JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Flatness properties of Rees weakly projective acts and homological classification of monoids

QIAO Hu-sheng, MA Ping-ting

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 1-6. doi:10.6040/j.issn.1671-9352.0.2021.143

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Rees weakly projective property of acts and the homological classification of monoids by Rees weakly projective acts are investigated. The conditions over which Rees weakly projective property are preserved under coproducts and products.

Maximal idempotent-generated subsemigroups of the semigroup PCn

ZHANG Chuan-jun, ZHAO Hai-qing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 7-10. doi:10.6040/j.issn.1671-9352.0.2021.246

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The authors studied the semigroup PCn, consisting of all partial decreasing and order-preserving transformations on a finite chain. Analyzing the idempotent elements, completely obtained the classification of the maximal subsemigroups as well as the maximal idempotent-generated subsemigroups of the semigroup PCn.

Dependence of P-dual information and acquirement-discovery

HAO Xiu-mei, LI Ming-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 11-16. doi:10.6040/j.issn.1671-9352.0.2020.540

Abstract ( 640 )

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The concepts of inner and outer P-dual information and P-dual attribute information are defined by using dynamic characteristic of P-sets. On the basis of these concepts, dependence and dependence degree, dependence coefficient of P-information and P-dual attribute information are given. Inner and outer P-attribute information dependence theorems, P-dual information acquirement-discovery theorem and inner hidden theorem are discussed. Two dependence-acquirement criterions are gotten on P-dual information. In the end, the application of P-dual information is presented.

Finite element method of Cahn-Hilliard equation based on adaptive moving mesh method

LU Chang-na, CHANG Sheng-xiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 17-25. doi:10.6040/j.issn.1671-9352.0.2021.327

Abstract ( 1036 )

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A finite element method is proposed for the two-dimensional Cahn-Hilliard equation based on the adaptive moving mesh. Since the Cahn-Hilliard equation changes rapidly in the initial stage and slowly changes in the later stage, the use of the moving mesh rule based on the moving mesh partial differential equation(MMPDE)can better capture the phase diagram. The method is discretized by using linear finite element in space and fifth-order Radau IIA scheme in time. Numerical results shows that the numerical solution can well maintain the law of conservation of mass and the law of energy stability, and improve the calculation efficiency, which verifies the effectiveness and feasibility of the method.

Picard-GPSS iteration method for solving the generalized absolute value equations

LI Xu, YIN Xiao-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 26-32. doi:10.6040/j.issn.1671-9352.0.2021.146

Abstract ( 842 )

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Based on the out-inner iteration, Picard-GPSS iteration method for solving the generalized absolute value equations is established. Convergence theory is studied in detail. Numerical experiments show that the proposed method is efficient and better than the Picard-HSS iteration method in terms of inner iteration steps and CPU time.

Solvability for a class of third-order m-point boundary value problems at resonance with dim Ker L=2

DU Rui-juan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 33-39. doi:10.6040/j.issn.1671-9352.0.2021.428

Abstract ( 453 )

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The author consider the solvability for a class of third order m-point boundary value problems at resonance with dim Ker L=2{u(t)=f(t,u(t),u'(t),u″(t))+e(t), t∈［0,1］,u(0)=∑^m-2_i=1α_iu(ξ_i), u(1)=∑^n-2_j=1β_ju(η_j), u″(0)=0,where f:［0,1］×R³→R satisfies Carathéodory conditions, e:［0,1］→R∈L1［0,1］, α_i,β_j∈R,ξ_i,η_j∈(0,1),0<ξ1<ξ2<…<ξ_m-2<1,0<η1<η2<…<η_n-2<1, and satisfy the following condition(C₁): ∑^m-2_i=1α_i=1,∑^m-2_i=1α_iξ_i=0,∑β_j=1,∑β_jη_j=1.

Oscillation conditions of certain nonlinear damped fractional differential equations

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

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 40-44. doi:10.6040/j.issn.1671-9352.0.2021.145

Abstract ( 506 )

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By using integral averaging technique and Riccati transformations, some new sufficient criteria are obtained for oscillation of solutions of a class of nonlinear fractional differential equations with damping term. Some examples are provided to illustrate the relevance of the main results.

Existence of nontrivial weak solutions for fractional boundary value problems with variable coefficients

XUE Ting-ting, XU Yan, LIU Xiao-ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 45-51. doi:10.6040/j.issn.1671-9352.0.2021.058

Abstract ( 582 )

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The existence of nontrivial weak solutions for a class of fractional Dirichlet boundary value problems with variable coefficients is studied by using Linking theorem and Mountain pass theorem. Under the variational framework, Ambrosetti-Rabinowtiz condition is mostly needed for the study of such problems, and the weaker condition than Ambrosetti-Rabinowtiz condition is given.

Existence, nonexistence and multiplicity of positive solutions for a class of nonlinear third order three point boundary value problems

ZHANG Rui-yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 52-58. doi:10.6040/j.issn.1671-9352.0.2021.191

Abstract ( 483 )

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This paper considers the existence, nonexistence and multiplicity of positive solutions for a class of nonlinear third-order three-point boundary value problems {u(t)+λf(t,u(t))=0, t∈［0,1］,u(0)=u'(0)=0, u'(1)=αu'(η),where λ>0 is a parameter, 0<η<1, 1<α<1/η, f:［0,1］×［0,∞)→(0,∞)is a continuous function. The proof of the main theorems is based on fixed point index theorems, Leray-Schauder degree and the method of upper and lower solutions.

