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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
    Abstract313)   HTML0)    PDF(pc) (931KB)(381)       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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    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
    Abstract462)   HTML11)    PDF(pc) (7010KB)(338)       Save

    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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    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
    Abstract216)   HTML3)    PDF(pc) (1443KB)(332)       Save

    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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    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
    Abstract236)   HTML15)    PDF(pc) (2578KB)(307)       Save

    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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    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
    Abstract225)   HTML0)    PDF(pc) (639KB)(299)       Save

    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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    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
    Abstract193)   HTML1)    PDF(pc) (1672KB)(296)       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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    A new modified efficient Shamanskii-like Levenberg-Marquardt method for solving systems of nonlinear equations
    Minglei FANG,Defeng DING,Ming WANG,Yuting SHENG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 118-126.   DOI: 10.6040/j.issn.1671-9352.0.2022.597
    Abstract157)   HTML2)    PDF(pc) (721KB)(277)       Save

    A new Shamanskii-like Levenberg-Marquardt method(SLM) to solve systems of nonlinear equations is presented by introducing parameters in this paper. With m order nonmonotone Armijo line search, the global convergence of the new algorithm is proved and the convergence rate of whom is shown to be m+1. Numerical experiments demonstrate that the new algorithm can solve large scale problems effectively.

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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
    Abstract183)   HTML0)    PDF(pc) (2133KB)(271)       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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    Parameter estimation for the sub-fractional Vasicek model based on discrete observation
    Cuiyun ZHANG,Jingjun GUO,Aiqin MA
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 15-26.   DOI: 10.6040/j.issn.1671-9352.0.2022.317
    Abstract142)   HTML1)    PDF(pc) (457KB)(254)       Save

    The problem of statistical analysis of the Vasicek model driven by sub-fractional Brownian motion is mainly investigated. Firstly, based on discrete observations, the estimation of drift parameters μ and θ in Vasicek model are given by the least square estimation method. Secondly, for the θ≠0 and θ=0 cases, the consistency and the asymptotic distribution of the estimators are obtained, respectively. Finally, simulations are performed with the Monte Carlo method to demonstrate the unbiasedness and validity of the estimates.

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    Strategic limit theory and strategic statistical learning
    Xiaodong YAN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2024, 59 (1): 1-10, 45.   DOI: 10.6040/j.issn.1671-9352.0.2023.512
    Abstract126)   HTML3)    PDF(pc) (2306KB)(252)       Save

    The nonlinear expectation is an original research direction pioneered by Academician Peng Shige of Shandong University, which is becoming increasingly important in various fields of scientific research. The rise of big data and artificial intelligence has provided stronger impetus for innovative theoretical and applied research in nonlinear expectation. Recently, Shandong University's Nonlinear Probability Team has developed the "Strategy Limit Theory" based on the strategic game process of multi-armed bandits, representing a significant breakthrough in the intersection of nonlinear probability theory and reinforcement learning. This has tran-sformed the research paradigm of traditional statistical methods. Based on the proposed 10 basic mathematical problems of artificial intelligence by Academician Xu Zongben, the declaration guide of 2022 major research plan projects issued by the National Natural Science Foundation of China for the research about universal and interpretable artificial intelligence technologies, and the application guide for basic mathematical theory research of artificial intelligence in 2021 and 2022 the key projects of "Mathematics and Applied Research" issued by the Ministry of Science and Technology, this article adopts the concept of "strategy" to reveal the nature of artificial intelligence and explore and the motivation source and theoretical basis for initiating and promoting the innovation of artificial intelligence technology. Different from the applications of the traditional law of large numbers and the central limit theorem in the field of artificial intelligence, we propose novel theory about the strategic law of large numbers and the central limit theorem in the new generation of artificial intelligence. The discussed topics in this work include but not limited to: (1) strategic sampling of massive data; (2) online learning of streaming data; (3) the central limit theorem of reinforcement learning; (4) differential privacy protection of data; (5) strategic integration of federal learning; (6) information reconstruction of transfer learning and meta learning; (7) the fusion of knowledge reasoning and data driving.

