Table of Content

  

20 November 2021
Volume 56 Issue 11

A privacy-preserving multi-coupon system based on prepaid model

LIU Xin, XU Qiu-liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  1-14.  doi:10.6040/j.issn.1671-9352.0.2021.230

Abstract ( 503 )   PDF (671KB) ( 263 )   Save

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Multi-coupon(MC)is a popular form of e-commerce promotion. However, the existing MC systems have many shortcomings, such as low efficiency in the redeem phase, efficiency improvement at the expense of customer privacy, and the adoption of unnecessary system parameters, etc. A new MC system based on pre-paid model is proposed that is based on the technique of Au-Susilo-Mu signature scheme, exact range proof, signatures of knowledge, etc. The new system satisfies provable security under the new security model based on simulation. Besides, the new system has several practical features, such as supporting multiple types of goods, allowing customers to redeem multiple coupons at one time, and allowing customers to choose the number of coupons contained in the MC. The efficiency analysis shows that the new system does not require customers to perform inefficient bilinear pairing operations online or in advance, thus significantly improving the efficiency of customers in the coupon redemption stage.

Sentiment classification combining graph convolution neural network

YIN Ai-ying, LIN Jian-zhou, WU Yun-bing, LIAO Xiang-wen

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  15-23.  doi:10.6040/j.issn.1671-9352.0.2021.425

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Document-level sentiment classification aims to predict users sentiment polarity labels on review text. Recent studies have found that incorporating user and product information can effectively improve the performance of review sentiment classification. However, most of the pervious arts only concentrate on the relation between users and reviews, products and reviews, ignoring the inhere correlation between users and users, products and products. Therefore, we propose a sentiment classification combining graph convolution neural network. Firstly, we construct a relation graph of user-to-user and a relation graph of user-to-product based on the datasets and merge them into a heterogeneous graph. Secondly, utilize the graph convolutional neural network to learn the inhere correlation between users and users, products and products to obtain better user and product representation. Finally, use a hierarchical user attention and product attention network combined with CNN to make sentiment polarity classification. Experiments on benchmark datasets of IMDB, Yelp2013 and Yelp2014 show that our method can achieve state-of-the-art performance.

Method of recommendation based on knowledge driven by BERT and law

TANG Guang-yuan, GUO Jun-jun, YU Zheng-tao, ZHANG Ya-fei,GAO Sheng-xiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  24-30.  doi:10.6040/j.issn.1671-9352.1.2020.043

Abstract ( 712 )   PDF (604KB) ( 313 )   Save

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Aiming at the problem of insufficient knowledge utilization of traditional law recommendation methods, this article combines the pre-training BERT(bidirectional encoder representation from transformers)model to propose a law recommendation method based on knowledge-driven legal provisions in the judicial field. First based on the BERT pre-training model, the legal knowledge and the case description are characterized separately, and the case description text is extracted based on the two-way LSTM, and then the case description text features combined with the legal knowledge are extracted based on the attention mechanism, and the intelligent recommendation of the legal clause is finally realized. Using this method on the law research cup public data set, the recommended F₁ value of the law can reach 0.88. From this effect, it can be seen that the BERT model fused with knowledge of the law can significantly improve the law recommendation and can effectively solve the easily confused method of recommended questions.

Rules acquisition based on OE-approximate concept lattice in incomplete formal decision contexts

CHANG Li-na, WEI Ling

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  31-37.  doi:10.6040/j.issn.1671-9352.4.2021.033

Abstract ( 606 )   PDF (576KB) ( 195 )   Save

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First, OE-consistency of incomplete formal decision contexts is defined through the finer relation between the object-induced three-way condition approximate concept lattice and the object-induced three-way decision approximate concept lattice. Then, object induced three-way rules acquisition method is proposed based on the OE-consistent incomplete formal decision contexts, rules are acquired and interpreted from positive and negative perspectives respectively. Moreover, the judgement theorem of redundant rules and the extraction algorithm of irredundant rule sets are given. Finally, three-way rules acquisition method with confidence is proposed by using the inclusion degree theory, which provide more details and make the acquired rules more complete.

Properties and improvement of GM(1,1)models

PAN Hao, GAO Shang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  38-42.  doi:10.6040/j.issn.1671-9352.4.2021.227

Abstract ( 1885 )   PDF (503KB) ( 316 )   Save

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Based on theoretical analysis of GM(1,1)model, the conclusion, which the initiative number has no effect on the prediction, is got. GM(1,1)model is improved and GM(1,1)model I is given. When add an identical number to the original series, the forecast values will change. GM(1, 1)model Ⅱ is given, and using particle swarm algorithm, the best increase is got. Simulation results show that the improved GM(1, 1)model Ⅰ and GM(1, 1)model Ⅱ have higher accuracy.

Analysis on plant community dynamics and succession in the Confucian Cemetery, Shandong Province, China

ZHANG Wen-xin, WANG Hui, FAN Xiao-li, WANG Qiang, FANG Yong, LIANG Yu

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  43-50.  doi:10.6040/j.issn.1671-9352.0.2021.337

