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    Meta computing: a new computing paradigm under zero trust
    Xiuzhen CHENG,Weifeng LYU,Minghui XU,Runyu PAN,Dongxiao YU,Chenxu WANG,Yong YU,Xue XIAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 1-15.   DOI: 10.6040/j.issn.1671-9352.0.2023.168
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    The popularity of the Internet has had a significant impact on the development of computing paradigms. With the continuous improvement of the new generation of information technology infrastructures, academia and industry have been constantly exploring new computing paradigms to fully exploit computing powers. The huge data generated by massive IoT devices gradually exceeds the processing capability of the high-performance back-end represented by cloud servers. Edge computing alleviates this problem through cloud-edge-end coordination, but there still exist difficulties and challenges such as low computing power utilization, low computing and storage fault tolerance capability, and low integration of computing resorces. "Meta Computing" is a new computing paradigm that aims to break down the barriers of computing powers in a zero-trust environment. It can integrate all available connected computing and storage resources, provide efficient, byzantine fault-tolerant, and personalized services, while protecting the data and user privacy. Furthermere, meta computing can ensure the correctness of results, and realize "the entire network can be regarded as a giant computer for a user", that is, "Network-as-a-Computer, NaaC", which is also called "Meta Computer". The meta computer architecture includes a number of function modules including a device management module and a zero-trust computing management module, as well as the cloud-edge-end device resources. The device management module abstracts massive heterogeneous device resources into objects that can be freely manipulated, while the zero-trust computing management module can transparently allocate computing resources to user tasks according to service requirements, complete the tasks with strong fault tolerance and verifiable outputs, and finally settle accounts. Based on the analysis of the architecture and the functional characteristics of meta computing, we put forward suggestions and advice on the development path of meta computing, that is, transitioning from local to global, and analyze the most-influential future application scenarios of meta computing and provide a reasonable plan for the implementation and development of meta computing in future.

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    Milloux type inequality on holomorphic curves
    Fei LI,Liu YANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 99-106.   DOI: 10.6040/j.issn.1671-9352.0.2022.214
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    Based on the derived holomorphic curves, the Milloux type inequality of holomorphic curves is established, and the Picard type theorem is proved: let $f$ be a holomorphic curve from $\mathbf{C}$ to $P^{n}(\mathbf{C}), \nabla f$ is a derived holomorphic curve of $f$ and $\left\{H_{j}\right\}_{j=1}^{2 n+1}$ be hyperplanes in $P^{n}(\mathbf{C})$ located in general position, if $f$ omits the hyperplane family $\left\{H_{j}\right\}_{j=1}^{n+1}, \nabla f$ omits the hyperplane family $\left\{H_{j}\right\}_{j=n+2}^{2 n+1}$, then $f$ is constant, where $H_{1}, H_{2}, \cdots, H_{n+1}$ are $n+1$ coordinate hyperplanes. And some examples are given to show that the number of hyperplanes cannot be reduced and the coordinate hyperplanes cannot be generalized to arbitrary hyperplanes when $n \geqslant 2$.

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    Quasi-J-clean rings
    Yao WANG,Jianghuan CHEN,Yanli REN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 1-8.   DOI: 10.6040/j.issn.1671-9352.0.2022.507
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    The concept of quasi-J-clean rings is introduced using quasi-idempotent elements. Some examples of quasi-J-clean rings are given and their basic properties are discussed. The following results are proved. (1) If R is a quasi-J-clean ring, then the full matrix ring Mn(R) is a quasi-J-clean ring; (2) A ring R is a UJ-ring if and only if all quasi-clean elements in R are quasi-J-clean elements; (3) If R is a commutative ring, then the necessary and sufficient condition for R to be a quasi-J-clean ring is that R/I=J(R/I)∪U(R/I) if I is an ideal of R contained in J(R) and such that R/I is an indecomposable ring.

