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    20 April 2014
    Volume 49 Issue 04
    P-information law intelligent fusion and soft information #br# image intelligent generation
    SHI Kai-quan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  1-17.  doi:10.6040/j.issn.1671-9352.9.2014.001
    Abstract ( 552 )   PDF (1455KB) ( 610 )   Save
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    Function P-sets is the function form of P-sets, which has the dynamic and law characteristics. Function P-sets is a dynamic law model. Function P-sets is a set pair composed of function internal P-set S and function outer P-set SF, or (S, SF) is function P-sets. P-information law reasoning is obtained by introducing function concept into P-reasoning and improving it. P-information law reasoning is a dynamic information law reasoning, which is presented by using P-sets. P-information law reasoning is composed of internal P-information law reasoning and outer P-information law reasoning. By using the intersection and osmosis of function P-sets and P-information law reasoning, the studies about P-information law intelligent fusion and soft information image intelligent generation are given, which are P-information law reasoning structure, P-information law intelligent fusion and its P-information law reasoning generation, intelligent fusion redundance-deletion and attribute internal-outer fusion characteristic, P-information law intelligent fusion and its expansion-contraction theorem of attribute conjunction normal form, the intelligent P-separation and reduction of P-information law intelligent fusion, split-synthesis of information law and soft information image intelligent generation. Function P-sets is a novel method and theory studying information law fusion.
    Edge colorings of 1-planar graphs for maximum degree eight #br# without adjacent 4-cycles
    ZHANG Jia-li, MIAO Lian-ying, SONG Wen-yao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  18-23.  doi:10.6040/j.issn.1671-9352.0.2013.138
    Abstract ( 425 )   PDF (542KB) ( 301 )   Save
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    It is proved that every 1-planar graph of maximum degree 9 without adjacent 4-cycles can be 9-edge-colorable by the discharging method.
    A(d,1)-total labeling of Cartesian products of some classes of graphs#br#
    ZHOU Wei-na, ZUO Lian-cui*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  24-28.  doi:10.6040/j.issn.1671-9352.0.2013.426
    Abstract ( 593 )   PDF (596KB) ( 422 )   Save
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    (d,1)-total labelings of the Cartesian products of wheel Wn and path Pm, Wn and fan Fm, and Wn and Wm are studied, and the exact values λTd (Wn-Pm), λTd (Wn-Fm) and λTd (Wn-Wm) are obtained.
    On the edge-magic total labellings of spliced trees#br#
    WANG Hong-yu, YAO Bing*, YANG Chao
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  29-37.  doi:10.6040/j.issn.1671-9352.0.2013.024
    Abstract ( 538 )   PDF (1402KB) ( 314 )   Save
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    It has been known that graphs can be used as models in researching scale-free networks, such as hierarchialnetworks and self-similar networks and so on. We study theedge-magic total labellings on splitting and recombining trees. We can adjoin a pair of non-adjacent vertices of a tree having set-ordered graceful labellings to obtain a new graph,  then delete another edge on a cycle of the new graph to form a tree having edge-magic total labellings. And we split a tree M intopieces, and then assemble them on another tree T with |T|<|M| to result a new graph G. After a series of the reducing cycle operations on G, we obtain a tree that admits edge-magic total labellings.
    An upper bound on the linear 2-arboricity of planar graph
    XU Chang-qing1, AN Li-sha1, DU Ya-tao2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  38-40.  doi:10.6040/j.issn.1671-9352.0.2013.287
    Abstract ( 419 )   PDF (523KB) ( 459 )   Save
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    Let G be a planar graph with maximum degree Δ.  The linear 2-arboricity of G is the least integer k such that G can be partitioned into k edge disjoint forests, whose component trees are paths of length at most 2. It is denoted by la2(G). We get that la2(G)≤「Δ/2-+8 if Δ≡0,3(mod 4) and la2(G)≤「Δ/2-+7 if Δ≡1,2(mod 4).
    Independent numbers of graphs and fractional uniform graphs#br#
    CAI Jian-sheng1, GE Lian-sheng2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  41-43.  doi:10.6040/j.issn.1671-9352.0.2014.016
    Abstract ( 383 )   PDF (513KB) ( 241 )   Save
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    Let G be a graph with vertex set V(G), minimum degree  δ(G) and independent number α(G). Let k≥2 be an integer. A spanning subgraph F of G is called a fractional k-factor if dhG(x)=k for every x∈V(F). A graph G is called a fractional k-uniform graph if for each edge of G, there is a fractional k-factor containing it and another one excluding it. In this paper, we prove that if δ(G)≥k+2 and α(G)≤4k(δ-k-1)(k+1)2, then G is a fractional k-uniform graph.
    Acyclic edge coloring of triangle-free toroidal graphs
    CHEN Guang1, HOU Jian-feng2*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  44-49.  doi:10.6040/j.issn.1671-9352.0.2013.417
    Abstract ( 453 )   PDF (562KB) ( 260 )   Save
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    A proper edge coloring of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a′(G), is the least number of colors in an acyclic edge coloring of G. It is proved that if a trianglefree toroidal graph G has maximum degree Δ(G), then a′(G)≤Δ(G)+3.
