Table of Content

  

20 August 2016
Volume 51 Issue 8

Jensens inequality, moment inequality and law of large numbers for weighted g-expectation

JIANG Long, CHEN Min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  1-9.  doi:10.6040/j.issn.1671-9352.0.2016.312

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We propose the notion of weighted g-expectation ε^λ_g ［·］ based on g-expectation. We prove that if the generator g is non-increasing with respect to y and positive-homogeneous with respect to (y,z), the moment inequality for weighted g-expectation holds in general. When λ≥1/2 and the generator g is independent of y, we establish Jensens inequality for weighted g-expectation when g is super-homogeneous with respect to z, and we establish the law of large numbers for weighted g-expectation when g is sublinear with respect to z.

Characterization of Lie centralizers on B(X)

FU Li-na, ZHANG Jian-hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  10-14.  doi:10.6040/j.issn.1671-9352.0.2015.266

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Let X be a Banach space over the real or complex number field F with dim X>1 and φ:B(X)→B(X) be an additive map. We prove that if there are positive integers m,n such that (m+n)φ(［A,B］)=m［φ(A),B］+n［A,φ(B)］ holds for all A,B∈B(X), then there exist λ∈F and an additive map h:B(X)→F vanishing on commutators such that φ(A)=λA+h(A)I for all A∈B(X).

Weyls theorem for the cube of operator and compact perturbations

DONG Jiong, CAO Xiao-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  15-21.  doi:10.6040/j.issn.1671-9352.0.2015.530

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An operator T∈B(H) is said to satisfy Weyls theorem if σ(T)\σw(T)=π00(T). T∈B(H) is said to have the compact perturbations of Weyls theorem if T+K satisfies Weyls theorem for all compact operators K∈B(H). In this note, a variant of the Weyl spectrum is discussed. Using the variant, we characterize the conditions for T ³ and T satisfying the compact perturbations of Weyls theorem.

Inequalities of Hermite-Hadamard and Sandaor for fuzzy integral

LU Wei, SONG Xiao-qiu, HUANG Lei-lei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  22-28.  doi:10.6040/j.issn.1671-9352.0.2015.634

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On the basis of the definitions of r-convex function and Orlicz-convex function, Sandors type inequality for fuzzy integrals upon r-convex function is proved. Hermite-Hadamard type inequality for fuzzy integrals based on Orlicz-convex function is investigated. Some examples are given to illustrate our theorems.

The contractible edges of a spanning tree and a perfect matching in k-connected graphs

WANG Qian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  29-34.  doi:10.6040/j.issn.1671-9352.0.2016.148

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The numbers of contractible edges of a spanning tree and a perfect matching in k-connected graphs are given. The conclusions are that if every fragment of a k-connected graph has an order more than 「k/2, then there exist at least four contractible edges on the spanning tree of this graph. Furthermore, if this graph has a perfect matching, then there exist at least 「k/2+1 contractible edges on the perfect matching.

Pomonoids over which all strongly flat left S-posets are I-regular

WEN Hai-cun, QIAO Hu-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  35-38.  doi:10.6040/j.issn.1671-9352.0.2015.351

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Let S be a pomonoid. All strongly flat left S-posets are I-regular if and only if S is a left PSF and left semiperfect pomonoid are presented. It is also equivalent with S is a left PP pomonoid, and satisfying property(FP₂). Furthermore, pomonoids over which every I-regular left S-poset satisfying Condition(P)are characterized.

Global dimensions of cocycle deformations

YU Xiao-lan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  39-43.  doi:10.6040/j.issn.1671-9352.0.2015.428

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Let H be a commutative Hopf algebra with global dimension d. It is proved that the global dimension of any cocycle deformation of H is at most d. That is, cocycle deformations of commutative Hopf algebras preserve the boundedness of global dimensions.

On relative homological dimensions

XU Ai-min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  44-48.  doi:10.6040/j.issn.1671-9352.0.2016.216

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It is shown that pdC(X)=pdC(Y) and fdD(X)=fdD(Y), where X and C are two classes of left R-modules, D a class of right R-modules and Y={M|M is X-filtered}. As an application, the(weak)Gorenstein global dimensions of special rings are computed.

Unipotent congruences on a proper weakly left type B semigroup

LI Chun-hua, XU Bao-gen, HUANG Hua-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  49-52.  doi:10.6040/j.issn.1671-9352.0.2015.248

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The notion of a weakly left type B semigroup is introduced. A characterization of a unipotent congruence on a proper weakly left type B semigroup is given, and some results are obtained. Finally, a sufficient and necessary condition for a weakly left type B semigroup to be proper is given by using the notion of a structure mapping.

On derivations of monadic MV-algebras

LIU Hui-zhen, XIN Xiao-long, WANG Jun-tao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  53-60.  doi:10.6040/j.issn.1671-9352.0.2015.610

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We define the notion of M-derivations on monadic MV-algebras(M,∃)and discuss some properties of it. Based on it, the notions of the strong M-derivations and regular M-derivations are introduced. By use of strong M-derivations, we give some equivalent conditions in which a MV-algebra becomes a boolean algebra. Next, some characterizations about the isotone M-derivations in monadic MV-algebras are provided by regular M-derivations. Moreover, the notion of the fixed set of a derivation in monadic MV-algebras is introduced and discussed. The notion of additive derivations of monadic MV-algebras are given and some of its properties are investigated. Also, we prove that an additive derivation of linearly ordered monadic MV-algebras is isotone. Finally, monadic differential ideals of monadic MV-algebras are studied. In particular, algebraic structures of the set ID(M)of all monadic differential ideals on regular monadic MV-algebras are researched.