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    Probabilistic q-rung hesitant fuzzy TODIM method and its application
    Yu ZHOU,Ligang ZHOU,Zhichao LIN,Xin XU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 9-17.   DOI: 10.6040/j.issn.1671-9352.0.2022.260
    Abstract308)   HTML0)    PDF(pc) (931KB)(362)       Save

    To measure differences in probabilistic q-rung hesitant fuzzy information, a novel measure of the probabilistic q-rung hesitant fuzzy distance is proposed based on the score function and overall hesitancy. The properties of this measure are discussed. A probabilistic q-rung hesitant fuzzy TODIM method is proposed based on the new distance measure. Finally, a practical example is presented to illustrate the reasonableness and effectiveness of the proposed method, and a sensitivity analysis is performed.

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    The number of homomorphisms from dihedral groups to any finite groups
    Jie TAN,Liang ZHANG,Jidong GUO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 31-34.   DOI: 10.6040/j.issn.1671-9352.0.2022.305
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    Automorphism groups and normal subgroups of dihedral groups are studied, and the number of homomorphisms from dihedral groups to any finite group is obtained. As an application of this result, the conjecture of Asai and Yoshida is verified for dihedral groups.

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    The k-path vertex cover in some products graphs of star graph and bipartite graph
    Huiling YIN,Jingrong CHEN,Xiaoyan SU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 18-24, 39.   DOI: 10.6040/j.issn.1671-9352.0.2021.420
    Abstract280)   HTML0)    PDF(pc) (671KB)(227)       Save

    For a subset $S \subset V(G)$, if any k-path contains at least one vertex from S, then it is called a k-path vertex cover set of the graph G. The minimum cardinality of k-path vertex cover set is called the k-path vertex cover number, which is denoted by ψk(G). The k-path vertex cover problem is studied for Cartesian product graphs, lexicographic product graphs, directed product graphs of star graph and bipartite graph, and obtain an upper and a lower bound by enumeration and related concepts of subgraphs.

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    Global existence of large solutions for a class of chemotaxis-fluid model
    Zhongbo CAI,Jihong ZHAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 84-91.   DOI: 10.6040/j.issn.1671-9352.0.2022.414
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    In this paper, we are concerned with a class of chemotaxis-fluid models, which is a coupled system by parabolic-parabolic Keller-Segel equations and incompressible Navier-Stokes equations. Making full use of the weighted Chemin-Lerner type norm, the interpolation theory in Besov spaces and Fourier localization technique, the global existence of large solutions is obtained in critical Besov spaces.

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    Entire solutions of differential-difference equation of Fermat type
    Mingxin ZHAO,Guirong SUN,Zhigang HUANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 107-112.   DOI: 10.6040/j.issn.1671-9352.0.2022.540
    Abstract255)   HTML1)    PDF(pc) (625KB)(133)       Save

    By using Nevanlinna value distribution theory, this paper investigates the existence of transcendental entire solution with finite order of Fermat type differential-difference equation, and obtains one result.

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    Channel entry and buyback strategies of heterogeneous products under mixed leasing and retail channels
    Youguo JING,Junling REN,Xiaoyang LIU,Hailong WANG,Jian SONG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 1-17.   DOI: 10.6040/j.issn.1671-9352.0.2021.617
    Abstract253)   HTML0)    PDF(pc) (1615KB)(204)       Save

    A supply chain of mixed leasing and retail channels comprising of a manufacturer, a leaser and a retailer is considered. The manufacturer distributes two kinds of heterogeneous products through leasing and retail channels respectively, and buybacks part of the old rental products from the leasing channel in order to avoid the competition conflict between the retail channel and the leasing channel through which these old rental products may flow into the retail market. The following channel entry and buyback strategies of two heterogeneous products: high-quality and low-quality products entering the leasing (retail) and retail (leasing) channels respectively, which are referred to as strategies of H and L. Two two-cycle dynamic game models of channel entry and buyback strategies are compared and analyzed by using the dynamic game theory. The results show that, under the above two strategies, when the buyback price is high, a so-called buybacks situation will arise. In the case of buyback situation, the buyback price is always lower than the resale price, the manufacturer's profit margin through the retail channel is always higher than that of the leasing channel, and the manufacturer's profit margin of the strategy L is higher than that of the strategy H; the buyback price, buyback quantity and resale price of the strategy H are always higher than that of the strategy L. Finally, the numerical simulation analysis shows that when the product quality difference coefficient is small, the manufacturer should choose the strategy L; otherwise, the manufacturer should choose the strategy H.