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    Construction of Gorenstein projective modules over tensor rings
    Guoliang TANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (8): 33-37.   DOI: 10.6040/j.issn.1671-9352.0.2022.634
    Abstract148)   HTML2)    PDF(pc) (654KB)(246)       Save

    Let R be any ring, M a nilpotent R-bimodule, TR(M) is the associated tensor ring. Suppose that ExtR1(G, MRiRP)=0=Tor1R(M, MRiRG), where P is a projective R-module, G is a Gorenstein projective R-module, and i≥0. It is proved that a TR(M)-module: (X, u) is a Gorenstein projective TR(M)-module if u is a monomorphism and the cokernel of u is a Gorenstein projective R-module.

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    Stability of a single population delayed reaction-diffusion model with Dirichlet boundary condition
    Yonghua LI,Cunhua ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 122-126.   DOI: 10.6040/j.issn.1671-9352.0.2023.131
    Abstract113)   HTML4)    PDF(pc) (344KB)(241)       Save

    This paper studies the dynamics of a single population delayed reaction-diffusion model with Dirichlet boundary condition in a bounded domain. The existence and multiplicity of spatially nonhomogeneous steady-state solution is investigated by employing Lyapunov-Schmidt reduction method. Then, the stability of spatially nonhomogeneous steady-state solution is derived by analyzing the distribution of the eigenvalues.

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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
    Abstract284)   HTML0)    PDF(pc) (671KB)(239)       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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    On the generalized characteristic polynomial of a family of graphs
    Ranran WANG,Fei WEN,Shucheng ZHANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 165-174.   DOI: 10.6040/j.issn.1671-9352.0.2022.062
    Abstract101)   HTML0)    PDF(pc) (957KB)(225)       Save

    Firstly, a class of graphs called thresholdlike graphs is defined. Then, combined with algorithm, the generalized characteristic polynomial (i.e., Φ-spectrum) of such graphs is obtained. The Φ-characteristic polynomial and its spectrum of a class of threshold graphs are derived. As an application, some infinite classes of Φ-cospectra have also been constructed.

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    Polytomous knowledge structure and learning path in formal context
    Yujing LIN,Jinjin LI,Huiqin CHEN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (9): 114-126.   DOI: 10.6040/j.issn.1671-9352.0.2022.504
    Abstract126)   HTML0)    PDF(pc) (1108KB)(223)       Save

    Based on the polytomous evaluation system of problem solving, a method of formal concept analysis is employed to construct the polytomous knowledge structure, to find the learning path and to evaluate operation procedure, in order to effectively guide the learning of learners. Firstly, a method of constructing polytomous knowledge structure from the formal concept lattice of operation procedure is proposed. Secondly, the formal context of well-formed operating procedure is introduced, in which step-by-step learning and effective evaluation of operating procedures can be carried out. Finally, the algorithm steps to find the learning path under the disjunctive model are designed, and the effectiveness of the algorithm steps is illustrated with examples.

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    Embedded generation of micro-information and its intelligent hiding-restoration
    Shuzhen CHEN,Kaiquan SHI,Shouwei LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 1-9.   DOI: 10.6040/j.issn.1671-9352.0.2023.160
    Abstract155)   HTML6)    PDF(pc) (879KB)(223)       Save

    Based on the P-set model with dynamic properties and attribute ensemble-fetching properties, the embedding generation and hiding of $\alpha^{F}$-micro-information, $\alpha^{\bar{F}}$-micro-information and ($\alpha^{F}$, $\alpha^{\bar{F}}$)-micro-information are given. Using these concepts, the micro-information system and its structure, and the intelligent hiding of micro-information and its restoration-acquisition are given, and finally the applications of these concepts are introduced.

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    Dynamics of a reaction-diffusion predator-prey model incorporating prey refuge and fear effect
    Qian CAO,Yanling LI,Weihua SHAN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 43-53.   DOI: 10.6040/j.issn.1671-9352.0.2022.308
    Abstract133)   HTML0)    PDF(pc) (5701KB)(223)       Save

    For a reaction-diffusion predator-prey system with prey refuge and fear effect, the Turing instability of the positive constant solution for the system and a priori estimates of solutions for the system are investigated. It is proved that there is no nonconstant positive steady-state solution for the system under certain parameter conditions. Moreover, taking the diffusion coefficient of the predator as the bifurcation parameter, the global structure of the bifurcation solution is constructed. It is found that the bifurcation solution can be extended to infinity when the diffusion coefficient of predator is greater than some critical value. Finally, by numerical simulations, the theoretical results are verified and supplemented.

