JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Joint optimisation of beam formation and rate allocation for STAR-RIS assisted RSMA systems

PENG Yi, LE Shuzhen, YANG Qingqing, LI Hui, WANG Jianming

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 1-10. doi:10.6040/j.issn.1671-9352.0.2024.331

Abstract ( 181 )

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In order to enhance the communication performance of downlink rate-split multiple access(RSMA)systems assisted by simultaneously transmissive and reflective intelligently reconfigurable surface(STAR-RIS)and to solve the problem of limited performance of non-orthogonal multiple access(NOMA)when the channel gains are close to each other.In this paper, we propose a method of joint beam formation and rate allocation optimization. Firstly, the optimization problem of maximizing the sum rate is constructed that sets the optimization parameters as the beam formation vector, the rate allocation vector, and the STAR-RIS transmitted and reflected beam formation matrices. And then we decompose the optimization problem into two sub-problems by block coordinate descent. We optimize the beam formation vector and the rate allocation vector by successive convex approximation, and the STAR-RIS transmission and reflection beamforming matrices are optimized based on fractional programming and semi-definite programming methods. Finally, the sum-rate maximization under the power condition is achieved by alternating iterations. The simulation results demonstrate that the proposed algorithm exhibits superior performance in comparison to the existing benchmark scheme, achieving an overall enhancement in system sum rate ranging from 28.0% to 37.3%.

Evaluation method of used truck value based on GA-BP neural network model

YAN Shengyu, LIU Yang, LIU Jixiang, CHEN Haifeng, ZHENG Yuanwang, WEN Fuhua, WANG Hongyu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 11-20. doi:10.6040/j.issn.1671-9352.0.2024.243

Abstract ( 149 )

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To accurately evaluate the value of the used trucks, a GA-BP(genetic algorithm-backpropagation)neural network evaluation method is proposed, based on the historical transaction data of e-commerce platform. Considering the use features of the used trucks, 11 key indicators affecting the transaction value are selected and the quantitative standards of the indicators are put forward. The consistency of each index is tested by Pearson correlation coefficient method to verify the rationality of index selection. By compromising Genetic Algorithm and BP neural network, the evaluation model of the used trucks value by GA-BP neural network is proposed, and the model is trained and verified by using 9 016 transaction data. Compared with the unoptimized BP neural network model, the mean square error(MSE)of the model is reduced by 74.85%. Through the analysis of the average impact value, it is found that the cumulative mileage, cumulative driving time, emission standard, specific power and loading situation show the greatest influence on the value evaluation of used trucks, and the emission standard has gradually become an important indicator affecting used trucks.

Concept lattice construction method based on granular concept network

WU Hai, NIU Jiaojiao, TIE Wenyan, ZUO Jiankun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 21-31. doi:10.6040/j.issn.1671-9352.4.2024.350

Abstract ( 90 )

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Aiming at the problem of how to construct the whole concept lattice of the formal context based on the granular concepts, this paper proposes a concept lattice construction method based on the granular concepts. The concept learning mechanism of generating general concepts through granular concepts is discussed, and a granular concept network(GraCN)containing an input layer, a granular concept generation layer and a concept generation layer is constructed based on this mechanism. The concept lattice of the formal context is constructed by deduplicating concept nodes in GraCN and adding the concept node whose intent is the whole attribute set and whose extent is the whole object set. Numerical experiments validate the feasibility and effectiveness of using the granular concept network to generate the concept lattice.

Application of matrix theory in solving a class of differential equations

CAO Haisong, WANG Chenxu, LI Hengyan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 32-37. doi:10.6040/j.issn.1671-9352.0.2023.424

Abstract ( 114 )

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From the perspective of matrix, this paper discusses the application of matrix theory in solving a class of differential equations, and its effectiveness is verified by numerical examples.