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    The numerical range of the operator P+QP
    Chen ZHANG,Weiyan YU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 92-98.   DOI: 10.6040/j.issn.1671-9352.0.2022.485
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    In this paper, the numerical range of the combination P+QP of two orthogonal projections P and Q on a complex separable Hilbert space $\mathscr{H}$ is studied. Firstly, the support function of the numerical range of P+QP is given by using the method of operator block. Next, by using the properties of the support function, a geometric characterization of the numerical range of the operator P+QP is given. That is, the closure of its numerical range is a closed convex hull of some explicit ellipses parameterized by points in the spectrum.

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    R&D innovation strategy and behavior choice of competition drug supply chain
    Yan WEN,Xiyuan YU,Jinsong HU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 18-31.   DOI: 10.6040/j.issn.1671-9352.0.2021.417
    Abstract237)   HTML1)    PDF(pc) (2658KB)(134)       Save

    Based on the short-sighted and far-sighted behaviors of members of competitive drug supply chain, four dynamic differential game models were constructed to study the influences of different behavior choices, changes in competition intensity and reimbursement ratio of medical insurance on drug manufacturers' R & D innovation investment, medical institution' cost-sharing strategies and supply chain performance. The study found that although the competition between drug manufacturers harms the profits of short-sighted manufacturer, it increases the overall performance of the drug supply chain and promotes the higher R & D innovation investment of far-sighted manufacturer. With higher reimbursement rate, both far-sighted drug manufacturer and medical institution have increased their profits, but not short-sighted drug manufacturer. In addition, medical institution sharing costs with one manufacturer would depress the profits of the other, when medical institution choose the behavior mode of sharing drug R & D innovation costs for two competing manufacturers simultaneously, they can benefit the profits of all members of the drug supply chain.

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    Existence of mild solutions for the nonlocal problem of second-order impulsive evolution equations
    Li LI,He YANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 57-67.   DOI: 10.6040/j.issn.1671-9352.0.2022.595
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    A new definition of mild solutions of the second-order impulsive evolution equations involving nonlocal condition $ u(0)=\sum\limits_{k=1}^n C_k u\left(\tau_k\right)$ is given by introducing a Green function. Then, the existence of mild solutions of the concerned problem is proved by applying the Sadovskii fixed point theorem. At last, an example is provided as an application of the obtained abstract result.

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    Rational conjugacy of torsion units in integral group rings of nilpotent-by-Abelian groups
    Xian LING,Jinke HAI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 1-5.   DOI: 10.6040/j.issn.1671-9352.0.2022.555
    Abstract235)   HTML0)    PDF(pc) (652KB)(215)       Save

    Let G be a semidirect product of a finite nilpotent group N by a finite Abelian group A with (|N|, |A|)=1, it is shown that under some conditions any normalized torsion unit of the integral group ring ZG of G is rationally conjugate to an element of G.

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    A new method of neighbor sum distinguishing total coloring of graphs
    Jingzhi CHANG,Chao YANG,Bing YAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 35-39.   DOI: 10.6040/j.issn.1671-9352.0.2022.220
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    The neighbor sum distinguishing 2-total coloring of a tree is presented along with the independence of the minimum decycling set of a 3-regular graph and the acyclicity of the corresponding decycling subgraphs. This method provides a simple way to prove that the neighbor sum distinguishing total chromatic number of a 3-regular graph satisfies the 1-2 Conjecture. The independent decycling set method is used to determine the neighbor sum distinguishing total chromatic number of an r-regular graph, Halin graph, and Cartesian product graph of paths.

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    Graph N[S]-T reconstruction based on neighbor connectivity optimization
    Le CHANG,Zongtian WEI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 40-45, 76.   DOI: 10.6040/j.issn.1671-9352.0.2021.454
    Abstract228)   HTML0)    PDF(pc) (2214KB)(120)       Save

    Considering the neighbor invulnerability recovery of a damaged network based on the optimization idea, the neighbor subversion strategy and the concept of reconstruction are proposed. The problem of graph reconstruction based on neighbor connectivity optimization is studied. An optimal reconstruction method and an algorithm of Cartesian product graph of two complete graphs under the optimal neighbor subversion strategy are presented.

