JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Topics in L-functions

HU Pei-chu, WU Ai-di

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 1-15. doi:10.6040/j.issn.1671-9352.0.2016.185

Abstract ( 2595 )

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In this survey, we introduce some propositions of L-functions in the extended Selberg class.

Two mixed conjugate gradient methods based on DY

WANG Kai-rong, GAO Pei-ting

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 16-23. doi:10.6040/j.issn.1671-9352.0.2015.267

Abstract ( 1949 )

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Based on DY method, two mixed conjugate gradient methods(GDY₁ and GDY₂)were proposed. The search directions generated by GDY₁ and GDY₂ are sufficiently decent directions under some specific conditions, and are global convergence with general wolf line search. Numerical experiments show that the new methods outperform DY conjugate gradient method.

Almost sure central limit theorem for arrays of random variables

LIU Yang, FENG Zhi-wei, CHEN Ping-yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 24-29. doi:10.6040/j.issn.1671-9352.0.2015.386

Abstract ( 1410 )

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It is different between sequence and array of random variables on the almost sure central limit theorem, and the selection of its weight coefficient has certain requirements. In this paper, we study two kinds of different weight selection conditions for arrays of random variables, and obtain the almost sure central limit theorems and inferences for arrays of random variables.

Complete moment convergence for arrays of rowwise NSD random variables

ZHANG Yu, XIAO Ben-qiong, XU Ke, SHEN Ai-ting

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 30-36. doi:10.6040/j.issn.1671-9352.0.2015.340

Abstract ( 1619 )

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We mainly study the complete moment convergence for maximal partial sums of arrays of rowwise negatively superadditive dependent(NSD)random variables by using the truncation method of random variables and Rosenthal type inequality. Some sufficient conditions to prove the complete moment convergence are provided. The results obtained in this paper generalize some corresponding ones for independent random variables and some negatively dependent random variables.

Existence of solutions for second-order discrete Neumann problems at resonance

SU Yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 37-41. doi:10.6040/j.issn.1671-9352.0.2015.385

Abstract ( 1086 )

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We consider the existence of solutions for the following nonlinear second order discrete Neumann problem at resonance{Δ²u(t-1)=f(t,u(t),Δu(t)), t∈［1,T］_Z,Δu(0)=0, Δu(T)=0,where t∈［1,T］_Z={1,2,…,T}, f:［1,T］_Z×R2→R is continuous, T≥2 and T∈Z. The methods of lower and upper solutions are developed for the problem by using the connectivity properties of the solution sets of parameterized families of compact vector fields.

Existence of multiple of solutions of first order multi-point boundary value problem

ZHU Wen-wen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 42-48. doi:10.6040/j.issn.1671-9352.0.2015.434

Abstract ( 1222 )

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We use the method of the upper and lower solutions and topological degree theory to study existence of multiple solutions of first order differential equations multi-point boundary value problem{u'(t)=f(t,u(t)), t∈［0,T］,u(0)+∑^m_k=1a_ku(t_k)=cwhere c∈R, t_k(k=1,2,3,…,m)satisfy 0<t₁<t₂<…<t_m<T, a_k<0 are constants, and 1+∑^m_k=1a_k>0, f∈C(［0,T］×R, R). Finally, an example is presented to illustrate the application of the obtained result.

New perturbation results and characterization on approximately dual g-frames in hilbert spaces

ZHANG Wei, FU Yan-ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 49-56. doi:10.6040/j.issn.1671-9352.0.2015.397

Abstract ( 1363 )

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In this paper, some new results on approximately dual g-frames perturbation are presented. An explicit expression and some sufficient conditions for approximately dual g-frames are given.

Continuous directed-complete ordered semigroups and their categorical properties

LIU Ni, ZHANG Miao-miao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 57-64. doi:10.6040/j.issn.1671-9352.0.2015.270

Abstract ( 1378 )

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Firstly, the concept of continuous directed-complete ordered semigroup is introduced. Secondly, some equivalent characterizations of continuous directed-complete ordered semigroup are obtained. Finally, it is proved that the category CDOSG with objects all continuous directed-complete ordered semigroups and morphisms all ordered semigroup homomorphisms preserving directed sups between them is finite complete. Moreover, its full subcategory CCDOSG with objects all commutative continuous directed-complete ordered semigroups is finite complete and closed for function space.

Neighborhood systems

LU Tao, HE Wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 65-69. doi:10.6040/j.issn.1671-9352.0.2015.536

Abstract ( 1582 )

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The concept of neighborhood systems which is common generalizations of topological spaces, locales and topological systems is introduced. And it is proved that the topological space category Top, the topological neighborhood systems category TopN, the localic neighborhood systems category NSL and the topological systems category TopS can be embedded as full subcategories of the category NS of neighborhood systems.

