Table of Content

  

20 August 2025
Volume 60 Issue 8

Boundedness of fractional maximal operators with doubling measure on homogeneous trees

YE Xiaofeng, XIONG Shoulong, JIANG Zhicong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  1-5.  doi:10.6040/j.issn.1671-9352.0.2023.477

Abstract ( 76 )   PDF (1298KB) ( 48 )   Save

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We defined the fractional maximal operators and found a control function related to the maximal operators. We obtain the boundedness of fractional maximal operators on homogeneous trees from the weak(1,1)type of maximal operators.

A note on zero product determined algebras

PAN Shaoze, SU Shanshan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  6-12.  doi:10.6040/j.issn.1671-9352.0.2023.503

Abstract ( 64 )   PDF (2662KB) ( 22 )   Save

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This paper primarily demonstrates that several classes of algebras possess the property of zero Lie product determinacy. Firstly, it provides some equivalent characterizations of zero product determinacy along with an application. Secondly, we prove that the triangular UHF algebras, countable dimensional locally matrix algebra, and algebras consisting of finite rank operators in J -subspace lattices are all zero Lie product determined. Furthermore, the paper explores the preservationof the zero product determinacy property under certain mappings and presents several counterexamples.

Ruled surfaces in four-dimensional Euclidean space and their structural functions

QU Ruixiang, TIAN Hanyu, YU Yanhua

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  13-20.  doi:10.6040/j.issn.1671-9352.0.2023.453

Abstract ( 43 )   PDF (2115KB) ( 18 )   Save

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In four-dimensional Euclidean space, utilizing the definition of a waist curve, the structure functions of ruled surfaces is proposed, extending the non-developable ruled surfaces and their standard equations in three-dimensional Euclidean space to four-dimensional Euclidean space. By studing the properties of the surface itself through the structural function of the ruled surface, the relationships between the structural functions, directors, and waist curves of four types of special associated ruled surfaces are obtained, and these four kinds of ruled surfaces are classified. Finally, specific expressions for the structural functions are given when the director is a Mannheim curve and a skew helix of the third type, and the mean curvature vector field of the associated ruled surface in these cases is calculated.

Stock market risk measurement based on W-G-VaR model

ZHANG Hui, WEI Jiaqi, MENG Wenyu, ZHU Qingfeng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  21-33.  doi:10.6040/j.issn.1671-9352.0.2023.322

Abstract ( 60 )   PDF (9536KB) ( 26 )   Save

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In order to verify that capturing the uncertainty features of the probability distribution of financial time series based on different frequency domain scales can effectively improve the measurement accuracy of VaR model, the W-G-VaR model is constructed by combining wavelet multi-resolution analysis with nonlinear expectation theory for the first time. Standard & Poors 500 composite stock price index(S& P 500 Index)and Shanghai(securities)composite index are selected as samples for empirical analysis. The results show that, compared to the G-VaR model, the W-G-VaR model constructed from the dual perspectives of the time domain and the frequency domain has more accurate risk measurement results throughout the sample period, especially during the occurrence of major risks, and the size of the window when capturing uncertainties does not affect the superiority of the W-G-VaR model.

Interval hesitant trapezoidal fuzzy Choquet Muirhead mean operator and its application in multi-attribute decision making

JIANG Lihui, XU Jinhui, CHEN Huayou

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  34-51.  doi:10.6040/j.issn.1671-9352.0.2023.373

Abstract ( 58 )   PDF (5991KB) ( 28 )   Save

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In order to ensure the integrity of decision information, we extend the Muirhead mean operator in the environment of interval hesitant trapezoidal fuzzy sets. The concepts of interval hesitant trapezoidal fuzzy Muirhead mean operator and interval hesitant trapezoidal fuzzy geometric Muirhead mean operator have been proposed. Their properties and theorems are given, and several degenerate forms of the operators are introduced. Considering that the Choquet integral can objectively calculate the weights of attributes, this paper introduces the Choquet integral into the above operators, and proposes the concepts of interval hesitant trapezoidal fuzzy Choquet Muirhead mean operator and interval hesitant trapezoidal fuzzy geometric Choquet Muirhead mean operator. Meanwhile, a multi-attribute decision making model based on interval hesitant trapezoidal fuzzy Choquet Muirhead mean operator is constructed. Finally, it was applied to the green battery supplier selection problem to analyze its feasibility and effectiveness.

The relationship between global Roman domination number and Roman domination number of graphs

HAO Guoliang, WU Yuqi, JIANG Haining

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  52-56.  doi:10.6040/j.issn.1671-9352.0.2023.301

Abstract ( 53 )   PDF (1695KB) ( 13 )   Save

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The new inequality relationships between global Roman domination number and Roman domination number are obtained by using the graph parameters such as the order, the number of edges and degree.

Adjacent vertex reducible total labeling of some joint graphs

WANG Jiang, LI Jingwen, GAO Xin, SUN Liangjing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  57-67.  doi:10.6040/j.issn.1671-9352.0.2023.465

Abstract ( 42 )   PDF (4571KB) ( 13 )   Save

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For an undirected connected graph G(V,E), if there exists a single mapping f:V(G)∪E(G)→{1,2,…,|V|+|E|}, and conditions uv∈E(G) and d(u)=d(v) are satisfied, then there exists S(u)=S(v), where S(u)=f(u)+∑ holds. Let d(u) denote the degree of vertex u; thus, f is referred to as an adjacent vertex reducible total labeling(AVRTL)of G. This study combines genetic algorithms and particle swarm algorithms to design a heuristic search algorithm that can determine whether a random graph with a finite number of vertices contains an AVRTL. Through the analysis of experimental results, several theorems regarding linked graphs are summarized and proved. Finally, the following conclusion is drawn: if subgraphs G1 and G2 are AVRTL graphs, then the graph operation ↑ab exhibits closure, meaning the linked graph G1↑_abG2 is also an AVRTL graph.

