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    ASR-UNet: an improved retinal vessels segmentation algorithm based on attention mechanism
    San-li YI,Jian-ting CHEN,Jian-feng HE
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (9): 13-20.   DOI: 10.6040/j.issn.1671-9352.0.2020.655
    Abstract1682)   HTML160)    PDF(pc) (5369KB)(553)       Save

    Factors such as tiny blood vessels in the retina and light will cause the problem of low segmentation accuracy of existing algorithms. This paper proposes a new retinal vessel segmentation algorithm model based on U-Net segmentation model combined with attention mechanism. The improved measures of this paper are as follows: first, we use SE-Resnet to replace the common convolution used in U-Net, thereby introducing a channel attention mechanism to enhance the original features. After that, AG are added to the jump connection part to enhance the spatial characteristics, thereby improving the models ability to segment the microstructure of blood vessels. The algorithm of this paper is verified on the public datasets DRIVE and CHASE_DB1, and the results are 0.9697 and 0.9657 on Acc, 0.8044 and 0.7673 on sensitivity, and 0.9859 and 0.9866 on specificity. Experimental results show that the proposed algorithm has better performance than recent retinal blood vessel segmentation algorithms.

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    Strategies for boosting the catalytic performance of palladium-based electrocatalysts for oxygen reduction reaction
    YANG Jun, LIU Dan-ye, ZENG Qing, CHEN Dong, LIU Hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (10): 79-98.   DOI: 10.6040/j.issn.1671-9352.9.2021.006
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    Oxygen reduction reaction is the key reaction of many electrochemical devices and technologies, and massive and increasing efforts have been devoted to develop more efficient ORR electrocatalysts in recent decades. Owing to its analogous physical properties to Pt, e.g. phase structure, atomic size and electronic configuration as well as its higher abundance in earth, palladium(Pd)-based nanomaterials, which have been regarded as good substitutes for platinum(Pt), have been extensively studied and their electrocatalytic performance for ORR is continuously improved. Herein, we focus this review on the strategies developed in recent years for boosting the catalytic performance of Pd-based electrocatalysts for ORR, including substrate tailoring, morphological control and composition optimization. These strategies would alter the electronic coupling, ligand effect, lattice strain, and synergistic effect around the Pd atoms, equipping them favorable features for catalyzing oxygen reduction. In the final section of this review, we put forth some perspectives/challenges for further development of Pd-based electrocatalysts, which might be helpful for designing and fabrication of high-efficiency ORR catalysts.
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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
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    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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    Stability of the bidirectional ring networks with multiple time delays and multiple parameters
    PANG Yu-ting, ZHAO Dong-xia, BAO Fang-xia
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2022, 57 (8): 103-110.   DOI: 10.6040/j.issn.1671-9352.0.2021.618
    Abstract549)      PDF(pc) (586KB)(366)       Save
    The dynamic analysis of the four-neuron ring neural network with multiple time delays and multiple parameters is carried out. Firstly, the system is linearized near the trivial solution, and the characteristic equation of the system is obtained. Then the characteristic equation is factorized into four first-order exponential polynomials. Furthermore, by using the zero-point distribution property of exponential polynomial, sufficient conditions for the delay-dependent and delay-independent stability are established. Moreover, an exhaustive comparison analysis is made between the results obtained and those in the existing literature. Finally, some numerical simulations are presented to show the effectiveness and superiority of the results.
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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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    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
    Abstract214)   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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    An extractive topic brief representation generation method to event
    WANG Wei-yu, SHI Cun-hui, YU Xiao-ming, LIU Yue, CHENG Xue-qi
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (5): 66-75.   DOI: 10.6040/j.issn.1671-9352.1.2020.029
    Abstract759)      PDF(pc) (1427KB)(331)       Save
    This paper takes advantage of the fact that event description contents are highly similar, and proposes an extractive topic brief representation generation method, which takes the titles in the event document set as the processing object, and extracts the common information retaining the original word order from different titles, further integrates these common information to generate a topic brief representation of the event. The experimental results on the event data from search engines show that this method can well generate the topic brief representation with concise and accurate form, clear and complete semantics and good readability.
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    Topological structure of graphbased networked evolutionary games
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (10): 11-22.   DOI: 10.6040/j.issn.1671-9352.9.2021.001
    Abstract766)      PDF(pc) (888KB)(326)       Save
    For a graph-based networked evolutionary game, the strategy evolutional equations for typical nodes are first calculated. A method is proposed to assemble typical node equations together to form the profile evolutional equation. The formula for calculating fixed points and limit cycles of logical networks is applicable to reveal the topological structure of networked evolutionary games, including the fixed points and limit cycles of networked evolutionary games. Next, for each player the unilateral profile updating equation is introduced. Using them, a formula for calculating pure Nash equilibrium(s)is obtained. Some numerical examples are presented.
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    Cognition of network concepts based on variable precision possibility operator
    FAN Min, LUO Shan, LI Jin-hai
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2022, 57 (8): 1-12.   DOI: 10.6040/j.issn.1671-9352.0.2022.066
    Abstract552)      PDF(pc) (650KB)(323)       Save
    Concept cognition in a network is an important direction in the field of network data analysis. Starting from the necessity operator and possibility operator in formal concept analysis, this paper puts forward variable precision possibility operator, and illustrates that the classical possibility operators are special cases of the variable precision possibility operators. Furthermore, some properties of the possibility operators are studied, and their significances in the study of infectious disease networks are explained. Then, based on the variable precision possibility operators, two generalized network concepts and their upper approximations, lower approximations and boundary regions are proposed, and the upper and lower approximations and their boundary regions under variable precision possibility operators are illustrated to have much richer semantics through an example. After that, combined with the network eigenvalue method in complex network analysis, the network weak concepts are defined, and a network weak concept acquisition method based on variable precision possibility operator is presented. Finally, our algorithm is used to conduct some experiments on the UCI database, and the obtained results show that variable-precision possibility operators have advantages in network concept cognition.
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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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    Strongly Gorenstein projective objects in comma categories
    CHEN Mei-hui, LIANG Li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (8): 81-85.   DOI: 10.6040/j.issn.1671-9352.0.2020.709
    Abstract658)      PDF(pc) (408KB)(300)       Save
    Introduce the comma category(F,B )and give an equivalent characterization of strongly Gorenstein projective objects in(F,B )in terms of strongly Gorenstein projective objects in A and B.
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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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    Community discovery algorithm based on attention network feature
    Jing-hong WANG,Li-na LIANG,Hao-kang LI,Yi ZHOU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (9): 1-12,20.   DOI: 10.6040/j.issn.1671-9352.4.2021.174
    Abstract740)   HTML122)    PDF(pc) (10148KB)(288)       Save

