Table of Content

  

20 December 2016
Volume 51 Issue 12

Quasi-linearly Armendariz modules

ZHANG Dong-qing, YIN Xiao-bin, GAO Han-peng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  1-6.  doi:10.6040/j.issn.1671-9352.0.2015.629

Abstract ( 1099 )   PDF (747KB) ( 460 )   Save

References | Related Articles | Metrics

The quasi-linearly Armendariz modules which are a common generalization of linearly Armendariz modules and quasi-linearly Armendariz rings is introduced. Some basic properties of such modules are studied, some equivalent characteristics of quasi-linearly Armendariz modules are given, and the relationships between quasi-linearly Armendariz modules and the other modules are discussed.

On Gorenstein injective comodules

XU Ai-min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  7-9.  doi:10.6040/j.issn.1671-9352.0.2016.337

Abstract ( 1093 )   PDF (645KB) ( 496 )   Save

References | Related Articles | Metrics

Let C be a right semiperfect coalgebra over a field. It is shown that every right C-comodule has a Gorenstein injective envelope. Moreover, if the projective dimension of C as a right C-comodule is finite, an equivalent characterization of Gorenstein injective right C-comodules is given.

Some properties of GWCN rings

ZHANG Zi-heng, CHU Mao-quan, YIN Xiao-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  10-16.  doi:10.6040/j.issn.1671-9352.0.2016.192

Abstract ( 1177 )   PDF (662KB) ( 589 )   Save

References | Related Articles | Metrics

Some examples of GWCN rings are given. Some extensions of GWCN rings are studied. And the regularity and exchange properties of GWCN rings are discussed.

Semisimplicity of the categories of Hom-Yetter-Drinfeld modules

GUO Shuang-jian, LI Yi-zheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  17-23.  doi:10.6040/j.issn.1671-9352.0.2016.112

Abstract ( 891 )   PDF (668KB) ( 417 )   Save

References | Related Articles | Metrics

Let k be a field, and(H,α)a monoidal Hom-Hopf algebra with bijective antipode. If(H,α)is commutative, noetherian, semisimple and cosemisimple, then the category _HHYD ^H of Hom-Yetter-Drinfeld modules is semisimple. That is Let(H,α)be commutative. Assume that HHYD ^H satisfies some condition, and that the functor(-)^coH:_HHYD ^H→H(M_k)is exact. If (M,μ)∈_HHYD ^H is finitely generated as an(H,α)-module, then (M,μ) is a projective object in HHYD ^H.

Intra-regular semigroups of N(2,2,0)algebra

CHEN Lu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  24-28.  doi:10.6040/j.issn.1671-9352.0.2016.147

Abstract ( 981 )   PDF (646KB) ( 490 )   Save

References | Related Articles | Metrics

Some description about intra-regularity of semigroups of N(2,2,0)algebra is given. Some properties about two special sets P(a), H(a) and left(right)nil element of semigroups of N(2,2,0)algebra are discussed. It is provided that a relationships between left(right)nil element and regular element and intra-regular element.

Existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation

LI Xiao-yan, XU Man

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  29-35.  doi:10.6040/j.issn.1671-9352.0.2016.078

Abstract ( 966 )   PDF (729KB) ( 507 )   Save

References | Related Articles | Metrics

In this paper, we study the existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation{u″(t)+f(t,u(t))=0, t∈(0,1), t≠t_i,Δu|_t=ti=α_iu(t_i), i=1, 2,…,k,u(0)=u(1)=0,where α_i>-1, i=1, 2,…,k are given constants, 0=t0<t1<t2<…<t_k<t_k+1=1 are given impulsive points. Δu|_t=ti=u(t⁺_i)-u(t^-_i), u(t⁺_i), u(t^-_i) denote the right and left limit of u at t=t_i, respectively. f∈C(［0,1］×R, R). The main results extend and improve some results on existence and multiplicity of nontrivial solutions of Dirichlet problems for second-order impulsive differential equation. The proof of the main results are based on the López-Gómezs bifurcation theory established in 2001.

Existence and multiplicity of positive solutions of first order periodic boundary value problems with parameter

ZHU Wen-wen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  36-41.  doi:10.6040/j.issn.1671-9352.0.2015.310

Abstract ( 997 )   PDF (657KB) ( 629 )   Save

References | Related Articles | Metrics

We study the relationship λ between and the number of positive solutions of first order periodic boundary value problems{u'(t)+a(t)u(t)=λf(t,u(t)), t∈［0,T］,u(0)=u(T),where λ is a positive parameter, a∈C(R, ［0,+∞))且∫^T₀a(θ)dθ>0, f∈C(［0,T］×［0,+∞),(0,+∞))and f_∞=lim_u→∞ inf(f(t,u))/u=∞ uniformly for t∈［0,T］. By using the method of the upper and lower solutions and topological degree techniques, we obtain that the problem has no positive solution, exactly one positive solution and at least two positive solutions, when λ>λ^*, λ=λ^*, 0<λ<λ^*, respectively.

