JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Characterization of monoids by inverse S-acts

QIAO Hu-sheng, BAI Yong-fa

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 1-4. doi:10.6040/j.issn.1671-9352.0.2016.377

Abstract ( 1024 )

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Let S be a monoid. The properties of inverse S-acts is investigated, and the homological classification of inverse S-acts and flatness properties is discussed.

L-R-smash products over monoidal Hom-bialgebras

ZHOU Nan, ZHANG Tao, LU Dao-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 5-8. doi:10.6040/j.issn.1671-9352.0.2016.365

Abstract ( 1093 )

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The L-R-smash products over monoidal Hom-bialgebras is constructed. Furthermore, it is proved that the L-R-smash product is isomorphic with two-sided smash product.

Hopf algebra structures on unified products and smash coproducts

WANG Wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 9-13. doi:10.6040/j.issn.1671-9352.0.2016.157

Abstract ( 1304 )

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Let A be a Hopf algebra and H a coalgebra. The bialgebra structure of AH is constructed, and the antipode of bialgebra AH is given when A and H are both Hopf algebras.

Strongly 2-good Rings

WANG Yao, ZHOU Yun, REN Yan-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 14-18. doi:10.6040/j.issn.1671-9352.0.2016.062

Abstract ( 1283 )

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The concept of 2-good rings is proposed. A ring R is called strongly 2-good if for any a∈R, there exist units u1, u2∈R such that a=u1+u2 and u1u2=u2u1. Some examples of strongly 2-good rings are presented and their ring extensions are investigated.

ZWGP-injectivity and nonsingularity of rings

LU Qi, BAO Hong-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 19-23. doi:10.6040/j.issn.1671-9352.0.2016.173

Abstract ( 1300 )

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ZWGP-injective modules and ZWGP-injective rings are introduced; equivalent characterizations of ZWGP-injective rings are obtained. The properties of ZWGP-injective modules(rings)are explored, the relations between ZWGP-injective rings and nonsingular rings are illustrated by some examples, and sufficient and necessary conditions that rings are nonsingular are given. It is proved that:(1)If left annihilators of R are W-ideals of R, and any essential ideals of R are left ZWGP-injective, then R is left nonsingular;(2)If for any essential left ideal I,R/I is ZWGP-injective, and l(a1)⊆l(a1a2)⊆l(a1a2a3)⊆… is stable, a_i∈Z(_RR), i=1,2,3,…, then R is left nonsingular.

On strongly g(x)-J-clean rings

GAO Han-peng, YIN Xiao-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 24-29. doi:10.6040/j.issn.1671-9352.0.2016.269

Abstract ( 1152 )

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The concept of strongly g(x)-J-clean rings is introduced. It is proved strongly J-clean rings are strongly x(x-1)-J-clean. Moreover, equivalent characters for strongly g(x)-J-clean rings and J-clean rings are given. It is proved that strongly (xⁿ-x)-J-clean rings are directly finite and have stable range one (n≥2).

On the maximal eccentric distance sum of tree with given domination number

ZHU Xiao-ying, PANG Shi-you

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 30-36. doi:10.6040/j.issn.1671-9352.0.2016.113

Abstract ( 1150 )

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The eccentric distance sum of graph G is defined as ξ^d(G)=∑_v∈Vε_G(v)D_G(v), where ε_G(v) is the eccentricity of the vertex v and D_G(v) is the sum of all distances from the vertex v. The trees having the maximal eccentric distance sum among n-vertex trees with domination number four are characterized by using the method of structure graph theory.

Classification on f-coloring of graphs with some restrictions

YANG Chun-hua, CAI Jian-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 37-38. doi:10.6040/j.issn.1671-9352.0.2016.343

Abstract ( 1269 )

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A special class of f-coloring of graphs is investigated, and a sufficient condition is obtained for the special class of f-coloring of a simple graph being f-class 1 by the first moment principle.

Sumsets and subsets of Bohr sets in finite abelian groups

LI Fang, GUANG Ai-xia, LI Guo-quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 39-43. doi:10.6040/j.issn.1671-9352.0.2016.125

Abstract ( 1046 )

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Let G be a finite abelian group and A,B⊂G. It is proved that there exist a Bohr set B(Γ,δ)and a constant D>0 such that A+B contains a translate of any set T⊂B(Γ,δ)of size at most D.

Linear extension of isometries between the unit spheres of two-dimensional normed spaces

LIU Xiao-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 44-48. doi:10.6040/j.issn.1671-9352.0.2016.225

Abstract ( 1272 )

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We study the extension of isometries between the unit spheres S(E) and S(F), where E and F are both 2-dimensional real normed space. It is proved that surjective isometry V₀ defined from S(E) to S(F) can be extended to be a linearly isometry V defined on the whole space S(E) under the some conditions.

Class of fuzzy bounded operators in Felbins type fuzzy normed linear spaces

CHANG Xiao-xuan, JI Pei-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 49-54. doi:10.6040/j.issn.1671-9352.0.2016.191

Abstract ( 1063 )

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The definition of the fuzzy norm of a class of fuzzy bounded operators in Felbins type fuzzy normed spaces is introduced. Furthermore,it is showed that the class of fuzzy bounded operators endowed with this fuzzy norm is still a fuzzy normed space, and its topological structure as well as completeness is studied.

