Table of Content

  

20 August 2015
Volume 50 Issue 08

Study on cities' logistics industry co-competition relation in Blue and Yellow Zones based on SNA

MENG Qing-chun, LI Hui-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  1-9.  doi:10.6040/j.issn.1671-9352.0.2014.575

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Based on the development of cities' logistics industry in Blue and Yellow Zones, quantitative study on the cities' logistics industry co-competition relation in these zones is given by SNA. Firstly, the cities in Blue and Yellow Zones are classified into three levels. Secondly, the cities' logistics industry co-competition relation model of the Blue and Yellow Zones is built by methods of grey relation degree and location quotient. Lastly, the density, centrality degree, central potential and betweenness of the cities' logistics industry co-competition relation in the Blue and Yellow Zones are analyzed by using SNA and then some useful conclusions and suggestions are given.

Strong edge coloring of a class of planar graphs

MENG Xian-qing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  10-13.  doi:10.6040/j.issn.1671-9352.0.2015.165

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A strong edge coloring of a graph G is an assignment of colors to the edges of the graph such that any two edges at distance at most 2 receive distinct colors. It is known that every planar graph has a strong edge-coloring with at most 4Δ+4 colors. It is proved that planar graph G has a strong edge-coloring with at most 3Δ+1 colors if G has no k-cycles with 4≤k≤10 and no intersecting 3-cycles (that is, every vertex is incident with at most one cycle of length 3).

Potential influence of maximum interactive number on non-homogeneous T-S fuzzy system

SUO Chun-feng, WANG Gui-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  14-19.  doi:10.6040/j.issn.1671-9352.0.2014.540

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Maximum interactive number is to describe the degree of density of the antecedent fuzzy sets. It is very important to the approximation problem of all kinds of fuzzy systems. Firstly, the non-homogeneous T-S fuzzy system is established by introducing piecewise linear function (PLF) and minimum inference engine again. Secondly, the effects of the maximum interactive number to this fuzzy system are explained based on the geometric intuitiveness, and the actual output value of the system can be calculated by changing maximum interactive number and randomly selecting sample points. The results show that the internal structure and values of the non-homogeneous T-S fuzzy system have potential influence to the maximum interactive number when the subdivision number is not changed.

Additive maps on standard operator algebras preserving divisors

MENG Jiao, JI Guo-xing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  20-23.  doi:10.6040/j.issn.1671-9352.0.2014.284

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Let A and B be standard operator algebras on complex Banach spaces X and Y, respectively. A characterization of additive surjection Φ: A →B which preserves left(right) divisors in both directions or preserves divisors in both directions is given.

Multidimensional backward doubly stochastic differential equations with generators of Osgood type

WANG Xian-fei, JIANG Long, MA Jiao-jiao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  24-33.  doi:10.6040/j.issn.1671-9352.0.2015.038

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A class of multidimensional backward doubly stochastic differential equations whose generator f satisfies the Osgood condition in y and generator g satisfies non-Lipschitz condition in y was studied. An existence and uniqueness theorem and a stability theorem of solutions for this kind of equations were established, and a comparison theorem for solution of the class of one-dimensional situation was proposed.

Local multigrid method for higher-order finite element discretizations of elasticity problems in two dimensions

LIU Chun-mei, ZHONG Liu-qiang, SHU Shi, XIAO Ying-xiong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  34-39.  doi:10.6040/j.issn.1671-9352.0.2015.055

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Due to few limited vertexes increase during every refinement of adaptive finite element method (AFEM), only some limited basis functions change between two finite element spaces based on two adjacent refinement meshes. By use of this special property, a type of multigrid method based on the local relaxation is applied to the high-order AFEM discrete systems of elasticity problems in two dimensions, that is, during each iteration, the part of the homogeneous high-order systems based on hierarchical basis functions is solved by a symmetric Gauss-Seidal method once, and then these residual systems are projected onto linear finite element space, and discrete systems based on linear finite element spaces are generated. Finally, these linear finite element discretizations are solved by a symmetric local Gauss-Seidal method once. The numerical experiments show that the local multigrid method is robust.

Soft filters of pseudo-BL algebras related to fuzzy set theory

PENG Jia-yin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  40-45.  doi:10.6040/j.issn.1671-9352.0.2015.051

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The notions of ∈-soft set and q-soft set based on a fuzzy set are introduced, and characterizations for an ∈-soft set and a q-soft set to be soft (implicative) filters of a pseudo-BL algebra are given. Using the notion of (∈,∈∨q)-fuzzy (implicative) filters of pseudo-BL algebras, characterizations for an ∈-soft set to be soft (implicative) filters are established.