Existence of periodic solutions for a class of Hamiltonian systems with p-Laplace

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  42-46.  doi:10.6040/j.issn.1671-9352.0.2015.627

Abstract ( 1200 )   PDF (676KB) ( 491 )   Save

References | Related Articles | Metrics

By introducing a new control function, the existence of periodic solutions for a class of Hamiltonian systems with p-Laplace by using the minimax methods in critical point theory is considered. Some new existence theorems are obtained via saddle point theorem.

Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations

GUO Li-jun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  47-53.  doi:10.6040/j.issn.1671-9352.0.2016.243

Abstract ( 1316 )   PDF (658KB) ( 661 )   Save

References | Related Articles | Metrics

The third order differential equation has a wide application background and an important theoretical value, Green function plays an important role in the existence of positive solutions for the third order three point boundary value problems. This paper is concerned with the following boundary value problem{u(t)+a(t)f(u(t))=0, t∈(0,1),u(0)=u″(0)=0, u'(1)=αu(η),where 0<η<1 and 0<α<1/η. By establishing Green function for the associated linear boundary value problem, the solution for the above boundary value problem is obtained. Then some existence criteria of at least two positive solutions are obtained by using the fixed point index theorem.

Perturbation theorems of inverse P-sets and perturbation-based data mining

REN Xue-fang, ZHANG Ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  54-60.  doi:10.6040/j.issn.1671-9352.0.2016.375

Abstract ( 1294 )   PDF (681KB) ( 631 )   Save

References | Related Articles | Metrics

Inverse P-sets were proposed by introducing dynamic characteristics into finite ordinary element set; inverse P-sets have dynamic characteristics, which characteristics come from element(attribute)transferring. Elements transferred into set make the boundary of the set expanding, while elements transferred from the set makes the boundary of the set contracting. Based on inverse P-sets, this paper proposes F-perturbation degree of internal inverse P-set, (-overF)-perturbation degree of outer inverse P-set and(F,(-overF))-perturbation degree of inverse P-set, and gives their measurements. Then this paper gives F-perturbation theorem, (-overF)-perturbation theorem and (F,(-overF))-perturbation theorem, and shows the relationships anong inverse P-sets, inverse P-sets faminly and finite ordinary element set under perturbations. By using the aforementioned results, F-perturbation based data mining theorem, (-overF)-perturbation based data mining theorem and (F,(-overF))-perturbation based data mining theorem are presented. Finally an application of data mining based on perturbation degree is shown.

P-augmented matrix reasoning and intelligent decomposition mining of information

TANG Ji-hua, CHEN Bao-hui, SHI Kai-quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  61-66.  doi:10.6040/j.issn.1671-9352.0.2016.428

Abstract ( 1165 )   PDF (673KB) ( 433 )   Save

References | Related Articles | Metrics

The intelligent internal decomposition, intelligent external decomposition and intelligent internal-external decomposition of information are put forward by using internal P-augmented matrix reasoning, external P-augmented matrix reasoning and P-augmented matrix reasoning. Their attribute relationships are discussed; then the intelligent decomposition mining of information, generated by internal decomposition, external decomposition and internal-external decomposition respectively are proposed. Finally an application of the decomposition mining theorems and decomposition mining criterion are given.

Collaborative transshipment strategy of service supply chain for emergencies based on stochastic and fuzzy simulation

HE Xin-hua, HU Wen-fa, XU Chang-yan, CHEN Ji-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  67-77.  doi:10.6040/j.issn.1671-9352.0.2015.625

Abstract ( 1305 )   PDF (1477KB) ( 568 )   Save

References | Related Articles | Metrics

Including two service supplies and multiple service integers based on the M/M/C/∞/m/FCFS queuing system, a two-echelon service supply chain system was considered. The lateral collaborative transshipment principle and partial inventory sharing strategy to satisfy the demand. When a service integers stock is more than the collaborative transshipment point, the service integer could transport service item to other service integers. Otherwise, other service integers or the shared warehouse should transport service item to this service integer. Then the model is developed with the constraint of individual service integers service level to maximize the system total profit and minimize the waiting time, in which service integers stock level and collaborative transshipment points are decision variables. Based on two-stage particle swarm algorithm which combined random fuzzy simulation, the proposed model is solved. At last, a numerical example is given to analyze the total profit difference and the waiting time among partial collaborative transshipment strategy and no collaborative transshipment strategy. It is shown that the strategy with collaborative partial transshipment is superior to that without collaborative transshipment and it proves that this study has theoretical and practical values.

A compact construction for non-monotonic online/offline CP-ABE

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  78-86.  doi:10.6040/j.issn.1671-9352.0.2015.479

Abstract ( 1415 )   PDF (792KB) ( 652 )   Save

References | Related Articles | Metrics

We proposed an online/offline ciphertext-policy attribute-based encryption scheme that could support non-monotonic access structure. In the offline phase, most of the computations for encryption are done; in the online phase, we transform the non-monotonic access structure with positive attribute sets into a monotonic access structure which is based on the linear secret sharing scheme with positive and negative attribute sets, then it only needs a small amount of addition and multiplication operations for the rest components of encryption. The selective security of the scheme under the n-(B)assumption was proved. Compared with the original non-monotonic CP-ABE scheme, our scheme remains the same on the public keys and the master secret keys, with only a small increase in computational complexity. However, the computational complexity during online phase is very small. We can combine our scheme with outsourcing techniques, thus the online encryption phase and the decryption phase could be completed on the resource-constrained small devices.

