JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Uniqueness of meromorphic functions sharing four distinct finite values with L-functions

LI Xiao-min, WU Cong-cong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 1-8. doi:10.6040/j.issn.1671-9352.0.2019.474

Abstract ( 1283 )

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This paper studies a uniqueness question of a nonconstant meromorphic function f sharing three distinct finite values IM and a fourth finite value CM with an L-function L belonging to the extended Selberg class. The main result obtained in this paper improves and extends many known results.

Pointwise approximation of Lupas operators to locally bounded functions

WANG Tao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 9-15. doi:10.6040/j.issn.1671-9352.0.2019.067

Abstract ( 1347 )

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In this paper the approximation properties of new type Lupas operators are studied to the locally bounded functions by means of probability methods and Bojanic-Cheng methods combining with analysis technique and interval division technique. The asymptotic estimate of Lupas operators is obtained.

Boundedness for commutator of multilinear Hardy-Littlewood maximal operator

WANG Min, FANG Xiao-zhen, QU Meng, SHU Li-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 16-22. doi:10.6040/j.issn.1671-9352.0.2019.353

Abstract ( 1149 )

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By using the method of intermediate value and the properties of binary cubes, the mapping property from L^p1(Rⁿ)×L^p₂(Rⁿ)×…×L^p_m(Rⁿ)to L^q(Rⁿ)of the commutator M_{b_j}(j=1,2,…,m) generated by local integrable function b_j and multilinear Hardy-Littlewood maximal operator M is obtained.

Non-spectrality of some self-affine measures under the similarity in space

QIN Ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 23-32. doi:10.6040/j.issn.1671-9352.0.2019.509

Abstract ( 1248 )

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The spectrality or non-spectrality of the self-affine measure μ_M,D corresponding to matrix M=diag［p₁, p₂, p₃］ and the digit set D={0, e1, e2, e3} has had many conclusions with previous researching, where p1, p2, p3∈Z\{0, ±1}, e₁, e₂, e₃ are the standard basis of unit column vectors in R³. For the expanding integer matrix M=［p₁, p₂, p₃; p₄, p₅, p₆; p₇, p₈, p₉］ and the digit set D={0, e1, e2, e3}, a method is presented here to deal with the non-spectrality of μ_M,D. As an application, the non-spectrality of a class of such self-affine measures are clarified.

Some properties of Drazin order

PANG Yong-feng, WEI Yin, WANG Quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 33-42. doi:10.6040/j.issn.1671-9352.0.2019.407

Abstract ( 1164 )

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Let B(H) be the set of all bounded linear operators on Hilbert space H. Firstly, some characterizations and related properties of Drazin order in H=R(A^k)⊕N(A^k) space are studied. Secondly, the Drazin inverse of idempotent is generalized in the general algebra, and then some properties of Drazin order are studied.

k-uniform rotund points in Orlicz sequence spaces equipped with the generalized Orlicz norm

DUAN Li-fen, ZUO Ming-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 43-47. doi:10.6040/j.issn.1671-9352.0.2019.129

Abstract ( 1262 )

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Using the characteristics of the generalized Orlicz norm and techniques for dealing with sequence space theory, k-uniform rotund points of the Orlicz sequence spaces equipped with the generalized Orlicz norm are discussed. The criterion of k-uniform rotund points in above spaces is given. And both sufficient and necessary conditions are obtained to make above spaces be locally k-uniform rotund.

Global regularity for very weak solutions to non-homogeneous A-harmonic equation

XU Xiu-juan, YAN Shuo, ZHU Ye-qing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 48-56. doi:10.6040/j.issn.1671-9352.0.2019.408

Abstract ( 1289 )

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This paper deals with boundary value problem for non-homogeneous A-harmonic equation div(A(x,∇u))=f(x). A global regularity result is derived for very weak solutions under some controllable and coercivity conditions and some proper integrable assumptions on the nonlinear term, by using the Hodge decomposition theorem and the methods in Sobolev spaces. The results generalize the corresponding results in related literatures.

Asymptotic formula for eigenvalues and eigenfunctions of Sturm-Liouville question

RAN Mao-jun, GAO Cheng-hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 57-62. doi:10.6040/j.issn.1671-9352.0.2019.626

Abstract ( 1991 )

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According to the classical analysis method, the asymptotic formula of eigenvalues and eigenfunctions of Sturm-Liouville question with boundary conditions dependent on nonlinear eigenparameters are studied. By means of constant variation method of ordinary differential equation and asymptotic estimation of eigenfunction zero, the asymptotic formula of eigenvalues and eigenfunctions of boundary conditions with nonlinear eigenparameters are obtained.

Structure of eventually C-L-weakly regular semigroups

WANG Xu-dong, SUN Yan, GONG Chun-mei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 63-67. doi:10.6040/j.issn.1671-9352.0.2019.133

Abstract ( 984 )

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The relation L⁽⁺⁾ on semigroups is defined and the concept of eventually C-L-weakly regular semigroups is introduced. As a special case, the equivalent condition of L⁽⁺⁾-simple eventually C-L-weakly regular semigroups is given. By using the inflation of semigroups, the structure theorem of eventually C-L-weakly regular semigroups is obtained.

