV-algebras
    FENG Min1, XIN Xiao-long1*, LI Yi-jun1,2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  50-56.  doi:10.6040/j.issn.1671-9352.0.2014.006
    Abstract ( 446 )   PDF (596KB) ( 435 )   Save
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    Using the endomorphism of MV-algebra,  the notions of f derivations and g derivations of MV-algebras are introduced, which extend (⊙,)-derivations and (,⊙)derivations, respectively. And some related properties are investigated. Moreover, the set Fd(M)g of all fixed points for a g derivation d is proved to be an ideal of M and the set Fd(M)f of all fixed points for an isotone f derivation d is proved to be an ideal of M. Furthermore, characterizations of Boolean algebras and linear Boolean algebras are derived by properties of g derivations. Finally, the relationships between f derivations and g derivations are discussed.
    Structures of DISO fuzzy system induced by a class of#br# regular implication operators
    LI Yu, WANG Gui-jun*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  57-63.  doi:10.6040/j.issn.1671-9352.0.2013.608
    Abstract ( 297 )   PDF (989KB) ( 265 )   Save
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    A fuzzy system is the mapping relationship obtaining the input and output of the response by measuring the data or digital sensors, although it does not depend on the precise mathematical model, with the ability of logical reasoning, numerical calculation and approximation to the nonlinear function.However, the structure and approximation of the double-input and single-output (DISO) fuzzy system is the key to the further study on multiple input single (multiple) output fuzzy system. In this paper, we will popularize the conventional fuzzy inference machine to a class of regular implication operators, and constructed three kinds of DISO fuzzy systems based on the implication operators, parameter singleton fuzzifier and center of gravity defuzzifier, and then the analytical expressions of the input and output of the fuzzy system are derived.
    The univalency of nonlinear transformations of close-to-convex functions
    WANG Li-mei
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  64-66.  doi:10.6040/j.issn.1671-9352.0.2013.528
    Abstract ( 398 )   PDF (583KB) ( 348 )   Save
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    The sharp pre-schwarzian norm of nonlinear transformation Jc[f]=∫z0(f′(ξ))cdξ is given, where f is a close-to-convex function and c is an arbitrary constant. By using of Becker’s univalence criteria, the condition on which Jc[f ]-maps a close-to-convex function to a univalent function is also obtained.

    Note on the Schrdinger uncertainty relation#br#
    LI Hao-jing, CHEN Zheng-li*, LIANG Li-li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  67-73.  doi:10.6040/j.issn.1671-9352.0.2014.028
    Abstract ( 449 )   PDF (594KB) ( 291 )   Save
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    The two parameter extensions of the Wigner-Yanase-Dyson skew information about the bounded linear operators are introduced. Some properties of this generalization of the Wigner-Yanase-Dyson skew information are discussed. Particularly, the generalization of the Schr-dinger uncertainty relation and the proof are obtained.
    Study of a malaria model with population dynamic in two patches
    DONG Chan, ZHANG Ju-ping, LI You-wen
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  74-78.  doi:10.6040/j.issn.1671-9352.0.2014.026
    Abstract ( 443 )   PDF (830KB) ( 438 )   Save
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    A malaria model with population dynamic in two patches is established, which the hosts can migrate between patches, but not the vectors. The model is irreducible cooperative and strongly monotone.   The basic reproduction number R0 is computed. If R0≤1, then the disease-free equilibrium is globally asymptotically stable. When R0>1, there exists a unique endemic equilibrium, which is globally asymptotically stable.
    Finite time blowup of multi-dimensional Kaniadakis-Quarati equation#br#
    LIN Chun-jin1, XU Guo-jing2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  79-84.  doi:10.6040/j.issn.1671-9352.0.2013.633
    Abstract ( 424 )   PDF (580KB) ( 321 )   Save
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    The Kaniadakis-Quarati equation is used to describe the behavior of bosons. In this paper some weighted norms of solutions for the Kaniadakis-Quarati equation are studied. These weighted norms will converge to zero in finite time if the mass of the initial distribution is big enough. This phenomena is called Bose-Einstein condensation in physics.
    Single-species model with impulsive birth and contraception control#br#
    LI Qiu-ying, ZHANG Feng-qin, WANG Wen-juan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  85-90.  doi:10.6040/j.issn.1671-9352.0.2013.496
    Abstract ( 335 )   PDF (583KB) ( 276 )   Save
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    In this paper, we propose contraception control single species models with impulsive Birth. Using the stroboscopic map, we obtain the sufficient condition for periodic solution. Using comparison principle, the sufficient condition for globally asymptotically stable of zero solution is obtained. Lastly, the sufficient condition for persistence of system is obtained.
    Geometric inequalities for spacelike submanifolds of a #br# semi-Riemannian space form
    ZHANG Pan, ZHANG Liang, SONG Wei-dong
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(06):  91-94.  doi:10.6040/j.issn.1671-9352.0.2014.094
    Abstract ( 362 )   PDF (562KB) ( 503 )   Save
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    Inequalities relating δ(2) for spacelike submanifolds of a semi-Riemannian space form is obtained by using an algebraic technique. Also, inequalities between the Ricci curvature and the squared mean curvature are established.