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    Continuous dependence of solution for impulsive evolution equations with infinite delay
    Pan SUN,Xuping ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 77-83, 91.   DOI: 10.6040/j.issn.1671-9352.0.2022.469
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    By comprehensive applying the theory of operator semigroups and method of nonlinear analysis, this paper will investigate the existence of mild solutions and the continuous dependence of mild solutions to initial values for the initial problem of impulsive evolution equations with infinite delay.

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    Steady-state solutions of a Holling type Ⅱ competition model in heterogeneous environment
    Zipeng HE,Yaying DONG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 73-81.   DOI: 10.6040/j.issn.1671-9352.0.2021.782
    Abstract222)   HTML2)    PDF(pc) (712KB)(117)       Save

    The steady-state solutions of a competitive model with Holling type Ⅱ functional response function in heterogeneous environment is investigated. Using the spectral theory of linear operators and comparison principle of parabolic equations, the global asymptotic stability of the trivial and semi-trivial solutions of the model is obtained, and the sufficient conditions for the competitive repulsion of two species are derived. With the help of topological degree theory, the sufficient conditions for the existence of positive steady-state solutions are established, which gives the sufficient conditions for the coexistence of the two species.

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    Peak value and peak time of nonlinear heterogeneous epidemic model
    Shengqiang LIU,Ningjuan MA
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 1-12.   DOI: 10.6040/j.issn.1671-9352.0.2023.340
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    The study focuses on analyzing the transmission mechanisms of nonlinear heterogeneous epidemic models within a short-time frame. As a result, novel criteria for determining the peak value and peak time of a heterogeneous epidemic model are achieved, and numerical fitting is applied to prove the efficient of the mold.

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    θ-almost periodic solutions for stochastic differential equations in infinite dimensions with Stepanov almost periodic coefficients
    Yejun CHEN,Huisheng DING
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 113-126.   DOI: 10.6040/j.issn.1671-9352.0.2022.486
    Abstract220)   HTML2)    PDF(pc) (761KB)(131)       Save

    Based on the work of Raynaud de Fitte, in this paper, we consider almost periodicity of stochastic differential equations in infinite dimensions with Stepanov almost periodic coefficientsUnder the weaker conditions (C0-semigroup generated by A is not necessarily contractive, and F, G can be Stepanov almost periodic and not necessarily almost periodic), we obtain the existence and uniqueness of θ-almost periodic solutions of these equations, and furthermore, we prove that the solution is almost periodic in path distribution.

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    Balancing numbers which are concatenations of three repdigits
    Shanshan ZHU,Yunyun QU,Jianhua ZHOU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 25-30.   DOI: 10.6040/j.issn.1671-9352.0.2022.459
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    It is proved that 204 and 1 189 are the only Balancing numbers which are concatenations of three repdigits by using the linear forms in logarithms of algebraic numbers and the Baker-Davenport reduction method.

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    On S-acts satisfying Condition (PI)
    Xingliang LIANG,Yun DANG,Xueying CHEN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 6-12.   DOI: 10.6040/j.issn.1671-9352.0.2022.437
    Abstract207)   HTML0)    PDF(pc) (691KB)(135)       Save

    Let I be an ideal of a monoid S. Firstly, the basic properties of the S-acts satisfying Condition (PI) are investigated. The relations between coproducts, directed colimits, Rees short exact sequences, and Condition (PI) are established respectively, and a necessary and sufficient condition of Condition (PI) is provided by purity of epimorphisms for S-acts. Then, using the concept of I-(locally) cyclic S-acts, the sufficient and necessary conditions of direct products of S-acts preserving Condition (PI) are given. Finally, cover of S-acts with Condition (PI) is studied, and a new characterization of monoids over which every S-act has a Condition (PI)-cover is presented.