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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
    Abstract238)   HTML0)    PDF(pc) (652KB)(221)       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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    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
    Abstract326)   HTML0)    PDF(pc) (692KB)(217)       Save

    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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    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
    Abstract293)   HTML2)    PDF(pc) (613KB)(214)       Save

    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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    Integrability and Birkhoff normal form of the dispersive Camassa-Holm equation
    Xiaoping WU,Gezi CHONG,Ziwen JIANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 76-85.   DOI: 10.6040/j.issn.1671-9352.0.2023.063
    Abstract111)   HTML0)    PDF(pc) (437KB)(213)       Save

    Based on the infinitely many conserved quantites of the non-dispersive Camassa-Holm equation defined on the circle, we construct the infinitely many new ones whose quadratic parts have a consistent form for the corresponding dispersive equation. As an important application, we prove that the Birkhoff normal form of any order for the dispersive Camassa-Holm equation is action-preserving.

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    Equilibrium of dual-channel supply chain considering manufacturer online referral under different power structures
    Tingting GUO,Zhengxiang WU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 104-115.   DOI: 10.6040/j.issn.1671-9352.0.2022.213
    Abstract140)   HTML0)    PDF(pc) (521KB)(212)       Save

    Based on Stackelberg and Bertrand game theory, the optimization models of dual-channel supply chain with manufacturer online referral under three power structures are established, and the dual-channel supply chain equilibrium in different situations is studied. Through comparative analysis of the dual-channel supply chain equilibrium, the issue of whether the manufacturer and the physical retailer can reach an agreement on the selection of online referral method is discussed. The effect of the online referral method on product pricing, total market demand of the channel, and the first-mover advantage of the manufacturer or the physical retailer act as the supply chain leader are analyzed. The results show that the manufacturer and the physical retailer have the same preference for online referral method. Online referral method will not change the online retail price of the product, but it will change the wholesale price and the physical retail price. In addition, when the manufacturer promotes both the online direct channel and the physical retail channel, the total market demand of the online direct channel will be reduced, the total market demand of the physical retail channel will be increased. The online referral method will not affect the first-mover advantage when manufacturer or physical retailer act as supply chain leader.

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    A memory network model based on semantic expansion of text for query suggestion
    Naizhou ZHANG,Wei CAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 10-21.   DOI: 10.6040/j.issn.1671-9352.2.2022.484
    Abstract120)   HTML0)    PDF(pc) (4344KB)(210)       Save

    A novel memory network model based on the semantic expansion of text is proposed to generate context-aware query suggestions. An attention-based hierarchical encoder-decoder model is employed, utilizing an external memory network to generate the neural attention vector between the query and the related document. The model fuses query-layer, session-layer, and document-layer semantic information. Compared with state-of-the-art approaches, our model can generate context-aware query suggestions with higher relevance. Extensive experiments using real commercial search engine query logs demonstrate the effectiveness of the proposed model.

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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
    Abstract258)   HTML0)    PDF(pc) (1615KB)(208)       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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    Linear arboricity on embedded graphs without adjacent short cycles
    Hongjun DU,Huijuan WANG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 147-154.   DOI: 10.6040/j.issn.1671-9352.0.2022.221
    Abstract124)   HTML0)    PDF(pc) (582KB)(204)       Save

    Linear arboricity is an improper edge coloring. The linear arboricity of a graph refers to the minimum number that the edge set is divided into linear forests. By using discharging method, we proved a conclusion about a graph G which can be embedded in a surface of non-negative Euler characteristic with maximum degree Δ≥7. If there exist two fixed integers i, j∈{3, 4, 5, 6} such that G has no adjacent i- cycles or j- cycles, then its linear arboricity is $\left\lceil\frac{\Delta}{2}\right\rceil $.

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    Multimodal sentiment analysis based on text-guided hierarchical adaptive fusion
    Chan LU,Junjun GUO,Kaiwen TAN,Yan XIANG,Zhengtao YU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 31-40, 51.   DOI: 10.6040/j.issn.1671-9352.1.2022.421
    Abstract134)   HTML4)    PDF(pc) (1947KB)(203)       Save

    The paper proposes a multi-modal hierarchical fusion method based on text modal guidance, which uses text modal information as the guidance to achieve hierarchical adaptive screening and fusion of multi-modal information. Firstly, the importance information representation between two modalities is realized based on the cross-modal attention mechanism, then the hierarchical adaptive fusion based on the multimodal important information is realized through the multimodal adaptive gating mechanism, and finally the multimodal features are synthesized. and modal importance information to implement multimodal sentiment analysis. The experimental results on the public datasets MOSI and MOSEI show that the accuracy and F1 value of the baseline model have increased by 0.76% and 0.7%, respectively.

