JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)

Fusion-separation of information and explicit characteristics of implicit attributes

CHEN Shu-zhen, LI Shou-wei, SHI Kai-quan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 1-9. doi:10.6040/j.issn.1671-9352.0.2022.341

Abstract ( 687 )

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Based on the cross feature between the dynamic mathematical model with attribute conjunction and information fusion, the composite concept of information fusion and information separated generation is presented: information fusion-separation; Then, the fusion metric, separation metric and information fusion separation attribute theorem are given; The explicit principle of recessive attribute is given; The encryption-decryption of information fusion-separation and its secure acquisition are given. By using these theoretical results, the application of security authentication in case reconnaissance, evidence acquisition and case conclusion are given.

Uniform topological space base on ideals in bounded Heyting algebras

LIU Chun-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 10-20. doi:10.6040/j.issn.1671-9352.0.2022.125

Abstract ( 657 )

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In order to study the properties and structure of bounded Heyting algebras by using topological tools, based on a type of congruences induced by the notion of ideal, uniform topological space (H,τ) is established and some of its basic and topological properties are investigated in bounded Heyting algebra (H,≤,→,0,1). It is proved that (H,τ) is disconnected, locally connected, locally compact, zero-dimensional, first-countable and completely regular space. Moreover (H,τ) is a T₁ space if it is a Hausdorff space. Some necessary and sufficient conditions for (H,τ)to be discrete and compact space are obtained. It is showed that the lattice and implication operations in (H,≤,→,0,1) are continuous under the uniform topology τ, make (H,≤,→,0,1) to be a topological bounded Heyting algebra. Meanwhile, some properties of the quotient space of (H,τ) are discussed.

Bounds on the double Roman domination number of graphs

XIE Zhi-hong, HAO Guo-liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 21-25. doi:10.6040/j.issn.1671-9352.0.2021.003

Abstract ( 674 )

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A function f:V(G)→{0,1,2,3}defined on the vertex set V(G)of a graph G is called a double Roman dominating function if any vertex assigned 0 is adjacent to at least one vertex assigned 3 or two vertices assigned 2, and any vertex assigned 1 is adjacent to at least one vertex assigned 2 or 3. The weight of a double Roman dominating function is the sum of assigned values of all vertices. The double Roman domination number of a graph G is defined as the minimum weight of a double Roman dominating function on G. Using the number of vertices, girth, circumference and minimum degree of graphs, some lower and upper bounds on the double Roman domination number of graphs with a cycle are established.

Class of matching equivalent graphs of K1∪P2∪I_n

GAO Shang, MA Hai-cheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 26-36. doi:10.6040/j.issn.1671-9352.0.2021.137

Abstract ( 484 )

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The classes of matching equivalent graphs of K1∪P2∪I_n and its complement are characterized by using combination analysis, the number of matching equivalent graphs of K1∪P2∪I_n is also calculated by using combination counting.

The number of perfect matchings and k-resonance in n-prism

YANG Rui, LIU Cheng-li, WU Nan-nan

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 37-41. doi:10.6040/j.issn.1671-9352.0.2020.518

Abstract ( 600 )

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For n≥3, the cartesian product C_n×P2 is a polyhedral graph, the n-prism, where C_n is a n-cycle and P2 is a 2-path. Let G be a plane embedded graph of n-prism and k be a positive integer, the graph G is k-resonant, if the graph obtained by deleting any i pairwise disjoint even faces from the graph G has a perfect matching for any positive integer i(0≤i≤k). The formula of the number of perfect matchings in n-prism is obtained. Then the resonance of n-prism is discussed, its 1-resonance, 2-resonance and k-resonance are obtained(k≥3).

Generalized 3-connectivity of folded hypercubes

WANG Jun-zhen, ZHANG Shu-min, GE Hui-fen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 42-49. doi:10.6040/j.issn.1671-9352.0.2021.518

Abstract ( 475 )

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Let G be a connected graph and S⊆V(G). T=(V ',E ')is an S-Steiner tree which containing all the vertices in is S of G and make S⊆V '. Two S-trees T and T ' are said to be internally disjoint if E(T)∩E(T ')= and V(T)∩V(T ')=S. κ(S)is defined as the maximum number of the internally disjoint S-trees in G. The generalized k-connectivity(2≤k≤n)κ_k(G)of G is defined as κ_k(G)=min{κ(S)|S⊆V(G)and |S|=k}. Clearly, κ2(G)=κ(G). κ3(FQ_n)=n is proved where FQ_n is n-dimensional folded hypercube.

Optimal control of rational expectations model with multiplicative noise

CHANG Qing, QI Qing-yuan, LIU Zhi-qiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 50-57. doi:10.6040/j.issn.1671-9352.0.2022.458

Abstract ( 520 )

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The optimal control of a rational expectations model with multiplicative noise is investigated. By using the convex variational method, the maximum principle is derived, and the necessary and sufficient solvability conditions are shown. By decoupling the forward and backward stochastic difference equations, the optimal control is derived. Finally, numerical example is given to show the effectiveness of the obtained results.

