Table of Content

  

20 December 2018
Volume 53 Issue 12

Good congruences associated with multiplicative quasi-adequate transversals

KONG Xiang-jun, WANG Pei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  1-3.  doi:10.6040/j.issn.1671-9352.0.2018.305

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The good congruences on abundant semigroups with multiplicative quasi-adequate transversals are characterized.

Abelian extensions of Hom-Jordan Lie algebras

LI Qiang, MA Li-li, WANG Xiao-yan, LYU Li-jiao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  4-8.  doi:10.6040/j.issn.1671-9352.0.2018.059

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Using representations of Hom-Jordan Lie algebras T, the sufficient and necessary conditions of constructing Hom-Jordan Lie algebra T⊕V are obtained. The equivalent abelian extensions of Hom-Jordan Lie algebras giving the same representation is proved. A 2-cocycle by a section of the abelian extension is obtained.

Topological properties analysis of logical metric spaces on the residuated lattice

DUAN Jing-yao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  9-16.  doi:10.6040/j.issn.1671-9352.0.2017.645

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Firstly, the relation between logical metric space(［0,1］, ρ_R)and metric space (F(X),H_R) is analysized. Secondly, convergence of the Cauchy-sequences are investigate. Finally, the uniform topology is constructed on the general residuated lattice. The work provides a new way to study the structure of residuated lattice, and lay a solid theoretical foundation for the robustness analysis of logical inference systems.

Linear arboricity of graphs embedded in a surface of non-negative Euler characteristic

CHEN Hong-ling, WANG Hui-juan, GAO Hong-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  17-22.  doi:10.6040/j.issn.1671-9352.0.2017.539

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The linear arboricity of graph G, denoted by la(G), is the minimum number of linear forest required to partition the edge set E(G), which is an improper edge coloring. The linear arboricity of graph which can be embedded in a surface of non-negative Euler characteristic with maximum Δ(G)≥7 is mainly studied. If there is no adjacent chordal 6-cycle, then the arboricity of graph G is「Δ/2.

Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  23-30.  doi:10.6040/j.issn.1671-9352.0.2018.605

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Let G be a simple graph. An E-total coloring f of G is called that if there are no two adjacent vertices of G receive the same color, and no edges of G receives the same color as one of its endpoints. For an E-total coloring f of G, if C(u)≠C(v) for any two distinct vertices u and v of V(G), where C(x) denotes the set of colors of vertex x and of the edges incident with x under f, then f is called a vertex-distinguishing E-total coloring of G. Let χ^e_vt(G)=min{k|G has a k-VDET coloring}. Then χ^e_vt(G) is called the VDET chromatic number of G. By using analytical method and proof by contradiction, the VDET coloring of complete bipartite graph K10,n is discussed and the VDET chromatic number of K10,n(10≤n≤90) has been obtained.

Planar graphs without 4-cycle or chordal-6-cycle are(3,0,0)-colorable

LIU Jia, SUN Lei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  31-40.  doi:10.6040/j.issn.1671-9352.0.2017.642

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Let d1,d2,…,d_k be k non-negative intergers. A graph G is(d1,d2,…,d_k)-colorable, if the vertex set of G can be partitioned into subsets V1,V2,…,V_k such that the graph G［V_i］ induced by V_i has maximum degree at most d_i for i=1,2,…,k. There is a conclusion about the coloring of planar graphs: planar graphs without 4-cycle or chordal-6-cycle are(3,0,0)-colorable.

Vertex distinguishing edge coloring of a hexagonal system

ZHANG You, HUANG Li-na, LI Mu-chun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  41-47.  doi:10.6040/j.issn.1671-9352.0.2017.139

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Let H_(m,n) be a hexagonal system for the length of n and the width of m adjacent hexagons which the shape likes a parallelogram. The vertex distinguishing edge chromatic number of H₍1,n) satisfies vertex distinguishing edge coloring conjecture by designing the coloring algorithm. An upper bound of the vertex distinguishable edge chromatic numbers of H_(m,n) for m≥2 is given.

Existence of traveling wave solutions for hantavirus transmission model

MA Xia, YAO Mei-ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  48-52.  doi:10.6040/j.issn.1671-9352.0.2018.227

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In this paper, we consider a diffusion-reaction model for the spread of hantavirus. The existence of traveling wave solutions is obtained by Schauders fixed point theorem and the minimal wave speed is given. The nonexistence of traveling wave solutions is obtained by introducing a negative one-sided Laplace transform.

Coexistence solution of a predator-prey system with B-D functional response and toxin effects

FENG Xiao-zhou, XU Min, WANG Guo-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  53-61.  doi:10.6040/j.issn.1671-9352.0.2018.262

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The steady state of a predator-prey system with B-D reaction term and toxin effect under the homogeneous Dirichlet boundary condition is investigated. First, using the principle of maximum value and the comparison principle of eigenvalues, we give some prior estimates of coexistence solution on the system and obtain the necessary condition of non-coexistence solution. Secondly, by using the Leray-Schauder degree theory, the calculation of the fixed point index, the maximum principle and the method of upper and lower solutions, the sufficient condition for the existence of the coexistence solution is established. Finally, the local asymptotic stability of the trivial solution and the semi-trivial solution of the steady state system is proved by using the linearization operator and the Riesz-Schauder theory.