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    Dynamic neighborhood rough sets approaches for updating knowledge while attributes generalization
    Chengxiang HU,Li ZHANG,Xiaoling HUANG,Huibin WANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 37-51.   DOI: 10.6040/j.issn.1671-9352.4.2022.5896
    Abstract206)   HTML0)    PDF(pc) (9251KB)(154)       Save

    We propose the matrix-based dynamic methods for updating three-way regions in neighborhood decision systems while attributes generalizing. First, we construct the matrix representation strategy of three-way regions for each decision class by means of neighborhood relation matrix and neighborhood distance matrix.Subsequently, considering the variation of the attributes, the updating strategies for related matrices are analyzed by using prior knowledge. Based on these strategies, we propose the matrix-based incremental methods for updating neighborhood three-way regions of each decision class. Finally, we evaluate the efficiency of the proposed incremental methods on public available data sets.

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    Optimal reinsurance contract design based on Stackelberg game
    Peng YANG,Xiaoyan ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 1-14,26.   DOI: 10.6040/j.issn.1671-9352.0.2022.265
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    For the optimal reinsurance contract design problem, that is, the reinsurance premium pricing problem, we assume that there is an insurance company and a reinsurance company on the market. Among them, the insurance company is engaged in two types of insurance business, and the reinsurance company is engaged in one type of insurance business. To reflect the competition between the insurance company and the reinsurance company, we assume that these three insurance businesses are interdependent, and the insurance company can engage in the reinsurance business. Using the relative performance, the competition between the insurance company and the reinsurance company is quantified. The aims of the insurance company and the reinsurance company are to find an optimal reinsurance contract to maximize the mean of the terminal wealth and minimize the variance of the terminal wealth. Under the Stackelberg game framework, by using stochastic calculus and stochastic control theory, the explicit solutions for the optimal reinsurance contract and the optimal value function are obtained. Finally, the influence of model parameters on the optimal reinsurance contract is analyzed through numerical experiments and the relationship between some special cases and general cases is compared.

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    Extension sequential three-way decision model and its application
    Junyu WANG,Yafeng YANG,Jingxuan XUE,Lihong LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 67-79.   DOI: 10.6040/j.issn.1671-9352.4.2022.9768
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    The basic method of extension evaluation and the "rule by three divisions" decision-making idea are integrated, and the sequential idea is introduced to construct an extension sequential three-way decision model and realize the purpose of dynamic decision-making and mining optimization indicators. Firstly, the data is standardized and the weight of attributes is calculated. The extension evaluation method is used as the evaluation criterion of the three-way decisions, new decision rules are defined, and the rationality of dividing the three domains is explained. Then, according to the attribute weight, the sequential evaluation attributes of multiple granularity are obtained, the multi-stage three-way decision is made, and the decision results are given. Finally, according to the decision-making results, the indicators that cause changes in sample division are analyzed, and optimization suggestions are put forward. The model was applied to the analysis of water resources carrying capacity, and compared with the entropy weight matter-element extension decision-making model. The results show that the evaluation results obtained by using the extension sequential three-way decision model and the entropy weight matter-element extension decision-making model are basically consistent, the accuracy rate reaches 84.55%, which verifies the validity and practicability of the model.

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    Analysis of evaluation model on teaching effect based on cluster analysis and discrimination information
    Xin JIN,Feifan YU,Yutong DAI,Ziqian LI,Yongkui ZOU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 115-120.   DOI: 10.6040/j.issn.1671-9352.0.2022.523
    Abstract193)   HTML1)    PDF(pc) (826KB)(101)       Save

    In this paper, a cluster analysis algorithm and discriminant information method are used to construct a correlation model for evaluating the academic level of college students and student management measures. Based on the average number, median number, pass rate, excellent rate and the degree of distinction, a coefficient is proposed to evaluate the effectiveness of teaching reform measures and the effectiveness of the coefficient is analyzed. We apply this method to 9 years of cumulative grade data including multiple courses, analyze the correlation between grade changes and related management measures, and verify the validity of the model.

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    Global BMO estimations for obstacle problems of a class of non-uniformly elliptic equations
    Yanmin GUO,Song ZHAO,Yuxia TONG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 46-56.   DOI: 10.6040/j.issn.1671-9352.0.2022.520
    Abstract192)   HTML0)    PDF(pc) (724KB)(81)       Save

    The regularity of weak solutions to the obstacle problem for non-uniformly elliptic equations is studied. When the gradient of the solution to the asymptotic regular problem is close to infinity, the solution of the regular problem is used to obtain an approximate solution to the asymptotic regular problem, and the bounded mean oscillation (BMO) estimates of the weak solutions gradient of the obstacle problem are obtained based on the Young inequality and perturbation discussion.