    In the real world, many networks are closely organized according to the community structure. It has been found that the community is of great help in understanding the structure and relationship of complex networks. This paper proposes a community discovery algorithm based on attention network features (CANF algorithm). It uses the label node frequency and the inverse example node frequency to measure the initial network label characteristics, and introduces the attention mechanism, and updates each neighbor node of the example node. Combined the initial weight with the assigned weight, the network features of the initial measure can obtain more detailed information related to the target. In this paper, complex network preprocessing and community game merge are carried out through distributed attention network features. The experimental results show that the accuracy, modularity and running time of the community discovery algorithm based on attention network features are better than other community discovery algorithms.

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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
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    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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    Online monitoring of parameter changes in linear regression model with long memory errors
    NIANG Mao-cuo, CHEN Zhan-shou, CHENG Shou-yao, WANG Xiao-yang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2022, 57 (4): 91-99.   DOI: 10.6040/j.issn.1671-9352.0.2021.525
    Abstract580)      PDF(pc) (932KB)(269)       Save
    Based on the modified moving-sum-statistic(mMOSUM)method, this paper studies the online monitoring change points of the regression coefficients of linear regression model with long-memory time series errors. Under the null hypothesis, the limit distribution of the mMOSUM monitoring statistics is obtained by modifying the boundary function, and the consistency of the method is proved under the alternative hypothesis. The results of numerical simulation show that when linear regression model has long memory errors, the mMOSUM method is still effective except for the case where the long memory parameter value is larger. And the location of change point moves further back, the effect of modified method on the increase of the power and the reduction of the run length is more obvious. Finally, the feasibility of this method is demonstrated by an empirical analysis of a set of macroeconomic data for the United States.
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    Influence of σ-embedding system of subgroups on the structure of finite groups
    MA Xiao-jian, MAO Yue-mei
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2022, 57 (2): 67-71.   DOI: 10.6040/j.issn.1671-9352.0.2021.505
    Abstract719)      PDF(pc) (389KB)(269)       Save
    Let ∑={G0≤G1≤…≤Gn-1≤Gn} be a subgroup series of G. A subgroup H of G is said to be ∑-σ-embedded in G if H either covers or avoids every σ-abnormal pair (K,L)such that Gi-1≤Ki for some i. The influence of ∑-σ-embedded subgroups on the structure of finite groups G is studied. Some new conclusions of σ-supersoluble and σ-soluble will be given by using some related theories of σ-solvable groups, properties of complete Hall σ-set and some basic methods of finite group theory.
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    Semantics of the soft set induced by intuitionistic fuzzy set and its three-way decision
    GONG Zeng-tai, TA Guang-peng
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2022, 57 (8): 68-76.   DOI: 10.6040/j.issn.1671-9352.0.2021.419
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    In this paper, by means of the shadowed set, this paper transforms intuitionistic fuzzy set into pessimistic shadowed set and optimistic shadowed set by using intuitionistic fuzzy parameters, and proposes pessimistic three-way decision and optimistic three-way decision of intuitionistic fuzzy set. The method of inducting soft set by intuitionistic fuzzy set is given, and the qualitative model of three-way decision with soft set is proposed by using three-way decision theory. Combined with pessimistic three-way decision and optimistic three-way decision of intuitionistic fuzzy set, a quantitative model of three-way decision with soft sets is given by using intuitionistic fuzzy parameters.
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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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    Generalized interval-valued Pythagorean triangular fuzzy aggregation operator and application in decision making
    SU Xiao-yan, CHEN Jing-rong, YIN Hui-ling
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2022, 57 (8): 77-87.   DOI: 10.6040/j.issn.1671-9352.0.2021.448
    Abstract524)      PDF(pc) (639KB)(249)       Save
