Table of Content

  

20 January 2021
Volume 56 Issue 1

Tate cohomology over T₂-extension algebras

TAN Ling-ling, HUANG Yun-tao, ZHAO Ti-wei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  1-9.  doi:10.6040/j.issn.1671-9352.0.2020.570

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The intrinsic connections between Tate cohomology of modules over an algebra and that of modules over its T₂-extension are investigated.

(m,n)-Cotorson modules and (m,n)-flat modules

WANG Xi, SHEN Lei, LUO Xiao-qiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  10-17.  doi:10.6040/j.issn.1671-9352.0.2020.429

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Let R be a ring, m and n be two fixed non-negative integers. A right R-module C is called (m,n)-cotorsion if Ext^m+1_R(N,C)=0 for any right R-module with fdRN≤n. M is called (m,n)-flat if Ext¹R(M,C)=0 for any (m,n)-cotorsion right R-modules C. We prove that(F ^m_n,C ^m_n )is a complete hereditary cotorsion pair, where F ^m_n, C ^m_n denotes the class of all (m,n)-flat and (m,n)-cotorsion right R-modules respectively. Whats more, R is said to (m,n)-perfectring if all R-modules are (m,n)-cotorsion. Some properties are given.

Vertex-distinguishing general total coloring of K3,3,p

YANG Jia-rui, CHEN Xiang-en

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  18-23.  doi:10.6040/j.issn.1671-9352.0.2019.206

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The vertex-distinguishing general total coloring of complete tripartite graphs K3,3,p(p≥3)is discussed by using the methods of distributing the color sets in advance, constructing the colorings and contradiction. The vertex-distinguishing general total chromatic number of K3,3,p(p≥3)is determined.

2-factor of edge colored graph

ZHANG Shuang, ZHU Yan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  24-28.  doi:10.6040/j.issn.1671-9352.0.2019.156

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Let G be an edge colored graph. For a vertex x of G, the color neighborhood CN(x)of x is defined as the set {c(xy)|xy∈E(G), y∈V(G)}. G is properly colored if no adjacent edges have the same color. If every edge colored graph G has |CN(u)∪CN(v)|≥4n/3+8 for every pair of vertices u and v of V(G), the G contains a properly colored 2-factor.

Matching equivalent classes of union graphs of two vertices and a path

XIE Cheng-ling, MA Hai-cheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  29-34.  doi:10.6040/j.issn.1671-9352.0.2020.157

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The number of the matching equivalent graphs of 2K1 ∪ P_m is calculated, and the matching equivalent classes of 2K1∪P_m and its complement graphs can also be characterized.

Generalized orthopair fuzzy hybrid aggregation operator and its application to multiple attribute decision making

DU Wen-sheng, XU Tao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  35-42.  doi:10.6040/j.issn.1671-9352.4.2020.051

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Generalized orthopair fuzzy hybrid aggregation operator with its application to decision making is considered in this paper. For the advantage that generalized orthopair fuzzy membership space is larger than those of Pythagorean fuzzy sets and intuitionistic fuzzy sets, we combine hybrid aggregation operator and generalized orthopair fuzzy sets. Firstly, the generalized orthopair fuzzy hybrid aggregation operator is defined based on the concepts of generalized orthopair fuzzy sets and the hybrid aggregation operator. Secondly, we examine the properties of the generalized orthopair fuzzy hybrid aggregation operator. Meanwhile, we explain the degenerations of the developed operator under some special conditions. Finally, the application of generalized orthopair fuzzy hybrid aggregation operator in multiple attribute decision making is verified by an example which shows the feasibility and rationality of the proposed method, and the influence of the parameter within the operator on the ranking results is discussed.

Firing bifurcation characteristics and synchronization of Chay neuron under electromagnetic induction

GAO Yue-yue, LI Xin-ying, LI Ning

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  43-51.  doi:10.6040/j.issn.1671-9352.0.2020.466

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According to Faraday law of electromagnetic induction, charged ions inside and outside the cell through the cell membrane to produce an electromagnetic induction effect, and a four-dimensional Chay neuron model is established by introducing magnetic flux on the basis of the Chay neuron model. Firstly, the equilibrium point and stability of the system are studied by Matcont simulation, and it is found that the system undergoes saddle-node bifurcation, supercritical Hopf bifurcation and subcritical Hopf bifurcation as the parameters change; secondly, the firing mode of the neuronal system is investigated by numerical simulation; finally, the coupled neurons and global connections are analyzed by electrical synaptic coupling, using statistics such as correlation coefficient and synchronization parameter. The synchronization problem of neuronal networks is further explored by the influence of multiple parameters on the synchronization process of neurons.

2-Tessellable staggered quantum walk on finite even cycles

YANG Guang-bo, WANG Cai-shi, LUO Yan, WANG Yan-yan, NAN Xue-qi

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  52-59.  doi:10.6040/j.issn.1671-9352.0.2020.340

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A 2-tessellable staggered quantum walk is considered on finite even cycles, its evolution matrix is obtained, and properties of the matrix are analyzed. The probability distributions of 2-tessellable staggered quantum walk on 4-cycle are given. A comparison is made between 2-tessellable staggered quantum walk and the classical random walk.