Isoperimetric profile of factor-closed languages and isoperimetric profile of semigroups

CHEN Jun-zhu, WANG Zheng-pan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 70-72. doi:10.6040/j.issn.1671-9352.0.2015.236

Abstract ( 1252 )

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It is mainly proved that the isoperimetric profile of a factor-closed language on a finite alphabet is asymptotically equivalent to the isoperimetric profile of some finitely-generated semigroup.

(Full)oscillatory problems of certain quasilinear hyperbolic systems with damping term

LUO Li-ping, LUO Zhen-guo, ZENG Yun-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 73-77. doi:10.6040/j.issn.1671-9352.0.2015.399

Abstract ( 1237 )

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The(full)oscillation for a class of quasilinear hyperbolic systems with damping term are investigated. By using a new technique of treating quasilinear diffusion term and damping term, some new sufficient criteria for the(full)oscillation of each solution of such systems are established under second boundary value condition, which are illustrated by a example. The results obtained reflect the functions that damping term acts in determining the(full)oscillation of system.

Positive solutions for some singular fractional differential equation integral boundary value problems with p-Laplacian and a parameter

ZHONG Qiu-yan, ZHANG Xing-qiu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 78-84. doi:10.6040/j.issn.1671-9352.0.2015.632

Abstract ( 1291 )

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A special cone is constructed by means of the properties of Green function. By introducing height functions of the nonlinear term on some bounded sets and considering integrations of these height functions, several existence and multiplicity of local positive solutions theorems for some nonlinear fractional differential equation integral boundary value problems with p-Laplacian and a parameter are obtained. The nonlinear term f permits singularities with respect to both the time and space variables.

Representation dimension of one-point extension algebras

SUN Wei-kun, LIN Han-xing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 85-91. doi:10.6040/j.issn.1671-9352.0.2016.086

Abstract ( 1413 )

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Let A be a representation-infinite Artin algebra and M be a left A-module. Let Λ be the one-point extension algebra of A. If Fac(M)is a tilting torsion class and also that M is a direct summand of an Auslander generator about A, then the representation dimension of Λ is not greater than the maximum of representation dimension of A and global dimension of A plus 2. If M is an APR-tilting module or the projective part of a BB-tilting module, the conclusion still holds.

Application of a new accelerating Bregman iterative algorithm in the sparse least squares problems

WANG Wen-shu, LI Wei-guo, QIN Shu-lan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 92-98. doi:10.6040/j.issn.1671-9352.4.2015.004

Abstract ( 1294 )

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Based on the residual Bregman iterative algorithm and fixed point iteration, a novel Bregman iterative algorithm is proposed. Then, inspired by the equivalence of the linearized Bregman and the gradient descent algorithm of the dual problem, a new algorithm by introducing Nesterov accelerating technique into the predictor-corrector method is put forward for solving the sparse least squares problems. Simultaneously, It is proved that the solution sequence obtained by the new method is the optimal solution of the sparse least squares problems. Finally, we use the new method to the sparse signal recovery problem. The numerical results show that the new method is faster and more efficientthan the old ones.

Existence of weak solutions for a second order Dirichlet boundary value problem on time scales

JIANG Jing, GAO Qing-ling, ZHANG Ke-yu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 99-103. doi:10.6040/j.issn.1671-9352.4.2015.003

Abstract ( 1136 )

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The existence of weak solutions for a second order Dirichlet boundary value problem on time scales is studied. Under some conditions involving the first eigenvalues of relevant operator, utilize the variational method and critical point theory to establish our main results.

Application of variable structure pair copula model in the analysis of financial contagion

LIU Kun-lun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2016, 51(6): 104-110. doi:10.6040/j.issn.1671-9352.4.2015.001

Abstract ( 1374 )

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This paper constructed the variable structure pair copula model by using the methods of the diagnosis of the structure change points and pair copula model for the research of the contagion effect of subprime crisis. In the empirical analysis we choose to asset stocks portfolio composed by standard & poors 500 index, the Shanghai composite index, the nikkei 225 index and the financial times ordinary shares 100 index. We diagnose the variable structure of the yield rate of the stock.And we make the estimate parameter of the pair copula-GARCH(1,1)-t model. By the calculated results of the parameter θ and VaR, we elaborate the influence of the USA subprime mortgage crisis to China, Japan and Britain from the mathematical angle. The paper has the certain model function to the research of financial contagion.

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