Inequalities for Casorati curvatures of submanifolds in a Riemannian manifold of quasi-constant curvature with a semi-symmetric metric connection

LIU Xu-dong, PAN Xu-lin, ZHANG Liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 55-59. doi:10.6040/j.issn.1671-9352.0.2016.374

Abstract ( 1189 )

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By using a new algebraic inequality, we obtain two inequalities for generalized normalized Casorati curvatures of submanifolds in a Riemanian manifold of quasi-constant curvature with a semi-symmetric metric connection.

Property(z)and Weyl type theorem

DAI Lei, CAO Xiao-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 60-65. doi:10.6040/j.issn.1671-9352.0.2016.038

Abstract ( 1060 )

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An operator T∈B(X) defined on a Banach space X satisfies property(z), a new variant of Weyls theorem if the complement in the spectrum σ(T) of the upper semi-Weyl spectrum is the set of all isolated points of the approximate point spectrum which are eigenvalues of finite multiplicity. In this note, we first study the conditions between property(z)and other Weyl type theorem, then establish for a bounded linear operator and the calculus defined on a Banach space the sufficient and necessary conditions for which property(z)holds by means of the variant of essential approximate point spectrum. The perturbation of property(z)under finite rank operators is considered.

Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations

ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 66-72. doi:10.6040/j.issn.1671-9352.0.2016.213

Abstract ( 1582 )

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The existence and uniqueness of solutions is investigated for a class of three point boundary value problems of fractional differential equations with impulsive. By using the Schauder fixed point theorem and contraction mapping principle, some theorems about the existence and uniqueness of solutions for the boundary value problem are obtained.

Uniqueness of solution for singular boundary value problems of fourth-order differential equations

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 73-76. doi:10.6040/j.issn.1671-9352.0.2016.027

Abstract ( 1270 )

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We investigate the uniqueness of solution for{x⁽⁴⁾(t)-h(t)f(x(t))=0, 0<t<1,x(0)=x(1)=x'(0)=x'(1)=0,where h(t) is allowed to be singular at both t=0 and t=1. The main novelty of this paper is that the Lipschitz constant is related to the first eigenvalues corresponding to the relevant operators. We show the uniqueness of solution by applying the u₀-norm and contraction mapping principle.

Symmetry, reduction and exact solutions of the extended KP-Benjamin-Bona-Mahoney equation

LI Yu, LIU Xi-qiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 77-84. doi:10.6040/j.issn.1671-9352.0.2016.182

Abstract ( 1390 )

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By applying the direct symmetry method, the classical Lie symmetry and reduced equation of the extended KP-Benjamin-Bona-Mahoney equation are obtained. At the same time, through the reduced equation, a great many of solutions are derived by solving the reduction equations with(G'/G)-expansion method and the tanh function expansion method and Riccati auxiliary equation, including travelling wave solutions, the rational function solutions, hyperbolic function solutions, the trigonometric function solutions and so on. Finally, the conservation laws of the equation are obtained by using the symmetry and adjoint equations.

Interval estimation of VaR

REN Peng-cheng, XU Jing, LI Xin-min

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 85-90. doi:10.6040/j.issn.1671-9352.0.2016.033

Abstract ( 1375 )

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Value at risk(VaR)is a tool used for measuring financial risk, which is widely supported and recognized by international finance. To study the interval estimation method in normal population, we used three methods such as Bootstrap、MOVER(method of variance estimates recovery)and Fiducial, and numerically compare the performance of them. The simulation results show that generalized interval estimation based on Ficucial is more robust in coverage and balanced tail error. In the end, the VaR of logarithmic yield of SSE 180 was analyzed.

Maximal φ-inequalities for conditional N-demimartingales based on Y functions

FENG De-cheng, WANG Xiao-yan, GAO Yu-feng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 91-96. doi:10.6040/j.issn.1671-9352.0.2016.233

Abstract ( 1257 )

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We obtain the maximal φ-inequalities for conditional N-demimartingales based on Y functions in this paper.

Strong laws for extreme values from a class of Gaussian sequences

ZHANG Tao, LI Xiao-lin, CHEN Ping-yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 97-100. doi:10.6040/j.issn.1671-9352.0.2016.398

Abstract ( 1303 )

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In this paper, our goal is to prove the strong laws theorem for extreme values from a class of Gaussian sequences. The Gaussian sequence is neither mutually independent nor any condition on the correlation coefficient.

Three-way rules extraction in formal decision contexts with confidence

LIU Lin, WEI Ling, QIAN Ting

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2017, 52(2): 101-110. doi:10.6040/j.issn.1671-9352.0.2016.384

Abstract ( 1492 )

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A method of rules extraction based on the three-way concept lattice in inconsistent three-way formal decision context is put forward. Firstly, the confidence of rules is defined and the probability-distribution is given. And an example is used to demonstrate its feasibility and effectiveness in decision-making. Then several properties of irredundant three-way rules are presented in three-way consistent formal decision context. Finally, using of confidence the necessary and sufficient condition of irredundant rules is discussed in attribute-induced three-way consistent formal decision context.

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