Graph-based granularity reduction in pessimistic multi-granulation rough set

ZHANG Wen-juan, LI Jin-jin, LIN Yi-dong

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  60-67.  doi:10.6040/j.issn.1671-9352.0.2020.205

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This paper combines the theory of the vertex cover of graph, and a new method of the granularity reduction of pessimistic multi-granulation rough set is discussed. Firstly, the concept of the graph induced from pessimistic multi-granulation rough set is presented, and the graph characteristic of its granularity reduction is given. On this basis, the significance of granularity is depicted by the method of graph, and then a algorithm about granularity reduction of pessimistic multi-granulation rough set based on graph is designed. Secondly, the concept of the graph induced from multi-granulation decision-theoretic rough set is defined, the graph characteristic of its granularity reduction and the significance of granularity are proposed at the same way, then a algorithm of granularity reduction of pessimistic multi-granulation decision-theoretic rough set based on graph is designed. Finally, it is rational to give an example to illustrate the pessimistic lower approximate multi-granulation rough set algorithm.

 

F-C variable threshold concept lattices based on dependence spaces

Jing ZHANG,Jian-min MA

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  68-74.  doi:10.6040/j.issn.1671-9352.4.2020.156

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For a fuzzy formal context, a congruence relation is defined based on a variable precision operator on the power set of attributes. A congruence relation is obtained. Based on it, a dependence space is shown. By constructing a closure operator according to the congruence relation, the relationships between the closure operator and the variable precision concepts are discussed. Furthermore, applying the properties of the closure operator, we get that any fixed point of the closure operator is exactly the intension of some variable precision concept. Based on these, an algorithm to construct all variable precision concepts is obtained. Experiments are used to verify the feasibility of the proposed method.

Granule description using possible attribute analysis

Jie TANG,Ling WEI,Rui-si REN,Si-yu ZHAO

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  75-82.  doi:10.6040/j.issn.1671-9352.4.2020.149

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Granular computing is a method and effective tool of solving complicated problems by using information granularity. During the process of granularity, it is often accompanied with granule description, and granule description becomes a fundamental problem in granular computing. Inspired by necessary attribute analysis, this paper proposes granule description using possible attribute analysis. First, taking the extents of property oriented concepts as definable granules in the formal context, and defining the description of definable granule. Then, using the stability of concepts to define minimal generator of concept so that definable granule's description becomes concise. Finally, the advantage of granule description using possible attribute analysis is discussed by an example of task assignment.

Research on matching resumes and positions based on Arc-LSTM

Fei-fei XU,Yun-jie XU

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  83-90.  doi:10.6040/j.issn.1671-9352.4.2020.131

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An automatic scheme is proposed, which combines the deep neural network Arc-LSTM with Word2Vec model. In this paper, the CBOW model is used to extract resume text features. A new deep neural network, Arc-LSTM is put forward, which is optimized by ArcReLU. The experimental results show that Arc-LSTM can effectively improve the classification accuracy and convergence speed, and achieve the exact match between Chinese resumes and positions.

Overlapping community detection based on density peaks and network embedding

Yi-ming ZHANG,Guo-yin WANG,Jun HU,Shun FU

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  91-102.  doi:10.6040/j.issn.1671-9352.4.2020.145

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Density peaks is a density-based clustering algorithm. It assumes that the center points of the cluster have higher density and are surrounded by nodes with lower density. Due to the character of graph structure, density peaks cannot be directly applied to network structure, and most of density peaks based community detection algorithms based on density peaks are based on graph topology or adjacency matrix to measure node approximation, which often leads to great computational complexity. This paper proposes an overlapping community detection algorithm based on density and network embedding (OCDDNE). The proposed algorithm firstly embeds the network structure characteristics of nodes in network structure through network embedding, and then clusters the embedded node vectors based on the improved method of density peaks, so that the structural relationship between the encoded vectors can be better revealed and the overlapping communities which each node is located is determined. Experiments on synthetic networks and real networks data show that the proposed algorithm can efficiently find the overlapping community structure in networks, and it is superior to other algorithms especially in complex networks with high structural complexity.

Pricing decision of dual-channel supply chain considering altruistic preferences under reference price effect

Yan JIAO,Chuan-xu WANG,Yuan-wei WANG,Lang XU

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(1):  103-110.  doi:10.6040/j.issn.1671-9352.0.2019.004

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Considering the suggested retail price made by manufacturer in a dual-channel supply chain composed of a manufacturer and retailer, game theory was used to study how to set a reasonable price to maximize their own profits, and the influence of altruistic preferences and reference price effect on price was analyzed. By comparing the equilibrium decisions under different circumstances, it can be found that when the retailer's altruistic preference is under certain threshold conditions, the optimal decision profit exists. The altruistic preference of supply chain members can achieve the purpose of "altruism", but cannot achieve "win-win". At the same time, the increase of the market share of traditional channels is favorable for retailers and unfavorable for manufacturers. When the consumer sets the suggested retail price as the reference price, the suggested retail price can increase the supply chain revenue, and the supply chain revenue increases as the reference price effect increases.