Static output feedback robust H_∞ control for continuous-time positive systems

XU Yan-chao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  87-94.  doi:10.6040/j.issn.1671-9352.0.2015.510

Abstract ( 1313 )   PDF (962KB) ( 689 )   Save

References | Related Articles | Metrics

A necessary and sufficient condition of static output feedback H_∞ control for continuous-time positive systems was obtained via bounded real lemma and linear matrix inequality. Based on the above condition, a sufficient condition of static output feedback robust H_∞ control for continuous-time positive systems was given. The conditions were established in terms of linear matrix inequalities and a matrix equality constraint. Furthermore, the desired H_∞ controller gain matrix could be determined via cone complementarity linearization techniques. Final, a state controller asspecial case of static output feedback ones was given and a numerical example was provided to illustrate the validity of the results.

Optimal preventive maintenance policy for second-hand equipment under lease considering residual value

DONG Ke, LÜ Wen-yuan, WANG Yong-zhi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  95-102.  doi:10.6040/j.issn.1671-9352.0.2015.527

Abstract ( 996 )   PDF (1352KB) ( 561 )   Save

References | Related Articles | Metrics

For the lease of the second-hand equipment with certain past age, a periodic preventive maintenance strategy was presented. Several factors from the life cycle of the equipment which influence the profit of the lessor, such as the equipments residual value, age, preventive maintenance, minimal repair and punishment mechanism were considered. Under this maintenance scheme, a mathematical model based on the expected total profit of the lessor was established, and the optimal maintenance policies were derived such that the expected total profit was maximized. The proof was givern to obtain the optimal policy of the model. Finally, in case study, the numerical results show that the proposed strategy is practical and can provide effective maintenance solutions for lessors.

Formulation of networked evolutionary games with variation mechanism

XING Hai-yun, ZHAO Jian-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  103-107.  doi:10.6040/j.issn.1671-9352.0.2015.614

Abstract ( 1218 )   PDF (674KB) ( 541 )   Save

References | Related Articles | Metrics

This paper investigates the variation of snowdrift game with reward mechanism was investigated. Using the method of semi-tensor product of matrices, the mathematical model of the networked evolutionary game was built. The network-ed evolutionary game was expressed as a logical dynamic system and then converted into its algebraic form rely on the matrix expression of logic and the method of semi-tensor product of matrices. Then, the evolutionary logical dynamic process was analyzed and the final cooperation stability was discussed through an illustrative example.

Pattern shrinking least square regression for subspace segmentation

CHEN Xiao-yun, LIAO Meng-zhen, CHEN Hui-juan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  108-115.  doi:10.6040/j.issn.1671-9352.0.2016.274

Abstract ( 1015 )   PDF (2739KB) ( 622 )   Save

References | Related Articles | Metrics

Clustering of gene expression data is an important method to discover the new category of tumor. However, clustering directly on the original gene data will lose the hidden manifold structure information, and then affect the clustering effect of the subspace segmentation method. In order to solve this problem, the pattern shrinking least square regression model for subspace segmentation(PSLSR)is proposed. This model can perform pattern shrinking and learn the affine matrix of data simultaneously, and be solved by using the alternating optimization method. Experimental results on six gene expression data show that PSLSR significantly outperforms the existing subspace segmentation methods.

Fast pose estimation for on-board camera and scene reconstruction in monocular vision SLAM

YANG Yuan-hui, LI Guo-dong, WU Chun-fu, WANG Xiao-long

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(12):  116-124.  doi:10.6040/j.issn.1671-9352.0.2016.385

Abstract ( 1371 )   PDF (1123KB) ( 985 )   Save

References | Related Articles | Metrics

According to the simulaneous localization and mapping(SLAM), a fast pose estimation of on-board camera, together with 3D reconstruction of scene structure algorithm was proposed. The special properties of the Euclidean epipoles corresponding to the mobile robots 2-DOF movement were utilized to calibrate the relative pose information between real camera coordinate and virtual camera coordinate without the utilization of specific calibration object, and the active vision method was utilized to further calibrate the relative position information between mobile robot coordinate and virtual camera coordinate; An constructed infinite homography was adopted to turn the hypothesis Euclidean point correspondences obtained by SIFT algorithm into the virtual hypothesis Euclidean point correspondences, and the RANSAC based normalized 3-point algorithm was implemented to estimate and decompose the essential matrix; The previous 3D information of the observed landmarks were adopted to eliminate the scale uncertainty of the translation vector acquired by essential matrix decomposition, and the scene structure was reconstructed by linear triangulation method. Experimental results show that the proposed algorithm has the advantages of high precision, as well as the low computational complexity.