Lower bound of Mostar index with respect to tricyclic graphs

WANG Hui, LIU Mengmeng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  68-77.  doi:10.6040/j.issn.1671-9352.0.2023.422

Abstract ( 43 )   PDF (3228KB) ( 13 )   Save

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The Mostar index M(G) of a connected graph G is defined as M(G)=∑_e=uv∈E(G)|n_u(e)-n_v(e)|, where n_u(e) and n_v(e) are, respectively, the number of vertices of G lying closer to vertex u than to vertex v and the number of vertices of G lying closer to vertex v than to vertex u. The lower bound of the Mostar index among all tricyclic graphs is established, and the extremal graphs that attained the lower bound are determined.

Normal criterion concerning differential polynomials and omitted functions

YANG Qi, CHEN Pengbin, GONG Yihui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  78-85.  doi:10.6040/j.issn.1671-9352.0.2023.445

Abstract ( 44 )   PDF (2377KB) ( 12 )   Save

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This paper studies the normal criterion of holomorphic functions involving exceptional functions and differential polynomials by using Pang-Zalcman lemma. A new normal criterion is obtained by extending the previous results through the method of proof by contradiction.

Parametrized Littlewood-Paley operators and their higher order commutators on generalized Morrey spaces associated with ball quasi-Banach function spaces

LI Xuemei, ZHANG Zheng, LU Guanghui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  86-94.  doi:10.6040/j.issn.1671-9352.0.2023.433

Abstract ( 48 )   PDF (2651KB) ( 15 )   Save

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In this paper, the authors mainly discuss the boundedness of parametrized area integral μ^ρ_Ω,S and parametrized Littlewood-Paley g^*_λ-function μ^{*, ρ}_Ω,λ and their higher order commutators ［b^m, μ^ρ_Ω,S］ and ［b^m, μ^{*, ρ}_Ω,λ］ generated by b∈BMO and μ^ρ_Ω,S、 g^*_λ-function μ^{*, ρ}_Ω,λ on generalized Morrey spaces associated with ball quasi-Banach function spaces M_u(X).

Estimate of the bilinear θ-type C-Z operator on two weight Herz spaces with variable exponents

WU Qi, YANG Yanqi, TAO Shuangping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  95-105.  doi:10.6040/j.issn.1671-9352.0.2023.427

Abstract ( 50 )   PDF (2904KB) ( 9 )   Save

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The boundedness of the bilinear θ-type Calderón-Zygmund operator on the double-weight variable exponent Herz space is obtained by using the double-weight estimation and the function decomposition method, as well as the weighted boundedness on the product L^p(·) space.

Traveling wave solutions of a class of SEIR lattice differential equations with saturated recovery rate

LI Aoyu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  106-115.  doi:10.6040/j.issn.1671-9352.0.2023.188

Abstract ( 32 )   PDF (3139KB) ( 17 )   Save

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In this paper, the existence of traveling wave solutions for a kind of discrete diffusion SEIR model with saturated recovery rate and bilinear occurrence rate is studied. Firstly, the existence of solutions for truncationproblem is proved by using the method of upper and lower solutions and the Schauder fixed point theorem; Secondly, it is proved by the limit method that when R0>1, c>c^*, the system has traveling wave solutions connecting the disease-free equilibrium point and the positive equilibrium point. Finally, the asymptotic behavior of traveling wave solution at infinity is proved.

Hopf bifurcation of Brusselator model with cross-diffusion and delay

YANG Xiunan, XING Hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  116-124.  doi:10.6040/j.issn.1671-9352.0.2023.186

Abstract ( 42 )   PDF (3103KB) ( 12 )   Save

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In this paper, the Brusselator model with cross-diffusion and delay are studied. Firstly, by analyzing the distribution of the roots of the characterstic equation of the system using linearization method, the local asymptotic stability of the system and the existence of Hopf bifurcation at the unique positive equilibrium point are obtained. Then the effect of time delay parameters on the existence of Hopf bifurcation is analyzed. Finally, numerical simulation is carried out to support the theoretical results using MATLAB.

Method of moments, scaling transformation group analysis and self-similar solutions of a class of 3+1-dimensional macroscopic population balance equation

LIN Fubiao, YANG Yang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  125-134.  doi:10.6040/j.issn.1671-9352.0.2023.412

Abstract ( 52 )   PDF (2925KB) ( 21 )   Save

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Self-similar solutions and approaches for analytically solving a class of(3+1)-dimensional macroscopic population balance(integro-partial differential)equations with homogeneous collision kernels are studied.(3+1)-dimensional integro-partial differential equation is successfully transformed into(2+1)-dimensional partial differential moment equations by use of the method of moments. The admitted scaling transformation groups, reduced(2+1)-dimensional integro-partial differential equations, reduced(1+1)-dimensional ordinary differential equations, self-similar solutions, explicit exact solutions of(3+1)-dimensional integro-partial differential equations and(2+1)-dimensional partial differential moment equations are presented by use of the method of scaling transformation analysis. The dynamic behaviour analysis of the obtained solutions are also given.

Existence of forced waves for a predator-prey system in a discrete shifting habitat

ZHU Qiaoling, SHI Zhenxia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(8):  135-142.  doi:10.6040/j.issn.1671-9352.0.2023.337

Abstract ( 39 )   PDF (2296KB) ( 22 )   Save

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This paper studies a three-species predator-prey model in discrete patch environments, the existence of forced waves is obtained by using Schauders fixed point theorem and constructing appropriate upper-lower solutions.