Performance analysis of Geom/G/1 queue with multiple vacations and set-up/close down period based on simulation experiment

CHEN Li, YANG Rui, MA Zhan-you

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  46-50.  doi:10.6040/j.issn.1671-9352.0.2014.383

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A Geom/G/1 queue with multiple vacations and set-up/close down period was studied by using the simulation experiment method, and the change trend of the mean queue length and the waiting time of customer with parameters were calculated. The simulation results were compared with the theoretical analysis results, and the change trends which were obtained by using two methods were consistent. Therefore, this method was effective.

On conditions for transfer function to preserve solution configuration of semiring-induced valuation algebras

XU Ge-ni, LI Yong-ming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  51-56.  doi:10.6040/j.issn.1671-9352.0.2014.372

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The map preserving solution configuration of valuation algebra induced by a semiring is studied. The transfer function f preserves solution configuration is obtained if f is an order-reflecting semiring homomorphism. In addition, if the transfer function f is monotonous, then there exists a solution configuration x₀of the new valuation such that x₀ is also a solution configuration of the primal valuation when the set of solution configuration of the two valuations are not empty.

Soft quotient Boolean algebra of Boolean algebra

LIU Wei-feng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  57-61.  doi:10.6040/j.issn.1671-9352.0.2014.394

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The concepts of soft congruence relation, soft quotient algebra and soft quotient Boolean algebra of Boolean algebra are defined, and it is proved that soft congruence relation and soft ideal of Boolean algebra can be determined by each other. Then soft quotient Boolean algebra of Boolean algebra is obtained from soft proper ideal of Boolean algebra. Finally, the nature of preserving soft congruence relation of soft homomorphism of Boolean algebras is proved.

Choquet integral of set-valued functions with respect to multisubmeasures

GONG Zeng-tai, WEI Zhao-qi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  62-71.  doi:10.6040/j.issn.1671-9352.0.2014.340

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It is inevitable for the problem how to deal with two aspects of selections for a set-valued function and a multisubmeasure according to the classical definition method of the set-valued integral. The Choquet integral of a set-valued function with respect to a multisubmeasure is defined and discussed by using the real-valued Choquet integral of the set-valued function with respect to the non-additive measure, and some basic properties are characterized. It shows that a lot of characters could be well kept to their primitives such as the weakly null-additive, null-additive, converse null-additive, the pseudometric property and the Darboux property, and so on.

Existence of solutions for singular φ-Laplacian of periodic boundary value problems

XU Man

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  72-77.  doi:10.6040/j.issn.1671-9352.0.2014.485

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We consider the existence of solutions for singular φ-Laplacian of periodic boundary value problems
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where φ:(-a,a)→R(0< a <+∞) is an increasing homeomorphism such that φ(0)=0, g∈ C(R,R), e∈C[0,T], and s is a parameter. The proof of the main result is based on the continuation theorem and Leray-Schauder degree arguments.

High accuracy analysis of the lowest order new mixed finite element scheme for generalized nerve conductive equations

FAN Ming-zhi, WANG Fen-ling, SHI Dong-yang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  78-89.  doi:10.6040/j.issn.1671-9352.0.2014.410

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A lowest order new mixed element approximate scheme with the bilinear element and Nédélec?s element for the generalized nerve conductive equations is proposed, which can satisfy Brezzi-Babuška condition automatically. Based on high accuracy analysis of the mixed element and interpolation post-processing technique, the superclose properties and superconvergence results of original variable in H¹-norm and intermediate variable in L²-norm are deduced separately for semi-discrete scheme. At the same time, a second order fully-discrete scheme when is f(u) equal to f(X) is established and the superclose properties and the optimal order error estimates of original variable in H¹-norm and intermediate variable in L²-norm are separately derived.

Surplus-deficient theorem of cardinal number and data internal-outer mining-separation

ZHANG Ling, REN Xue-fang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2015, 50(08):  90-94.  doi:10.6040/j.issn.1671-9352.0.2014.576

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By intercrossing data mining and the concept of cardinal number, and adopting the structure of inverse P-set, the concept of dynamic cardinal number is proposed, and the surplus-deficient theorem and the discrete interval theorem of cardinal number are given, and then the relationship between data mining and the change of cardinal number, the surplus-deficient rule of attribute cardinal number for data mining and applications are also given.