Dynamics of a mosquito-borne model with distinct dispersal rates

YA Bao, HE Jie

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 38-48. doi:10.6040/j.issn.1671-9352.0.2023.434

Abstract ( 105 )

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In order to study the impact of host dispersal and spatial heterogeneity on the spread of mosquito-borne diseases, a reactive-diffusion mosquito-borne disease model with different diffusion rates is established. Firstly, the next-generation operator theory is applied to define the basic reproduction number R₀ of the model, and the asymptotic behavior of R₀ as the diffusion coefficient tending to zero and infinity is analyzed respectively. Secondly, according to the persistence theory of dynamical systems, it is proved that the sign of R₀-1 determines the global threshold dynamics of the model. Finally, numerical simulations validate the theoretical results and show that spatial heterogeneity may increase the risk of disease transmission.

Analysis of Mpox outbreak in Nigeria based on uncertain Logistic growth model

CHEN Lili, DING Chunxiao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 49-54. doi:10.6040/j.issn.1671-9352.0.2023.415

Abstract ( 90 )

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In order to deal with uncertainty in the transmission process of Mpox, an uncertain Logistic growth model was used to analyze the Mpox epidemic in Nigeria. Firstly, the cumulative confirmed cases of Mpox published by the Nigeria Center for Disease Control and Prevention were sorted out, and the scatter plot of the data was illustrated. Then, a Logistic growth model was developed and the fitted Logistic growth model was obtained using least squares estimation, which in turn calculated the residuals. Verification of the instability of residual frequencies through five tests illustrated the inapplicability of the stochastic Logistic growth model to study the Mpox outbreak in Nigeria. The uncertain Logistic growth model was further used for modeling. Finally, the forecast values of the cumulative number of confirmed Mpox cases in Nigeria were given, and 95% confidence intervals were obtained. And the feasibility of the model was verified by cross-validation method and the direct comparison among observed values, forecast values and confidence intervals. This study provided some theoretical support for the prevention and control of Mpox epidemic and policy formulation in Nigeria.

Modulus-based matrix splitting iteration method for the implicit complementarity problem

WEN Shuhong, KE Yifen, LI Keliang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 55-65. doi:10.6040/j.issn.1671-9352.0.2024.213

Abstract ( 74 )

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A new modulus-based matrix splitting iteration method is mainly established for a class of implicit complementarity problem in this paper. Any specificity of the initial vector is not depended on by the proposed method, and only one linear system needs to be solved at each iteration step. In particular, when the system matrix is a H₊-matrix, the sufficient conditions for global convergence are given. Numerical experiments are presented to show the efficiency of the proposed method,which is superior to the modified modulus-based matrix splitting iteration method in terms of numerical performances.

Global quasi-minimal residual method for solving quaternion matrix equation AX+XB=C

WU Yuling, ZHENG Jiali, KE Yifen, XU Xiaofang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 66-74. doi:10.6040/j.issn.1671-9352.0.2023.456

Abstract ( 122 )

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In this paper, the quaternion nonsymmetric Lanczos method is proposed. Based on this method, the global quaternion quasi-minimum residual method is established for solving the Sylvester quaternion matrix equation AX+XB=C, which can effectively reduce the storage space during algorithm execution. Further, some numerical examples are presented to demonstrate the feasibility and effectiveness of the proposed method.

Local analyticity of the solutions of Cauchy problems of a rotation- μ-Camassa-Holm equation and a rotation-Camassa-Holm equation

GAO Yaqin, WANG Haiquan, TENG Kaimin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 75-83. doi:10.6040/j.issn.1671-9352.0.2023.505

Abstract ( 102 )

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By utilizing the abstact Cauchy-Kovalevsky theorem, this paper first investigates the local analyticity of the solution of Cauchy problem of a rotation- μ-Camassa-Holm equation. Then, the local analyticity of the solution to Cauchy problem associated with a rotation-Camassa-Holm equation in some Sobolev-Gevrey spaces is studied by means of the generalized Ovsyannikov theorem. Besides, the lifespan of the analytic solutions will be given in detail.

Adaptive moving grid method for a second-order singularly perturbed delay boundary value problem

XU Yinuo, LIU Libin, YANG Xiu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 84-93. doi:10.6040/j.issn.1671-9352.0.2023.475

Abstract ( 101 )

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An adaptive grid algorithm for a second-order singularly perturbed delay boundary value problem is studied. Firstly, by integral transformation, the problem is rewritten into a first-order singularly perturbed delay Volterra integral differential equation. Secondly, a first-order finite difference format is constructed on an arbitrary mesh by using the backward difference and left rectangle formula. Using the discrete Grönwall inequality, a prior error estimation of the proposed discretization scheme is derived and an adaptive moving grid algorithm is designed based on the mesh equidistribution principle. It is proved that our proposed adaptive moving grid method is first-order uniformly convergent. Finally, some numerical results are given to support our presented theoretical result.