    Remarks on n-strongly Gorenstein FP-injective modules
    CHEN Wen-jing, LIU Zhong-kui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  50-54.  doi:10.6040/j.issn.1671-9352.0.2013.562
    Abstract ( 448 )   PDF (606KB) ( 309 )   Save
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    N-strongly Gorenstein FP-injective modules are investigated, that M is a n-strongly Gorenstein FP-injective module if and only if N-M is a n-strongly Gorenstein FP-injective module for any projective module N over left coherent rings which are right IF rings is proved, and that M is a n-strongly Gorenstein FP-module if and only if M is a nstrongly Gorenstein flat module over left and right IF rings is proved.
    Engel’s theorem for generalized H-Lie algebras#br#
    GUO Shuang-jian1, DONG Li-hong2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  55-57.  doi:10.6040/j.issn.1671-9352.0.2013.273
    Abstract ( 345 )   PDF (558KB) ( 258 )   Save
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    It is studied that the representation of the Lie algebras in the Yetter-Drinfel’d category HH YD(i.e. generalized H-Lie algebras). The Engel’s theorem for generalized H-Lie algebras is proved: Let L be a generalized H-Lie algebra, if every cyclic Yetter-Drinfel’d submodule of L is ad-nilpotent, then L is nilpotent.
    Strongly n-Gorenstein projective objects in triangulated categories#br#
    REN Lan-lan, YANG Xiao-yan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  58-65.  doi:10.6040/j.issn.1671-9352.0.2013.413
    Abstract ( 446 )   PDF (2038KB) ( 411 )   Save
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    The strongly n-ξ-Gorenstein projective objects in triangulated categories are introduced, strongly n-ξ-Gorenstein-projective objects are closed under finite direct sums is proved and a simple description of an object with ξ-Gorenstein projective dimension at most n is given.
    Infinite relative determinacy of smooth map-germs
    SHI Chang-mei1, 2, PEI Dong-he1*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  66-69.  doi:10.6040/j.issn.1671-9352.0.2013.064
    Abstract ( 480 )   PDF (530KB) ( 344 )   Save
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    The infinite determinacy of smooth map-germs relative to a subgroup of contact group will be investigated. It defines the infinite relative determination for smooth map-germs, then the necessary and sufficient conditions for a smooth map-germ to be infinitely relative determined are given.
    Infinitely connectivity of the wandering domain of#br# Baker’s original example
    ZHANG Guo-wei 1, CHEN Ang2
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  70-73.  doi:10.6040/j.issn.1671-9352.0.2012.535
    Abstract ( 404 )   PDF (524KB) ( 362 )   Save
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    Using the method of Bergweiler and Zheng, the detailed proof of the infinitely connectivity of the multiply connected wandering domain of Baker’s original example is given.
    Boundedness of linear operators on the anisotropic #br# weighted Herz-type Hardy spaces
    ZHOU Shu-juan, LIU Su-ying
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  74-78.  doi:10.6040/j.issn.1671-9352.0.2013.628
    Abstract ( 382 )   PDF (547KB) ( 251 )   Save
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    Applying the atomic decomposition of the anisotropic weighted Herz-type Hardy spaces, the boundedness of some linear operators on the anisotropic weighted Herz-type Hardy spaces are studied, and the interpolation theorem is obtained on those spaces.
    Shock solution for a quasilinear singularly perturbed problem#br#
    YANG Xue-jie, SUN Guo-zheng*, CHEN Wen
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  79-83.  doi:10.6040/j.issn.1671-9352.0.2013.653
    Abstract ( 373 )   PDF (532KB) ( 279 )   Save
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    A singularly perturbed differential equation boundary value problem with interior layer phenomenon is studied. The zero order approximate solution of this problem is constructed using the method of composite expansions and analytical skills. According to the fixed point theorem, the existence of solution is proved and the error estimate of asymptotic solution is given.
    A schematic extension of IMTL-logic algebras#br#
    ZHOU Jian-ren1,2, WU Hong-bo2*
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  84-89.  doi:10.6040/j.issn.1671-9352.0.2013.291
    Abstract ( 7072 )   PDF (630KB) ( 267 )   Save
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    IMTL and its related logic algebras are investigated in depth again and some new useful results are obtained. Firstly, the IMTL*-algebras are introduced by strengthening the conditions of IMTL-algebra, and the existence of IMTL*-algebras is explained by establishing structures of IMTL*-algebra. Secondly, an algebra structure is established that is IMTL-algebra and not IMTL*-algebra, which explains that IMTL*-algebras are truely strengthened form of IMTL-algebras, and  based on IMTL-algebras some equivalent characterization of IMTL*-algebras are given. At last, the pure implication representation of IMTL*-algebras is obtained. The results of this paper are necessary complementarity to the methods and contents of logic algebras.
    (σ,τ)-expansion model of P-sets and its properties#br#
    YU Xiu-qing
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2014, 49(04):  90-94.  doi:10.6040/j.issn.1671-9352.0.2013.610
    Abstract ( 387 )   PDF (548KB) ( 315 )   Save
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    P-sets(packet sets) is a set pair composed of internal P-set Xand outer P-set XF, while the (σ,τ)-generation of assistant sets of P-sets is also a set pair composed of σ-generation of internal assistant set Aσ(X) and τ-generation of outer assistant set Aτ(XF). Based on the above knowledge, (σ,τ)-expansion model of P-sets is proposed. The relationship theorem between P-sets and its (σ,τ)-expansion is presented. A series of propoties about the (σ,τ)expansion of  P-sets are discussed. (σ,τ)-expansion model of P-sets expands the research field of P-sets.