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    Optimization of blockchain sharding by profit incentive algorithm based on edge computing
    Yun LIU,Pengjun ZHU,Luyao CHEN,Kai SONG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 88-96.   DOI: 10.6040/j.issn.1671-9352.0.2021.681
    Abstract189)   HTML1)    PDF(pc) (1672KB)(285)       Save

    A Profit Incentive (PI) algorithm is proposed. First, the delay and energy consumption of a block generated by a single node are calculated, and the final profit of the node is calculated according to the delay and energy consumption. Next, the average partition credibility of the node is calculated according to the credibility model based on edge computing. Next, the node chooses the partition that can maximize its profit without reducing the other nodes′ profit and average partition credibility. Finally, a stable sharding structure is obtained to maximize the profit of all nodes and the reliability of sharding. Simulation results show that, compared with OmniLedger, domain based sharding scheme and credibility based blockchain algorithm, PI algorithm can improve the stability of blockchain sharding without reducing throughput.

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    Some equivalent characterizations on EP elements
    Mengge GUAN,Hainan ZHOU,Junchao WEI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 13-17.   DOI: 10.6040/j.issn.1671-9352.0.2022.345
    Abstract187)   HTML0)    PDF(pc) (660KB)(110)       Save

    By studying the properties of EP elements and their association with idempotents and Jacobson radicals, some equivalent characterizations of EP elements are presented. A new structure is introduced to facilitate the equivalent characterizations of EP elements through Moore-Penrose(MP) inverses and the relationship between group inverses. Finally, by constructing some equations on the ring, the equivalent characterizations of EP elements are established by finding solutions on specific sets.

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    Transition behavior of underdamped periodic potential system driven by Gaussian noise and Lévy noise
    Jiaxin DING,Yongfeng GUO,Lina MI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 111-117.   DOI: 10.6040/j.issn.1671-9352.0.2022.538
    Abstract185)   HTML1)    PDF(pc) (1348KB)(68)       Save

    In the study of an underdamped periodic potential system, multiplicative Gaussian white noise and additive Lévy noise are introduced simultaneously. First, the second-order underdamped periodic potential system is equivalent to two first-order stochastic differential equations. Then, Lévy noise is generated by Janicki-Weron algorithm, the steady-state probability density function of the equation is simulated by the numerical simulation, and the dynamic characteristics of the underdamped periodic potential system are analyzed. It is found that system parameter, friction coefficient, stability index, skew parameter, multiplicative noise intensity and additive Lévy noise intensity can induce phase transition. In addition, it can be observed that the increase of system parameter and the friction coefficient is conducive to the stable state of particles.

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    Existence and multiplicity of positive solutions for a class of second-order periodic boundary value problems
    Congcong KANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (6): 68-76.   DOI: 10.6040/j.issn.1671-9352.0.2022.433
    Abstract183)   HTML0)    PDF(pc) (653KB)(141)       Save

    This paper considers the existence and multiplicity of positive solutions for second-order periodic boundary value problems where p, q>0 are constants and satisfy p2>4q, λ>0 is a parameter, f: [0, 2π]×[0, +∞)→[0, +∞) is continuous. The proof of the main results are based on the fixed point theorem of cone expansion-compression.

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    Gorenstein cotorsion modules of Noetherian rings
    Yadong LUO,Gang YANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 38-42.   DOI: 10.6040/j.issn.1671-9352.0.2022.630
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    Let R be a left Noetherian ring. It is proved that if the Gorenstein flat cover of any injective precover of a left R-module M is injective, then the Gorenstein flat cover of M is injective if and only if every injective f : EM of M is surjective and Ker f is Gorenstein cotorsion.

