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Table of Content

      
    20 July 2020
    Volume 55 Issue 7
    Transcritical bifurcation for a pest management model with impulse and virus infection
    WANG Ai-li
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  1-8.  doi:10.6040/j.issn.1671-9352.2.2019.319
    Abstract ( 198 )   PDF (1462KB) ( 104 )   Save
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    The existence of a boundary periodic solution is investigated for a pest management model with state-dependent feedback control and virus infection. The condition is derived for the global stability of the boundary periodic solution. It is examined how the transcritical bifurcation occurs for this model. It is addressed the impact of the control intensity, including the pesticide function and the releasing ratio of infected pests, on the frequency implementing the control measures. The main results obtained in this paper show that the state-dependent control policy can be converted into a periodic impulsive one. The frequency implementing control measures diminishes as the releasing ratio of infected pests increases; while it may decrease or increase as the pesticide function increases.
    Bifurcation analysis of positive solutions for a predator-prey model with B-D functional response
    YANG Zhong-liang, GUO Gai-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  9-15.  doi:10.6040/j.issn.1671-9352.0.2020.028
    Abstract ( 167 )   PDF (414KB) ( 30 )   PDF(mobile) (414KB) ( 11 )   Save
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    The steady-state of the predator-prey model with Beddington-DeAngelis functional response and the fear effect is studied. We first obtain the local bifurcation solutions by the bifurcation theory, then the global structure of the coexistence solutions is established. Moreover, some stability results of the bifurcation solutions are given by linear eigenvalue perturbation theory.
    Existence and uniqueness of solutions for a class fourth-order periodic boundary value problems
    WANG Tian-xiang, LI Yong-xiang
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  16-21.  doi:10.6040/j.issn.1671-9352.0.2019.788
    Abstract ( 165 )   PDF (819KB) ( 79 )   Save
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    By using Leray-Schauder fixed point theorem, this paper discusses the existence and uniqueness of solutions for the fourth-order periodic boundary value problem{u(4)(t)=f(t,u(t),u'(t)), t∈[0,1],u(i)(0)=u(i)(1), i=0,1,2,3,where f:[0,1]×R2→R continuous. existence and uniqueness of solutions is obtained under the inequality conditions that allow the nonlinear term f(t,x,y) to grow superlinearly on x and y.
    Boundedness of fractional maximal operator on generalized Orlicz-Morrey spaces of homogeneous type
    LIU Ming, TAO Shuang-ping
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  22-31.  doi:10.6040/j.issn.1671-9352.0.2019.886
    Abstract ( 158 )   PDF (877KB) ( 89 )   Save
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    By applying the estimates of the maximal operator and the properties about the spaces of homogeneous type, the necessary and sufficient conditions are given for the boundedness of the fractional maximal operator and its commutators on the generalized Orlicz-Morrey spaces of homogeneous type. The corresponding results are also given in the generalized weak Orlicz-Morrey spaces of homogeneous space.
    A characterization of ξ-skew Jordan derivable mappings on factor von Neumann algebras
    ZHANG Fang-juan
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  32-37.  doi:10.6040/j.issn.1671-9352.0.2020.100
    Abstract ( 109 )   PDF (817KB) ( 26 )   Save
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    Let R be a factor von Neumann algebra with dim R>1. For given complex number ξ and ξ ≠0, if a map δ:R→R satisfies δ((A·B)ξ)=(δ(A)·B)ξ+(A·δ(B))ξ for all A,B∈R, δ is an additive *-derivation and δ(ξA)=ξδ(A). In particular, if the von Neumann algebra R is infinite type Ⅰ factors, a concrete characterization of δ is given.
    Linear 2-arboricity of planar graphs without intersecting 5-cycles
    CHEN Hong-yu, ZHONG Bin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  38-45.  doi:10.6040/j.issn.1671-9352.0.2019.095
    Abstract ( 130 )   PDF (950KB) ( 78 )   Save
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    Let G be a planar graph without intersecting 5-cycles. If G is connected and δ(G)≥2, then G contains an edge xy with d(x)+d(y)≤10 or a 2-alternating cycle is proved. By this result, its linear 2-arboricity la2(G)≤「Δ/2+5 is obtained, which improves the known upper bound of la2(G) for planar graphs without 5-cycles.
    Controlled remote preparation of n-qubit equatorial states
    PENG Jia-yin
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  46-54.  doi:10.6040/j.issn.1671-9352.0.2019.532
    Abstract ( 97 )   PDF (942KB) ( 61 )   Save
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    In order to solve the problem of preparing multi-particle states, a method of constructing 2n+1-qubit entangled quantum states is proposed, and its quantum circuit diagram is given. Secondly, a controlled remote preparation protocol for an arbitrary n-qubit equatorial entangled state is proposed by using this 2n+1-qubit entangled states as quantum channel. The protocol shows that under the control of the supervisor Charlie, and Alice uses multi-qubut projection measurement and classical communication, Bob can successfully reconstruct an arbitrary n-qubit equatorial state with 100% probability by using a simple unitary transformation. Furthermore, the feasibility of this protocol for remote preparation of the general multi-qubit equatorial entangled state is explicitly demonstrated by concrete examples of the preparation of arbitrary two-qubit state and arbitrary three-qubit state.
    Nyström extension based on circulant matrix projection
    LIU Jing-shu, WANG Li, LIU Jing-lei
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  55-66.  doi:10.6040/j.issn.1671-9352.0.2019.318
    Abstract ( 158 )   PDF (2227KB) ( 74 )   Save
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    Unlike the random sampling approximation method, a projection method based on circular matrix to approximate the kernel matrix is designed. Firstly, the approximation sketch of the matrix is obtained by random sampling, then constructing a circular matrix as a projection matrix to map the data of inputting data space to feature space approximately. At last, the traditional Nyström method is extended by singular value decomposition on the feature space. Compared with other typical matrix approximation methods, the improved Nyström method has the advantages of low time complexity and high reconstruction accuracy. Our empirical studies on four real datasets corroborate our theoretical findings and demonstrate that our proposed random projection method can indeed achieve satisfactory reconstruction precision.
    Method of uncertain temporal event flow sequence reasoning based on multiple attribute decision making
    ZHENG Huan-ke, ZHANG Jing, YANG Ya-qi, XIONG Mei-hui
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  67-80.  doi:10.6040/j.issn.1671-9352.0.2019.585
    Abstract ( 124 )   PDF (1468KB) ( 57 )   Save
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    In the cyber-physical system, the scheduling sequence of uncertain temporal event flows has a single decision-making problem. To solve this problem, this paper firstly uses the advantage of D-S evidence theory in multi-evidence source probability fusion, considering the influence of multiple attributes such as event priority, deadline, urgency and event dependency, to construct a basic probability distribution model for fuzzy end time with multi-attribute features. Then, an association model with intuitionistic fuzzy sets and D-S evidence theory is established, and through this model, the membership and non-membership of the IFS at the fuzzy end time can be obtained. On this basis, negative temporal reasoning of IFS and correlation scoring function are used to derive the fuzzy start time probability score, and finally obtain the time series reasoning result, which is used to determine the uncertain temporal event flow scheduling order based on multi-attribute criterion. The experimental results show that when the number of events increases, the methods scheduling accuracy rate can keep more than 85%. And when the size of the fuzzy interval limit is expanded, the scheduling accuracy rate does not decrease more than 15%.
    Construction of retrieval dataset of procuratorate legal documents
    Jia-qi WANG,Mu-yun YANG,Tie-jun ZHAO,Zhen-yu ZHAO
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  81-87.  doi:10.6040/j.issn.1671-9352.1.2019.048
    Abstract ( 128 )   HTML ( 7 )   PDF (940KB) ( 60 )   Save
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    Smart procuratorial is an important step in further developing procuratorial informationization. Prosecutors often deal with a large number of procuratorate legal documents. Failure to effectively organize and use the information in these instruments will reduce the efficiency of the procuratorate. Information retrieval technology can solve this problem precisely. In the legal field, the lack of Chinese retrieval datasets actually restricts the development of legal information retrieval. In this background, according to the characteristics of the procuratorate legal documents, this paper proposed a method for constructing a retrieval dataset for the procuratorate legal documents, and implements a small Chinese dataset that can be used for information retrieval research in the legal field. According to the experimental results, the performance of the dataset on different retrieval models has been verified.