Topological uniform descent and property (R) for bounded linear operators

ZHAO Xiao-peng, DAI Lei, CAO Xiao-hong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 59-66. doi:10.6040/j.issn.1671-9352.0.2021.051

Abstract ( 700 )

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Let H be a complex separable infinite dimensional Hilbert space and B(H) be the algebra of all bounded linear operators on H, T∈B(H) is said to satisfy property (R) if σ_a(T)\σ_ab(T)=π00(T), where σ_a(T) and σab(T)denote the approximate point spectrum and the Browder essential approximate point spectrum of T respectively, and π00(T)={λ∈iso σ(T):0<dim N(T-λI)<∞}. By using the property of topological uniform descent, the necessary and sufficient conditions for which the property (R) holds for bounded linear operators are given. In addition, the new judgements for operator functions satisfying property (R) according to the property of topological uniform descent are discussed. Also, the property (R) for upper triangular operator matrices is explored.

Jordan and Lie centralizers on quaternion rings

CAO Mei-hong, ZHANG Jian-hua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 67-71. doi:10.6040/j.issn.1671-9352.0.2021.192

Abstract ( 888 )

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Let S be a ring, H(S) be the quaternion ring on S. By studying Jordan centralizers and Lie centralizers on H(S), this paper obtains the sufficient condition for a centralizer to be proper. Further its proved that every Jordan centralizer is a centralizer on H(S) under certain assumption. Moreover, several equivalent conditions are given that the addictive mapping φ on H(S) is centralizer.

Approximation properties of Lupas-King type operators

WANG Tao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 72-77. doi:10.6040/j.issn.1671-9352.0.2021.152

Abstract ( 744 )

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The asymptotic approximation properties of Lupas-King operators are studied by means of analysis methods and techniques. This paper studies pointwise approximation properties of Lupas-King operators for functions with locally bounded derivatives by combining with decomposition technique of functions and interval division technique.

Law of the single logarithm for the self-normalized sums for arrays

KE Chun-mei, CHEN Liang-lu, HUANG Ying-qiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 78-83. doi:10.6040/j.issn.1671-9352.0.2021.447

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By the self-normalized sum moderate deviations, the law of the single logarithm for the self-normalized sums for arrays is obtained, which generalizes the current results. As the application, the law of the single logarithm for the t-statistics of arrays is derived.

A Bayesian approach for variable selection using spike-and-slab prior distribution

ZHANG Xian-you, LI Dong-xi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 84-93. doi:10.6040/j.issn.1671-9352.0.2021.065

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For ultra-high dimensional data, a Bayesian approach using a novel spike-and-slab prior for variable selection in high-dimensional linear regression models is presented. The proposed method aims to inherit the advantages of the elastic net and the EM algorithm to obtain sparse prediction models with faster convergence speed. Furthermore, a spike-and-slab setting of coefficients which allows for borrowing strength across coordinates, adjust to data sparsity information and exert multiplicity adjustment is proposed. Finally, the accuracy and efficiency of the proposed method are demonstrated via comparisons and analyses with common methods.

Bifurcation of hydraulic turbine governing system under color noise excitation

ZHANG Mei-jiao, ZHANG Jian-gang, NAN Meng-ran, WEI Li-xiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 94-99. doi:10.6040/j.issn.1671-9352.0.2021.410

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Based on the saturated nonlinear proportional-integral(PI)governing system of a hydraulic turbine, a hydraulic turbine governing system under the excitation of color noise is established, the stochastic bifurcation behavior of system is studied. The system is simplified to an equivalent nonlinear white noise model by using the uniform color noise approximation principle. The central manifold theorem is used to reduce the dimension of system, the Ito differential equations and FPK equations are obtained according to stochastic average method, the stochastic bifurcation condition of system is discussed. Through numerical simulation, the stochastic bifurcation behaviors of system under the influence of different autocorrelation time and noise intensity are discussed respectively, the validity of theory of stochastic averaging and the occurrence of bifurcation phenomenon are verified.

Dynamics of the stage-structured population system with two kinds of pulses

LYU Ning

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(12): 100-110. doi:10.6040/j.issn.1671-9352.0.2021.179

Abstract ( 752 )

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This paper studies the complex dynamics of the stage structure population system with birth pulse and harvest pulse. The discrete dynamical model of the system is determined by stroboscopic mapping, and the existence and stability of the equilibrium point are discussed. The central manifold theory is available to study the period-doubling bifurcation of the equilibrium point. By light of numerical simulation, it is revealed that a series of period-doubling bifurcation cascades connects together to form a Feigen-baum tree link(anti-monotonicity)with the parameters varying. What is the most interesting thing is that the topology of the periodic island formed by these Feigen-baum trees in the two-dimensional parameter space is arranged according to the Stern-Brocot tree instead of the familiar Farey tree.

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