    In this article, the interval-valued Pythagorean triangular fuzzy number is proposed for the decision making problems when the sum of membership degree and non-membership degree of decision variables exceeds 1 on continuous sets, and the decision application of its generalized aggregation operator is analyzed. Firstly, the concept of interval-valued Pythagorean triangular fuzzy numbers is given, and its algorithm is obtained. Secondly, the weighted average operator, weighted geometric operator, ordered weighted average operator, ordered weighted geometric operator, generalized ordered weighted average operator and generalized ordered weighted geometric operator of interval-valued Pythagorean triangular fuzzy numbers are defined, and their related properties are introduced. Finally, a multi-attribute decision making model based on generalized interval-valued Pythagorean triangular fuzzy aggregation operator is constructed, and the stability of generalized ordered weighted average operator and generalized ordered weighted geometric operator is analyzed according to an example. The figures are used to prove intuitively that the former is superior to the latter when dealing with decision making problems. The effectiveness and feasibility of the decision making model are illustrated.
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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
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    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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    Bifurcation of hydraulic turbine governing system under color noise excitation
    ZHANG Mei-jiao, ZHANG Jian-gang, NAN Meng-ran, WEI Li-xiang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (12): 94-99.   DOI: 10.6040/j.issn.1671-9352.0.2021.410
    Abstract648)      PDF(pc) (2263KB)(233)       Save
    Based on the saturated nonlinear proportional-integral(PI)governing system of a hydraulic turbine, a hydraulic turbine governing system under the excitation of color noise is established, the stochastic bifurcation behavior of system is studied. The system is simplified to an equivalent nonlinear white noise model by using the uniform color noise approximation principle. The central manifold theorem is used to reduce the dimension of system, the Ito differential equations and FPK equations are obtained according to stochastic average method, the stochastic bifurcation condition of system is discussed. Through numerical simulation, the stochastic bifurcation behaviors of system under the influence of different autocorrelation time and noise intensity are discussed respectively, the validity of theory of stochastic averaging and the occurrence of bifurcation phenomenon are verified.
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    Comparison analysis of microbial community structure in different functional areas of recirculating aquaculture system
    Zhan-sheng GUO,Yi DING,Hai-tao ZHANG,Xu-guang HOU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)    2021, 56 (9): 21-27,49.   DOI: 10.6040/j.issn.1671-9352.0.2020.621
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    In order to explore the microbial community structure in different functional areas of recirculating aquaculture system, as well as to understand the relationship between environmental factors and the microbial community, microbial community structure in recirculating aquaculture system was analyzed by using high-throughput sequencing with 16S rRNA in this study. The results showed that Proteobacteria and Bacteroidetes were the most dominant phyla in overall system, the compositions of dominant genera were quite different in different areas of system, while the relative abundances of Vibrio in whole system were both exceeding 1%. α-diversity (Shannon, ACE and chao1) of samples collected from biofilter and Rapana venosa pond were highest, and that in abalone pond and natural seawater were lowest. Non-metric multi-dimensional scaling (NMDS) analysis showed the system areas possessed distinctive distances of microbial communities except samples between biofilter and culture pond inlet. The removal rates of ammonia nitrogen and nitrite nitrogen from biofilter to the inlet of culture pond were 8.77% and 45.12%, respectively. The concentrations of nitrate nitrogen maintained a high level in the whole system (148.50~200.47 mg/L). There was no significant correlations between environmental factors and microbial community structure, temperature and nitrite nitrogen had relatively stronger effects on microbial community structure. This study provides a reference for the design improvement and daily management of recirculating aquaculture system in the next step.

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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
    Abstract138)   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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