Decentralized control of mean-field systems with asymmetric information controllers

LIU Zhi-qiang, QI Qing-yuan, CHANG Qing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 58-69. doi:10.6040/j.issn.1671-9352.0.2022.315

Abstract ( 513 )

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The finite horizon asymmetric information linear quadratic control problem for continuous-time mean-field systems is solved by the maximum principle and decoupled mean-field forward and backward stochastic differential equations. Eventually, the optimal control strategy and a set of asymmetric Riccati-type equations are obtained.

Dynamics of a spatially heterogeneous SI epidemic model with nonlocal diffusion

JIAO Zhan, JIN Zhen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 70-77. doi:10.6040/j.issn.1671-9352.0.2021.452

Abstract ( 624 )

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We study a spatially heterogeneous non-local dispersal SI epidemic model with the standard incidence. The basic reproduction number R₀ of the system is defined as the spectral radius of the next generation operator, and by means of suitable Lyapunov functional, the global asymptotic stability of the disease-free equilibrium is proved when R₀<1; the upper and lower solutions are used to prove the existence, uniqueness and global asymptotic stability of the endemic equilibrium of the system when the dispersal rate DS=0 of susceptible individuals and R0>1.

Study on monitoring the end points of tablet coating by classification method based on representative rate and voting mechanism

NIE Bin, CHEN Yu-feng, HE Yan, LUO Xiao-jian, RAO Xiao-yong, LI Huan, JIN Zheng-ji

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 78-88. doi:10.6040/j.issn.1671-9352.4.2021.080

Abstract ( 577 )

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A classification method based on representative rate and voting mechanism was established to monitor the end point of tablet coating by using near-infrared(NIR)technology. Firstly, the sample mean of each coating time point was clustered by hierarchical clustering, and establishing the classification model. Then, the representative rate proposed in this paper was used to verify the model at each time point. The method verified the mean clustering model through the representative rate to confirm the availability and feasibility of the model. Finally, the training model was used to predict the sample categories at each time point, and the final voting results at each time point were obtained through voting mechanism, which made up for the lack of model prediction in systematic clustering and avoided the wrong judgment caused by individual samples. The experimental data verified that the lowest representative rate was 73.33% for T100M, and the highest was 100.00% for T130M, with an average representative rate of 86.77%, The voting results show that the finishing points of the first batch of test data and the second batch of test data are 1T130M and 2T132M respectively. The voting mechanism can also monitor the process of coating at other time points.

Image classification based on low-rank inter-class sparsity discriminant least squares regression

ZHONG Kun-yan, LIU Jing-lei

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 89-101. doi:10.6040/j.issn.1671-9352.4.2021.199

Abstract ( 608 )

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Classifiers based on Least Squares Regression(LSR)are effective in multi-classification tasks. However, most of the existing methods use limited projections and cause a lot of loss of discriminative information. Some algorithms only focus on the accurate fitting of the sample and the target matrix and ignore the problem of overfitting. In order to solve these problems and improve the classification performance, this paper proposes a multi-class image classification method based on low-rank inter-class sparsity discriminative least squares regression(LRICSDLSR). Introducing the inter-class sparsity constraint in the discriminative least squares regression model, so that the margin of samples from the same class can be greatly reduced, while the margin of samples from different classes can be increased; Apply low-rank constraints to the relaxed labels obtained from the non-negative relaxation matrix to improve their intra-class compactness and similarity; An additional regularization term is introduced on the learning label to avoid overfitting. Experimental results show that it helps to learn more distinguished regression projections to achieve better classification performance.The experimental results on a series of image data sets prove the effectiveness of the method.

Temporal and spatial differentiation of the coupling coordination between eco-city urbanization and ecological environment

YU Jiao, YANG Hong-hui, CHEN Rong-rong, DING Zheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2022, 57(11): 102-110. doi:10.6040/j.issn.1671-9352.0.2022.169

Abstract ( 536 )

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Taking Xiamen City, Fujian Province, a typical ecological city on the southeast coast as an example, the urbanization index(CNLI)and the remote sensing ecological index(RSEI)were obtained by using the multi-source remote sensing image data from 2008 to 2018, and a coupling model of them was constructed. Analyze the leading factors of changes in ecological environment quality. Conclusion shows that: 1)The urbanization index of Xiamen has increased significantly, showing the urban distribution pattern of “high in the inside and low in the outside, high in the south and low in the west”, and the ecological environment distribution characteristics are opposite to it; 2)Xiamens urbanization and ecological environment development are in a stage of benign coordination, and gradually change from leading in ecological environment to leading in urbanization; 3)Urbanization is not a determinant of ecological environment quality, but its influence value is increasing year by year, and its effect is more and more obvious.

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