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    Analysis for the M/M/c+m queueing model with non-preemptive priority and contact matching
    Yuting TAN,Xiuli XU,Rui ZHENG
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 45-52.   DOI: 10.6040/j.issn.1671-9352.0.2022.212
    Abstract111)   HTML2)    PDF(pc) (874KB)(201)       Save

    The M/M/c+m queueing model with non-preemptive priority contact matching is established, and the state transition rule and infinitesimal generator matrix of the quasi-birth-and-death process are obtained. Then, the steady-state equilibrium condition, steady-state probability distribution, and main performance indices of the system are given by using the matrix geometric solution method. Finally, numerical examples are presented to discuss the influence of system parameters on the performance indices.

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    Optimal birth control of n species nonlinear competition system with age-structure
    Zijuan ZHOU,Zhixue LUO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 75-83.   DOI: 10.6040/j.issn.1671-9352.0.2023.207
    Abstract122)   HTML0)    PDF(pc) (1061KB)(201)       Save

    The optimal birth control of n species nonlinear competition system with age-structure is investigated. The existence and uniqueness of non-negative solution of the system is proved by using the fixed-point theorem. The extremization sequence is constructed, and Mazur?s theorem are used to verify the existence of the optimal solution of the optimal birth control problem, and the necessity conditions are derived out via normal cone and conjugate system techniques.

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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
    Abstract176)   HTML0)    PDF(pc) (1357KB)(196)       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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    Hopf bifurcation of a vegetation-water reaction-diffusion model with time delay
    Gaihui GUO,Jingjing WANG,Wangrui LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 32-42, 53.   DOI: 10.6040/j.issn.1671-9352.0.2023.279
    Abstract146)   HTML6)    PDF(pc) (3010KB)(190)       Save

    Taking the time delay τ as the bifurcation parameter, the effect of time delay on the stability of the positive steady state point and the existence of Hopf bifurcation are given by analyzing the characteristic equation. The criteria for the direction of Hopf bifurcation and the stability of periodic solutions are obtained by the normal form theory and the center manifold theorem. Finally, the theoretical results are verified by numerical simulations.

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    A reaction-diffusion model of avian influenza with imperfect vaccination
    Mengjie HAN,Junli LIU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 106-121.   DOI: 10.6040/j.issn.1671-9352.0.2022.666
    Abstract109)   HTML2)    PDF(pc) (2489KB)(189)       Save

    In this paper, a model of avian influenza with imperfect vaccination reaction-diffusion is established to study the transmission dynamics of avian influenza in birds considering the mobility of birds and environmental heterogeneity. The global existence of the solution of the model is proved, then the basic reproduction number of the model is calculated using the spectral radius of the next generation operator, and the threshold dynamics of the model are analyzed. We also consider the case where the vaccine has 100% preventive effect on birds, the explicit expressions of the basic reproduction number and the principal eigenvalue are given, extinction and persistence of viruses are investigated. Finally, numerical simulations are carried out to analyze the transmission dynamics of avian influenza, effective control strategies for the outbreaks of avian influenza are also discussed. It shows that increasing the coverage of bird vaccination, disinfecting the environment, removing the avian influenza virus in the environment, and reducing the migration of birds are very effective to control the spread of avian influenza.

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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
    Abstract181)   HTML3)    PDF(pc) (1486KB)(189)       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 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
    Abstract171)   HTML6)    PDF(pc) (1396KB)(183)       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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    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
    Abstract237)   HTML0)    PDF(pc) (685KB)(177)       Save

    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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    Two kinds of integral graphs based on complete graphs
    Ligong WANG,Zhiming YU,Feng ZHOU,Lijie TAO,Luqi XING
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 155-159.   DOI: 10.6040/j.issn.1671-9352.0.2022.095
    Abstract135)   HTML0)    PDF(pc) (343KB)(176)       Save

    Two kinds of new graphs q * Kn and K1, m·(q * Kn) are defined. We obtain their characteristic polynomials by using the properties of characteristic polynomials of coalescence of graphs. We also characterize sufficient and necessary conditions with parameters for these graphs to be integral. Furthermore, some sufficient conditions for these graphs to be integral are presented.