On p-central automorphisms of critical groups and applications

DONG Shen-juan, LI Zheng-xing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 68-72. doi:10.6040/j.issn.1671-9352.0.2019.032

Abstract ( 1328 )

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Let G be a critical group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph H of G is inner.

Lazy 2-cocycles on 9-dimensional Taft algebra

CHEN Chen, GAO Ying-ying, CHEN Hui-xiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 73-78. doi:10.6040/j.issn.1671-9352.0.2019.453

Abstract ( 988 )

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The normal lazy 2-cocycles on 9-dimensional Taft algebra are investigated. The structures of all such 2-cocycles are given. It is shown that each normal lazy 2-cocycle on 9-dimensional Taft algebra is exactly determined by one scale, and that the group of all normal lazy 2-cocycles on 9-dimensional Taft algebra with respect to convolution product is isomorphic to the additive group of the ground field.

Discussions on the Q-cleanness of rings and Q-clean corner

SUN Xiao-qing, XIAO Yan-ting, CUI ran-ran

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 79-83. doi:10.6040/j.issn.1671-9352.0.2018.633

Abstract ( 1185 )

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The concepts of Q-clean rings and Q-clean corners are defined by quasi-inverse elements. The Q-cleanness and Q-clean corners of rings are introduced, and some equivalent conditions of abelian Q-clean correspond are given. Moreover, some conclusions can correspond to Clean rings.

On JGR-clean rings

XU Ying-ying, YIN Xiao-bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 84-90. doi:10.6040/j.issn.1671-9352.0.2018.711

Abstract ( 1120 )

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The concepts of(strongly)JGR-clean rings are introduced. It is proved that JGR-clean rings are the real generalization of J-clean rings. Basic properties and extension properties of such rings are investigated. Moreover, the relationships between(strongly)JGR-clean rings and some special rings are discussed.

Gorenstein IFP-Flat modules

LIU Ting, ZHANG Wen-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 91-98. doi:10.6040/j.issn.1671-9352.0.2018.751

Abstract ( 1089 )

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Gorenstein IFP-flat modules are introduced, the homological properties of these modules are discussed, and the equivalent characterizations of Gorenstein IFP-flat modules under the right coherent ring are investigated.

n-IFP-gr-injective modules and n-IFP-gr-flat modules

ZHAO Jun-xiu, DI Rong-rong, DI Zhen-xing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 99-103. doi:10.6040/j.issn.1671-9352.0.2019.138

Abstract ( 870 )

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The notions of n-IFP-graded injective modules and n-IFP-graded flat modules are introduced and investigated, where n is a positive integer. It proves that both(gr-I F_n, gr-I I_n)and(gr-I I_n, gr-I F_n)form two duality pairs over any graded ring R, where gr-I F_n denotes the class of all n-IFP-graded flat right R-modules and gr-I I_n denotes the class of all n-IFP-graded injective left R-modules. As applications, it shows that every graded right R-module has a gr-I F_n-preenvelope, every graded left R-module has a gr-I I_n-cover, and(gr-I F_n, gr-I F ^⊥_n)forms a perfect cotorsion pair.

Principal congruences on modal algebras

CAO Fa-sheng, XIAO Fang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 104-108. doi:10.6040/j.issn.1671-9352.0.2019.068

Abstract ( 1270 )

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The principal congruences of Boolean algebras and modal algebras are studied. In strict accordance with the definitions of principal congruences of Boolean algebras and modal algebras, the characterization of principal congruences of Boolean algebras and modal algebras are given.

Application of local non-intrusive reduced basis method in Rayleigh-Taylor instability

WEN Xiao, LIU Qi, GAO Zhen, DON Wai-sun, LYU Xian-qing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 109-117. doi:10.6040/j.issn.1671-9352.0.2019.669

Abstract ( 1357 )

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A local non-intrusive reduced basis method(RBM)is proposed to simulate the evolution of Rayleigh-Taylor instability(RTI), in which the amplitude and time of initial small perturbations are considered as free parameters. RBM regards the solution as a linear combination of a set of reduced basis functions, which can be obtained by the proper orthogonal decomposition. Furthermore, the artificial neural network is used to establish the mapping relationship between the parameters and the coefficients of the reduced basis functions. Due to the structures of RTI becoming more and more complex with the increasing time, especially the rollup structures of small-scale vortices in the late stage, RTI is considered being divided into the early stage(linear)and the middle and late stage(quasi-non-linear and weak non-linear systems), i.e. time parameter is considered in stages. The time parameter is divided into three, five and six segments and the local RBM allows a potential speedup up to a factor of about four times faster than the global RBM with similar accuracy.

Input-output finite time stability of asynchronous switched systems with event-triggered

YANG Yang, WU Bao-wei, WANG Yue-e

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(2): 118-126. doi:10.6040/j.issn.1671-9352.0.2019.441

Abstract ( 978 )

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The input-output finite-time stability of asynchronous switched system due to the switching delays of controllers with uncertainties under event-triggered sampling scheme is investigated. Firstly, the concept of input-output finite-time stability of system is given, and a state feedback controller is designed based on event-triggered sampling scheme. Secondly, some sufficient conditions for input-output finite-time stability of uncertain asynchronous switched closed-loop systems are derived by applying multiple Lyapunov functions method and average dwell time approach. Finally, a numerical simulation example is given to illustrate the validity of the conclusions.

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