Properties of modified stochastic gradient operators in continuous-time Guichardet-Fock space

ZHOU Yu-lan, LI Zhuan, LI Xiao-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  62-68.  doi:10.6040/j.issn.1671-9352.0.2018.179

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The paper investigate the properties of the modified stochastic gradient operator and modified point-state stochastic gradient operators {_s;s∈R₊} in continuous-time Guichardet-Fock space L2(Γ;η). We show that the modified stochastic gradient operator is a unbounded, densely defined linear operator in L2(Γ;η); the family of modified point-state stochastic gradient operators {_s;s∈R₊} and its adjoint {^*_s;s∈R₊} are bounded linear operator, which have many properties. For example, they satisfies the canonical anti-commutation relations(CAR)and nilpotency; _s^*_s=^*_ss, for ∠s≠t, which means that, the family of operators{_s;s∈R₊} and {^*_s;s∈R₊} are commutive for ∠s≠t; the operator {^*_ss;s∈R₊} is a family of orthogonal projections on L2(Γ;η). Meanwhile, we construct a unitary operator group on L2(Γ;η) with the point-state modified stochastic gradient {_s;s∈R₊} and its adjoint {^*_s;s∈R₊}.

Consistency of estimator of nonparametric regression function for arrays of rowwise NSD

LI Yong-ming, NIE Cai-ling, LIU Chao, GUO Jian-hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  69-74.  doi:10.6040/j.issn.1671-9352.0.2018.076

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With the random error of arrays of rowwise NSD, the estimation of the unknown regression function in the nonparametric regression model is considered. Under certain conditions, the strong consistency of the weighted estimator of the unknown regression function is obtained.

Covariance of self-exciting filtered Poisson process

CHEN Hao-jun, ZHENG Ying, MA Ming, BIAN Li-na, LIU Hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  75-79.  doi:10.6040/j.issn.1671-9352.0.2017.633

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The expression of the covariance on the self-exciting filtered Poisson process is obtained by using the relationship between the characteristic function and the covariance and the properties of the multiple integral.

Calibrating option pricing models with cross entropy bat algorithm

LI Guo-cheng, WANG Ji-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  80-89.  doi:10.6040/j.issn.1671-9352.0.2018.057

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Parameter estimation of option pricing model is usually a nonlinear optimization problem with no convex, which leads to the classical optimization method cannot be applied. Based on cross entropy bat algorithm, we studied how to solve parameter estimation problems of option pricing models such as Mertons jump-diffusion model, Hestons stochastic volatility model and Batess stochastic volatility with jump model. The empirical results show that the cross entropy bat algorithm is feasible and effective for solving the parameter estimation problems of option pricing model.

A neural network for solving l₁-norm problems with constraints

LI Cui-ping, GAO Xing-bao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  90-98.  doi:10.6040/j.issn.1671-9352.0.2017.627

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This paper presents a one-layer neural network model for solving l₁-norm problems with constraints. Compared with some existing neural network models, the proposed model needs fewer neurons and has a simpler structure. The stability and convergence of the proposed model are proved by introducing a Lyapunov function. Some simulation examples are used to illustrate its validity and transient behaviors.

Some properties of measure frames

LI Chun-fang, MENG Bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  99-104.  doi:10.6040/j.issn.1671-9352.0.2017.505

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Measure frames is a generalization of vector frames in Hilbert spaces, but there are essential differences between them. Some inequalities and equalities are obtained for measure frames from the perspective of frame operator theory. At the same time, we also discuss the shift of a measure frame to a tight measure frame and the approximately dual frames and pseudo-dual frames.

Bidirectional controlled teleportation with a genuine five-qubit non-maximally entangled state as quantum channel

PENG Jia-yin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  105-113.  doi:10.6040/j.issn.1671-9352.0.2017.143

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By using projective measurement and positive operator-valued measurement, two bidirectional controlled teleportation schemes via a genuine five-qubit non-maximally entangled state are proposed, respectively. In our scheme, such a five-qubit non-maximally state is employed as the quantum channel linking three legitimate participants. And with certain probability, Alice many transmit an arbitrary unknown single-qubit state of qubit A to Bob and Bob many transmit an arbitrary single-qubit state of qubit B to Alice via the control of the supervisor Charlie. Our protocols are the generalization of deterministic bidirectional controlled teleportation.

Flocking under hierarchical leadership with white noise

WU Chen, JIN Ying-hua, WANG Shi-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  114-119.  doi:10.6040/j.issn.1671-9352.0.2017.504

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The flocking under hierarchical leadership with white noise was mainly studied. First we proposed a model with white noise under the hierarchical leadership, and then use the properties of Itô formula, mathematical induction and mathematical expectation function to prove that when the noise intensity satisfies certain conditions and the time tends to infinity, the hierarchical group can reach the flocking. Finally, an example of state diagram and error graph after cluster is affected by noise is given by numerical simulation. The experimental results demonstrate the correctness of the conclusions.

Algorithms of rule acquisition and confidence-preserved attribute reduction in covering decision systems

ZHANG Xiao, YANG Yan-yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2018, 53(12):  120-126.  doi:10.6040/j.issn.1671-9352.0.2017.400

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The data collected in practice is of diversity. How to obtain useful knowledge from the complex data is the objective of data mining. Since covering rough sets can deal with complex data, there exists much study on the attribute reduction and rule acquisition of covering decision systems based on covering rough sets. The existing research on the rule acquisition of covering decision systems considered the confidence measure as the only evaluation criterion. However, the extracted high-confidence rules may cover fewer instances and then be potentially spurious. Therefore, a measure that can assess the coverage ability of rules is introduced, which can eliminate the chance in data and thus acquire high-confidence rules with more generalization ability. Furthermore, in order to extract compact rules, we propose a rule confidence-preserved attribute reduction heuristic algorithm.