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    Exponential stability of reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions
    Lei LI,Yongsheng YE
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (10): 67-74.   DOI: 10.6040/j.issn.1671-9352.0.2023.157
    Abstract113)   HTML1)    PDF(pc) (1152KB)(176)       Save

    By constructing a suitable Lyapunov functional and combining it with mathematical analysis techniques, we discuss the exponential stability of impulsive time delay reaction-diffusion Cohen-Grossberg neural networks with Dirichlet boundary conditions and Markovian switching. Some sufficient criteria for exponential stability of neural networks are obtained by using the inequality technique and stochastic analysis theory. Finally, an example is given to verify the validity of the results.

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    Vertex reducibletotal labeling algorithm for graphs
    Linyu LAN,Jingwen LI,Shucheng ZHANG,Lijing ZHANG,Huayu SHEN
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (11): 135-146.   DOI: 10.6040/j.issn.1671-9352.0.2022.278
    Abstract159)   HTML0)    PDF(pc) (1106KB)(170)       Save

    For an undirected connected graph G(V, E), if there exists a injective function f: V(G)∪E(G)→{1, 2, …, |V|+|E|}, such that any edge $\operatorname{Sum}(u)=f(u)+\sum\limits_{u v \in E(G)} f(u v)=K $, K is a constant, where u is any vertex in G(p, q) with the same degree, then G(p, q) is a vertex reducible total labeling (VRTL) graph, and the injective function f is vertex reducible total labeling. By means of computer and the way of optimizing the solution space of the vertex reducible total labeling, the algorithm of the vertex reducible total labeling is designed, and the solution space of the vertex reducible total labeling is recursively searched. By observing the labeling law of graphs within finite vertices, the labeling law of graphs of the same kind that can describe infinite vertices is extended and the total labeling theorems with extensibility and mathematical proof are given.

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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
    Abstract234)   HTML0)    PDF(pc) (636KB)(170)       Save

    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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    Label guided multi-scale graph neural network for protein-protein interactions prediction
    Xinsheng WANG,Xiaofei ZHU,Chenghong LI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (12): 22-30.   DOI: 10.6040/j.issn.1671-9352.1.2022.8766
    Abstract110)   HTML2)    PDF(pc) (2804KB)(167)       Save

    A protein-protein interactions prediction method based on label guided multi-scale graph neural network is proposed, which not only enhances the representation ability of data, but also introduces label information to guide learning. Firstly, the multi-scale graph representation is obtained by graph data augmentation, and the multi-scale graph representation is input into graph neural network to obtain multi-scale protein representation, and comparative learning is introduced to further improve the protein characterization ability. Secondly, the self-learning label relation graph is constructed to learn the relationship between labels and obtain the feature representation of labels. Finally, the prediction of protein-protein interactions is guided by the feature representation of labels. Experiments are carried out on three public datasets. Compared with the optimal benchmark method, the proposed method has better performance. Specifically, compared with the best baseline method, the micro-F1 scores on the three datasets SHS27k, SHS148k and STRING increase by 2.01%, 0.94% and 0.93% respectively.

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    Prediction method of IDH1 mutation status of glioma based on improved EfficientNetV2
    Huachang XU,Qian XU,Yulin ZHAO,Fengning LIANG,Kai XU,Hong ZHU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2023, 58 (7): 60-66.   DOI: 10.6040/j.issn.1671-9352.4.2022.2945
    Abstract152)   HTML0)    PDF(pc) (2784KB)(165)       Save

    The paper proposes a method for predicting the IDH1 mutation status of gliomas based on improved EfficientNetV2. Firstly, k-means clustering algorithm is used to label pseudo-labels for unlabeled glioma MRI data, and the Vision Transformer network is used to correct the pseudo-labels to realize glioma data amplification. Secondly, the coordinate attention is added to the EfficientNetV2 model, and the fruit fly optimization algorithm is used to give the optimal weight to the pseudo-label data during the model training process. Finally, the glioma IDH1 mutation status is classified, and the prediction accuracy is 96.32%. The experimental results show that the proposed method can non-invasively and accurately predict the IDH1 mutation status of gliomas before surgery.

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