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    Time-controlled designated tester proxy re-encryption with keyword search scheme
    Jiao LYU,Xi ZHANG,Jing QIN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 16-27.   DOI: 10.6040/j.issn.1671-9352.0.2022.154
    Abstract176)   HTML1)    PDF(pc) (1881KB)(118)       Save

    To solve the problem that the proxy re-encryption with keyword search is used to implement ciphertext data exchange and sharing, but it does not support time-controlled access authorization and cannot resist off-line keyword guessing attack, a time-controlled designated tester proxy re-encryption with keyword search scheme is proposed, which supports the data owner to grant dynamically the search and decryption rights of the ciphertext data in the cloud to the data user within a specified time range, and can resist the off-line keyword guessing attack by external adversaries. In addition, the scheme is applied to the scenario of sharing patients electronic medical records between different hospitals, and a specific electronic medical records sharing scheme is designed based on the consortium blockchain.

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    Dynamics of a two-strain co-infection epidemic model with vaccination
    Gang CHEN,Rui ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 84-96.   DOI: 10.6040/j.issn.1671-9352.0.2022.543
    Abstract173)   HTML3)    PDF(pc) (1486KB)(188)       Save

    To explore the dynamics of co-infection of multiple strains in the same host population, a mathematical model of co-transmission dynamics of two strains after continuous inoculation with strain 1 vaccine is established and analyzed. Firstly, the sufficient conditions for the existence of four equilibrium points are obtained by calculating and analyzing the model. In addition to the disease-free equilibrium point and the two single endemic equilibrium points, the model also has an endemic equilibrium point where both strains 1 and 2 coexist. Secondly, Lyapunov stability theorem is used to prove that the disease-free equilibrium is globally stable when the basic reproduction number of two strains is less than 1. The invasion-reproduction number is introduced to determine the stability of the single-strain endemic equilibrium point. When the corresponding invasion reproduction number is less than 1, the endemic equilibrium point of the strain is locally stable. Then, using Castillo-Chavez and Song?s bifurcation theorem, it is proved that the model does not have backward bifurcation phenomenon, and then it is proved that the coexistence equilibrium point is locally asymptotically stable when the basic reproduction number of the two strains is greater than 1. Finally, the above conclusions are verified by numerical simulation.

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    An encryption scheme supporting wildcard and fuzzy search
    Bo ZHAO,Jing QIN,Jinlu LIU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 28-38.   DOI: 10.6040/j.issn.1671-9352.0.2022.471
    Abstract173)   HTML0)    PDF(pc) (2133KB)(257)       Save

    Based on n-gram technology, this paper proposes an encryption scheme that can support both wildcard and fuzzy search. In addition, using the Bloom filter optimization scheme, it reduces the index storage overhead and search time. The given security analysis shows that the scheme is non-adaptive semantic security. The performance analysis shows that the optimized scheme has less overhead in storage, communication and trapdoor generation than the previous schemes.

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    A new filled function method for global optimization
    Haiyan LIU,Shouheng TUO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 80-87.   DOI: 10.6040/j.issn.1671-9352.0.2022.344
    Abstract169)   HTML0)    PDF(pc) (1357KB)(184)       Save

    A new hybrid single-parameter filled function is proposed which is also continuous and differentiable. Combined with an evolutionary algorithm, a new filled function algorithm is proposed. The new filled function algorithm can improve the efficiency of the optimization by repeatedly escaping from current local optimum to better areas with better solutions. To enhance the explore ability of the proposed algorithm, we use uniform distribution to make better population diversity. Numerical experiments show the simplicity and efficiency of the proposed algorithm.

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    Assessment of procedural knowledge: from problem spaces to discriminative knowledge structures
    Xiyan CAO,Fucai LIN,Ming JIN,Jinjin LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 97-105, 114.   DOI: 10.6040/j.issn.1671-9352.0.2022.156
    Abstract161)   HTML0)    PDF(pc) (950KB)(46)       Save

    In order to reduce repeated testing and evaluate 'relative independence' items on assessment of knowledge, the paper proposes the approach based on the assessment of procedural knowledge that the problem space approach derives the discriminative (bi-discriminative) knowledge structure via skill map. Some theoretical conditions and an algorithm for deriving a discriminative (bi-discriminative) from a problem space are illustrated.