On integral inequalities of mean curvature for convex bodies in Rⁿ

LAN Yu, RAN Qiwei, ZENG Chunna

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 94-102. doi:10.6040/j.issn.1671-9352.0.2024.009

Abstract ( 115 )

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By applying integral inequalities for convex functions we obtain an estimate of the i-th order mean curvature integral powers of a convex body, thereby a strengthened form of Chen and Ros inequalities are given. Further more, by means of these obtained conclusions, we obtain the strengther form of Willmore inequality and Ross inequality, and an upper bound estimate for the curvature entropy inequality.

Periodic solutions of a second-order delay ordinary differential equation with derivative term

XI Xia, LI Yongxiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 103-109. doi:10.6040/j.issn.1671-9352.0.2023.463

Abstract ( 87 )

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In this paper, the existence and uniqueness of 2π-periodic solutions are discussed for the second-order delay ordinary differential equations with derivative term in the nonlinearity-u″(t)+a(t)u(t)=f(t,u(t),u(t-τ),u'(t)), t∈Rwhere a:R→(0,+∞)is a 2π periodic continuous function, f:R⁴→R is a continuous function and f(t,x,y,z) is 2π-periodic on t,τ>0 is a constant. The nonlinearity f satisfies some appropriate inequality conditions, the existence and uniqueness results of 2π-periodic solutions are obtained by using the Leray-Schauder fixed point theorem and the technique of prior estimates.

The existence of unique positive solution for boundary value problems of fractional differential equations with parameters and derivatives involving p-Laplacian operators

ZHENG Yanping, YANG Hui, WANG Wenxia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 110-120. doi:10.6040/j.issn.1671-9352.0.2023.438

Abstract ( 76 )

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This paper investigates the existence and uniqueness of positive solution for a class of boundary value problems of p-Laplacian fractional differential equations with a deviation and fractional derivatives involving nonlinear fractional integral terms in the boundary conditions and two parameters. Based on the cone theory and method operators, the maximum parameter interval for the existence of the unique positive solution is obtained and continuous dependence of the unique positive solution on parameters is discussed. Finally, two examples are given to illustrate the main results.

A class of three-point boundary value problems for implicit impulsive fractional differential equations

CHEN Xiao, ZHOU Wenxue, HOU Zerong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 121-129. doi:10.6040/j.issn.1671-9352.0.2024.190

Abstract ( 125 )

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In this paper, we study the existence and uniqueness of solutions for a class of semi-linear implicit impulsive Conformable fractional differential equations with three-point boundary value problems. We employ the Schaefer fixed point theorem and the Banach contraction mapping principle to derive sufficient conditions for the existence and uniqueness of solutions to the fractional differential equations, respectively. An example is given to verify the applicability and feasibility of the main conclusions.

Estimates of multilinear commutators of strongly singular Calderón-Zygmund operators on Campanato Spaces

QIANG Peipei, TAO Shuangping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 130-141. doi:10.6040/j.issn.1671-9352.0.2023.432

Abstract ( 69 )

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This paper studies the mappings properties of the multilinear commutators generated by the multilinear strongly singular Calderón-Zygmund operators and Lipschitz functions. It is proved that the multilinear commutators T_(→overb) of the strongly singular Calderón-Zygmund operators is bounded from Lebesgue spaces to Campanato spaces under some certain conditions.

Borel exceptional value of iterated order meromorphic functions with thier derivative and difference operator

LIU Jianming, WANG Qin, XIANG Xuxu, WANG Shiwen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 142-148. doi:10.6040/j.issn.1671-9352.0.2023.464

Abstract ( 102 )

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The Borel exceptional values of meromorphic functions of iterated order combined with their derivatives and n-order shift difference operators are studied by using the theory of Nevanlinna value distribution, and the conditions existenced of Borel exceptional values of meromorphic functions of iterated order combined with their derivatives and n-order shift difference operators are described in this paper.