    Channel decisions and coordination of closed-loop supply chain under demand and cost disruptions
    Dan-dan SUN,Ke LI,Li-bin XIE,Zong-yu MU
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  88-102, 110.  doi:10.6040/j.issn.1671-9352.0.2019.290
    Abstract ( 129 )   HTML ( 6 )   PDF (1202KB) ( 26 )   Save
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    Considering demand and cost are disrupted by emergency events, there are three CLSC emergency models, i.e. retailer collecting, manufacturer collecting and third-party collecting. In the three decentralized collecting systems and centralized decision system, compared with equilibrium decisions in normal environment, when the disruptions of demand and cost are not large, sales quantity of products and collecting rate of used products have some robustness, but the wholesale price and selling price of products should be adjusted along the same direction with demand disruption; when the disruptions of demand and cost are large, the wholesale price, selling price, sales quantity of products and collecting rate of used products should be adjusted along the same direction with demand disruption; when the degree of demand decreasing and cost increasing are large, the three decentralized collecting systems and centralized decision system are all destroyed. In each case of demand and cost disruptions, manufacturer can obtain more profits by MRCRM system; when the degree of demand decreasing and cost increasing exceeds a certain threshold, the profits of centralized decision system decrease resulted from assuming more extra disposing costs, which results in its profits are less than MRCRM system. Furthermore, in other disruption cases, emergency revenue and expense sharing contract can solve "double marginalization" problems in MRCRM system, which improves system's operation efficiency and makes each member get Pareto improved profits.

    Influencing factors of fermentation and flocculation characteristics of Klebsiella sp. LDX1-1 polysaccharide
    Sheng-nan WANG,Xing-she LUAN,Xin-juan GUO,Min XIAO,Mei-xue DAI
    JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2020, 55(7):  103-110.  doi:10.6040/j.issn.1671-9352.0.2019.667
    Abstract ( 148 )   HTML ( 8 )   PDF (2481KB) ( 94 )   Save
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    The best carbon source for the production of Klebsiella sp. LDX1-1 polysaccharide is the mixture of maltose and isomaltooligosaccharide, in which the mass fraction of isomaltooligosaccharide is 8%, and the best nitrogen source is NH4NO3 for 2g/L. 2g/L of cedar needle extract and 0.4% of Triton X-100 significantly promote the polysaccharide synthesis, and the yield increased by 12.46% and 14.38%, respectively. The optimum fermentation period is 24h, and the yield of crude polysaccharide is 23.46g/L, which is 43.14% higher than that under the basic fermentation conditions. The preliminary purified polysaccharide prepared from fermentation broth has high flocculation activity, and the flocculation rate of kaolin suspension and the Yellow River water is 98.43% and 96.31%, respectively. The qualitative analysis of the purified samples by infrared spectroscopy shows that the components of the viscous substances produced by fermentation are typical biological polysaccharides.