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    A object detection algorithm for aerial images
    Cheng LI,Wengang CHE,Shengxiang GAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 59-70.   DOI: 10.6040/j.issn.1671-9352.0.2022.349
    Abstract158)   HTML5)    PDF(pc) (13595KB)(157)       Save

    A object detection algorithm DSB-YOLO (depthwise separable convolutional backbone and YOLO) for aerial images is proposed. Based on YOLOv5s, firstly, from the perspective of extracting the perceptual field of the feature map from the backbone network, the perceptual field of the feature map is reduced by changing the interval sampling of the convolutional kernel to better extract the information of small objects. Secondly, the feature pyramid network (FPN) and path aggregation network (PAN) feature fusion paths in the Neck part of the network are improved, so that the large amount of location information in the shallow sampled feature maps can be better combined with the deep extracted feature maps of the network. This allows the network to combine the large amount of location information in the shallow sampled feature map with the deep extracted feature map, effectively improving the accurate detection rate of small objects. The C3Transformer module was then added to the backbone network to integrate the full image information; then, the network was lightened by replacing the partial convolution of the network backbone with a depth-separable convolution and integrating the SE attention mechanism, which aims to focus and select the information useful for the object detection task, thus improving the detection efficiency of the model. Comparative experimental results using the VisDrone dataset show that, at an input image resolution of 1 280×1 280 pixels, the DSB-YOLO algorithm proposed in this paper tests average accuracy metrics mAP50 and mAP0.5 ∶0.95 that are 11% and 17.5% higher, respectively, compared to the original model; Deployed on the embedded platform Jetson TX2, computing rates of up to 21FPS can be achieved and model performance meets applicable standards.

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    Lyapunov stability of decision evolution set
    Yuwen HU,Jiucheng XU,Qianqian ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 52-59.   DOI: 10.6040/j.issn.1671-9352.4.2022.6266
    Abstract157)   HTML0)    PDF(pc) (2066KB)(89)       Save

    By using the Lyapunov second method, the evolution matrix of the decision information system is extended and reconstructed, and the Lyapunov function of the decision information system at a certain point in time is established, and the stability of the decision information system is judged by the function.

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    An automatic protocol vulnerability detection framework for resource-constrained devices of LPWAN
    Feixu LI,Fei YAN,Binlin CHENG,Liqiang ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 39-50.   DOI: 10.6040/j.issn.1671-9352.0.2022.660
    Abstract157)   HTML6)    PDF(pc) (1396KB)(171)       Save

    LPWAN(low power wide area network)as a protocol that emphasizes low power consumption usually runs on resource-constrained devices. On the one hand, limited resources bring serious challenges to the security of protocol implementation. Manufacturers may have trouble balancing security demands and resource consumption. On the other hand, protocol stacks are deployed on constrained devices as bare-metal firmware. The varying hardware characteristics make automatic analysis difficult. Therefore, a protocol stack analysis framework called ProSE is proposed. Based on symbolic execution and taint analysis, ProSE is specifically designed for protocol vulnerability detection on the firmware of constrained devices. LoRaWAN is chosen for analysis due to its popularity. The framework is capable of detecting various types of vulnerability. ProSE successfully detected 20 potential security vulnerabilities in the implementation of LoRaWAN of 6 manufacturers.

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    Research on incentive mechanism of manufacturing workers based on fairness preference theory
    Guan WANG,Zhao WANG,Xinhong ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 95-103.   DOI: 10.6040/j.issn.1671-9352.0.2022.325
    Abstract156)   HTML0)    PDF(pc) (4118KB)(147)       Save

    Based on the cooperation between managers and workers of small and medium-sized manufacturing enterprises, the fair preference theory is introduced and the traditional principal-agent model is improved. The optimal incentive mechanism for workers with different degrees of fair preference is designed. Data simulation and example analysis are carried out on the model. The results show that the different fairness preference of both parties changes the optimal salary distribution plan, and the fatigue level of workers is also significantly different; the employment of workers with higher fairness preference increases the value of the enterprise output and managers' expected net income. In this regard, suggestions for the development of small and medium-sized manufacturing enterprises are put forward, which can provide a reference for the salary distribution of domestic small and medium-sized manufacturing enterprises.

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