On the space of harmonic mapping H ^p_H,1-α

HUANG Qiong, TANG Shu-an

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 149-155. doi:10.6040/j.issn.1671-9352.0.2024.191

Abstract ( 91 )

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In this paper, we introduce and investigate a class H ^p_H,1-α of harmonic space on the unit disk D and characterize some fundamental properties of this space. Then, we extend the classical Hardy-Littlewood theorem to the case of harmonic mappings. We consider the little harmonic space H ^p_H,1-α,0, and prove that it is a closed subspace of the space H ^p_H,1-α and provide a criteiton for belonging to H ^p_H,1-α,0.

S-T reconstruction of graph based on connectivity optimization

LYU Zhen, WEI Zongtian

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 156-160. doi:10.6040/j.issn.1671-9352.0.2023.462

Abstract ( 73 )

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The concept of subversion strategy and the S-T reconstruction of graphs is proposed, the problem of S-T reconstruction of graph based on connectivity optimization is discussed. A class of overlap graph with special structure is constructed, the optimal reconstruction problem of the overlap of two complete graphs based on connectivity optimization is solved.

Neighbor sum distinguishing edge coloring of join graphs C_m∨C_n

BAI Yu, QIANG Huiying, HE Jing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 161-166. doi:10.6040/j.issn.1671-9352.0.2023.385

Abstract ( 100 )

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The neighbor sum distinguishing k-edge coloring of graph G is the coloring of a proper edge coloring of graph G, where the chromatic sum of adjacent vertex associated edge are not equal. The minimum number of colors k used for coloring is called the neighbor sum distinguishing edge chromatic numbers of graph G. This paper studies the neighbor sum distinguishing edge coloring problem of the join graph C_m∨C_n, obtaining the neighbor sum distinguishing edgechromatic numbers of the join graph C_m∨C_n(n≠m) and the upper bounds of C_n∨C_n, and extending this result to join graphs of general graphs.

Distance colorings of the semistrong product and the strong product of paths

TIAN Shuangliang, CHEN Ping

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 167-172. doi:10.6040/j.issn.1671-9352.0.2024.094

Abstract ( 123 )

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A k-distance coloring of a graph G is a vertex coloring of G such that no two vertices lying at distance less than or equal to k in G are assigned the same color. The k-distance chromatic number of G, denoted χ_k(G), is the minimum number of colors needed for a k-distance coloring of G. The semistrong product of simple graphs G and H is the graph G·H with vertex set V(G)×V(H), in which (u,v) is adjacent to (u',v') if and only if either uu'∈E(G) and vv'∈E(H) or u=u' and vv'∈E(H). The strong product of simple graphs G and H is the graph GH with vertex set V(G)×V(H), in which (u,v) is adjacent to (u',v') if and only if uu'∈E(G) and vv'∈E(H), or u=u' and vv'∈E(H), or v=v' and uu'∈E(G). In this paper, for any integer k≥2, the k-distance chromatic numbers of the semistrong product and the strong product of two paths are obtained.

Spectral properties of some potential operators on Bernoulli noise functionals

DING Ruihe, WANG Caishi, ZHANG Lixia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 173-177. doi:10.6040/j.issn.1671-9352.0.2023.535

Abstract ( 66 )

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This paper considers some self-adjoint operators N_u in Bernoulli noise functionals that essentially belong to the category of potential operators. By the Full-Wiener integral transform, the unitarily equivalent multiplication operators are explicitly obtained, and thus the explicit expressions of their spectrums are further obtained. Under some mild conditions, the fact that these operators have only pure point spectra is proved. Finally, in application, the proof that the quantum system with such an operator as the Hamiltonian is stable is proved.

The Browders theorem of AB and BA

LIU Ni, JIAO Hongying, WANG Yali

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2025, 60(12): 178-182. doi:10.6040/j.issn.1671-9352.0.2024.106

Abstract ( 95 )

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Let H be complex separable Hilbert spaces. Let A,B denote the set of bounded linear operators on H. By using the method of operator block, the equivalence of Browders theorem holding for AB and BA is given, which is equivalent to Browders theorem holding for AB⊕BA.

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