On successive-overrelaxation acceleration of MHSS iterations

WANG Yang, ZHAO Yan-jun, FENG Yi-fu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  61-65.  doi:10.6040/j.issn.1671-9352.0.2015.402

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Modified Hermitian and skew-Hermitian splitting(MHSS)iteration method is an unconditionally convergent method for solving large sparse complex symmetric linear systems. Based on successive-overrelaxation technique, a class of accelerated MHSS iterative method is presented, then convergence theorems is established for the new method. Moreover, a selection method of the parameter ω is given. Numerical experiment demonstrate that new method can effectively improve the efficiency of MHSS iterative method for solving linear algebraic equations.

Existence of solution for fractional differential equation integral boundary value problem at resonance

SU Xiao-feng, JIA Mei, LI Meng-meng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  66-73.  doi:10.6040/j.issn.1671-9352.0.2015.352

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Existence of solutions for a class of fractional differential equations with integral boundary conditions is studied at resonance. By using coincidence degree theory, we obtain and prove the theorem about existence of solutions for the integral boundary value problem with dim Ker L=2.

Bifurcation structures for the 2-D Lengyel-Epstein system

LI Yue-xia, ZHANG Li-na, ZHANG Xiao-jie

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  74-78.  doi:10.6040/j.issn.1671-9352.0.2015.450

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The bifurcation problem is considered for the Lengyel-Epstein model by the local bifurcation method in R². Local bifurcation branches of stationary solutions are constructed, and the directions of the branches near the bifurcation points are obtained.

Third-order periodic boundary value problems with sign-changing Greens function

CHEN Bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  79-83.  doi:10.6040/j.issn.1671-9352.0.2015.476

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We study the existence of positive solutions of nonlinear periodic boundary value problemsu(t)+a(t)u(t)=λb(t)f(u(t)), a.e t∈［0,2π］,u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π), i=0,1,2where a≺0, b≺0 and the Greens function of the linear problemu(t)+a(t)u(t)=0, a.e t∈［0,2π］,u⁽ⁱ⁾(0)=u⁽ⁱ⁾(2π), i=0,1,2may change sign on ［0,2π］×［0,2π］.

The two grids population migration model based on birth-death process

LIU Hua, XIE Mei, JIANG Rui, WEI Yu-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  84-89.  doi:10.6040/j.issn.1671-9352.0.2015.575

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We built the birth and death process model of migration between two populations patches. We get the limit expectation of population in two patches by comparing with the single population model which has not include migration effect, and thus we get the sufficient condition of persistence and extinction of population in single patch. The results show that the immigration of individuals from the neighbor patch not only reduces the risk of population extinction when the number of population in single patch decreased, but also benefit to the population survived. The emigration of individuals to the neighbor patch increased the risk of the population extinction in this patch and go against population survival when the number of population in single patch increased.

Intelligent switch-camouflage of information laws and P-law augmented matrices

ZHANG Ling, REN Xue-fang, SHI Kai-quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  90-97.  doi:10.6040/j.issn.1671-9352.0.2015.425

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By using the dynamic structures of function P-sets to improve the concept of ordinary augmented matrix, the matrices such that law matrix, internal P-law augmented matrix, outer P-law augmented matrix and P-law augmented matrix are proposed, and their structure and generations, their attribute relationships are also given. Then the reasoning of P-law augmented matrices and the reasoning structures are proposed. Furthermore, using the reasoning of P-law augmented matrices, law intelligent separations and intelligent separation theorems are given. Finally, the intelligent separation algorithm of information laws is given, and its application in intelligent switch-camouflage of information images is shown.

Adaptive divide and conquer algorithm for cost-sensitive attribute reduction

HUANG Wei-ting, ZHAO Hong, ZHU William

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  98-104.  doi:10.6040/j.issn.1671-9352.0.2015.435

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Cost-sensitive attribute reduction problem is the natural extension of classical attribute reduction, and it is more practical than the classical one by introducing cost. Based on divide and conquer thought, this paper proposes a new algorithm to deal with cost-sensitive attribute reduction. Firstly, the dataset is splitted into disjoint sub-datasets according to the number of the column. Then some sub-datasets are merged after backtracking reduction on each sub-dataset. Finally, it continues reducting and merging, and gets minimal test cost reduction. The size of the sub-datasets and the number of the sub-datasets are adaptive to the scale of the dataset rather than fixed. This algorithm is tested on four UCI datasets to verify its effectiveness. Compared with other algorithms, the experimental results show that the proposed algorithm can provide the efficient solution in a relatively short time.

Relationships between dynamic data mining and P-augmented matrix

GUO Hua-long, REN Xue-fang, ZHANG Ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(8):  105-110.  doi:10.6040/j.issn.1671-9352.0.2016.200

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P-augmented matrix is proposed by adopting the structures and dynamic characteristics of packet sets to improve ordinary augmented matrix A^*. P-augmented matrix consists of internal P-augmented matrix A^(-overF) and outer P-augmented matrix A^F, denoted by(A^(-overF),A^F). Under some certain conditions, P-augmented matrix can be reduced into ordinary augmented matrix A^*. By using the structures and dynamic characteristics of P-augmented matrix, the research of dynamic data mining is carried out. Several relationships, theorems and criterion are obtained as follows: the relationships between dynamic data mining and P-augmented matrix; the internal P-augmented matrix decision theorem, the outer P-augmented matrix decision theorem and the P-augmented matrix decision theorem for data dynamic mining; the P-augmented matrix criterion for dynamic data mining. Finally, these results are verified by an application.