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Plant community type, species composition, diversity and diameter-class structure in the Confucian Cemetery were investigated by using the quadrat survey method, and the process and trend of the succession of the plant community were explored by comparing with the historical survey data. The results showed that the plant community types increased after 50 years of succession. In addition to the original Platycladus orientalis forest, Quercus acutissima forest and Pistacia chinensis forest, there are new broad-leaved forests such as Robinia pseudoacacia forest and Gleditsia sinensis forest, and mixed broadleaf-conifer forests such as Platycladus orientalis-Pistacia chinensis forest, Platycladus orientalis-Koelreuteria paniculate forest and Quercus acutissima-Platycladus orientalis forest. Broad-leaved tree species increased in plant community. The plant community is succeeding towards the climax deciduous broad-leaved forest. Compared with 50 years ago, the coverage of shrub layer decreased, the coverage of herb layer increased, and the number of exotic plant species increased. The species composition of shrubs and herbaceous plants varied significantly in 50 years. Platycladus orientalis and Robinia pseudoacacia population were in the stable development stage, Pistacia chinensis population was in the good growth stage, and Quercus acacia population had a declining trend. The plant diversity of arbor layer, shrub layer and herb layer of Platycladus orientalis-Myosoton aquaticum association was low, and the influence of human disturbance on plant diversity was much higher than that of natural habitat. Human activities such as shrub management, plant introduction and cultivation and tourism on a regular basis have a certain influence on the plant community of the Confucian Cemetery. It is suggested that on the basis of necessary artificial afforestation and artificial conservation, human interference should be appropriately reduced to promote the succession of the plant community to the near natural forest in the Confucian Cemetery.

Optimal control of nonlinear competing populations based on the size-structure

ZHENG Xiu-juan, LUO Zhi-xue, ZHANG Hao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  51-60.  doi:10.6040/j.issn.1671-9352.0.2021.140

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The optimal control of nonlinear competing population systems based on the size-structure is studied in this paper. Firstly, the existence and uniqueness of separable form solutions are proved by using the method of characteristic lines and the fixed point theorem. Then, the adjoint system is derived. Finally, the optimal control of Bang-Bang type and the necessary condition of optimal control are given by using the concept of tangent and normal cones.

Optimal control of competitive population system with hierarchical structure

XU Yang, ZHAO Chun

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  61-70.  doi:10.6040/j.issn.1671-9352.0.2021.063

Abstract ( 542 )   PDF (430KB) ( 333 )   Save

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The optimal control problem of a class of competitive population system based on individual level difference is studied. Firstly, the existence and uniqueness of the solution of this system are obtained by the fixed point theorem, then the continuous dependence of the solution on the control variable is proved and the necessary conditions of optimal control can be get by using the concepts of conjugate system and the tangent normal cone theory.

Total colorings of one type of planar graphs with maximum degree 6

TAN Xiang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  71-75.  doi:10.6040/j.issn.1671-9352.0.2020.358

Abstract ( 587 )   PDF (524KB) ( 212 )   Save

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Let G be a planar graph with maximum degree Δ≥6 and without 5-cycles, if Δ-vertex isnt incident with 8-cycles, then χ″(G)=Δ+1.

Vertex-distinguishing Ⅰ-total colorings and vertex-distinguishing Ⅵ-total colorings of mC7

YANG Han, CHEN Xiang-en

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  76-82.  doi:10.6040/j.issn.1671-9352.0.2020.362

Abstract ( 568 )   PDF (446KB) ( 198 )   Save

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By using the methods of constructing a matrix which was composed of color sets and empty set as the elements, distributing color sets in advance and coloring explicitly, to give the optimal vertex distinguishing Ⅰ-total colorings and the optimal vertex distinguishing Ⅵ-total colorings of mC7. Thus vertex distinguishing Ⅰ-total chromatic numbers and the vertex distinguishing Ⅵ-total chromatic numbers of mC7 are determined. The results show that the VDITC conjecture and VDVITC conjecture are valid for mC7.

2-distance sum distinguishing edge coloring of K₄-minor-free graphs

QIANG Hui-ying, YAO Li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  83-86.  doi:10.6040/j.issn.1671-9352.0.2020.198

Abstract ( 597 )   PDF (338KB) ( 207 )   Save

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Let φ be a proper edge coloring of graph G, for any u,v∈V(G), if d_G(u,v)≤2 such that f(u)≠f(v) where f(u)=∑_uw∈E(G)φ(uw), then φ is the 2-distance sum distinguishing edge coloring of graph G. The 2-distance sum distinguishing edge coloring of K₄-minor-free graphs are studied by using the methods of contradiction and constructing coloring function, and a upper bound of the 2-distance sum distinguishing edge chromatic number of K₄-minor-free graphs is obtained.

Inverse of Kronecker product of integrally invertible graphs

WANG Xia, BIAN Hong, YU Hai-zheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  87-92.  doi:10.6040/j.issn.1671-9352.0.2020.344

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The Kronecker product G1⊗G2 of graphs G1 and G2 is the graph with the vertex set V(G1)⊗V(G2), two vertices (u1,v1) and (u2,v2) being adjacent in G1⊗G2 if and only if u1u2∈E(G1) and v1v2∈E(G2). The inverse of Kronecker product of integrally invertible graph is characterized.

A class of maximal inequalities for demimartingales(demisubmartingales)based on concave Young functions

FENG De-cheng, LIN Xia, LU Ya-li

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  93-96.  doi:10.6040/j.issn.1671-9352.0.2020.420

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Fubini theorem is used to obtain a class of maximal inequalities for demimartingales(demisubmartingales)based on concave Young functions.

Representation of matrices and its applications to entropy

ZHAO Ya-qi, REN Fang-guo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  97-104.  doi:10.6040/j.issn.1671-9352.0.2020.424

Abstract ( 1030 )   PDF (375KB) ( 271 )   Save

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To study the properties about the representation for probabilistic distribution of unitary similarities of a matrix and the applications about the concavity of matrix entropy, some research about block matrix, projection matrix and the concavity of matrix entropy is studied. The probabilistic distribution of unitary similarities of any square matrix, the representation of the probabilistic distribution of unitary similarities for the transformation about a complete set of orthogonal projection matrix of any density matrix and some inequalities of matrix entropy are obtained.

A result on Kenmotsu statistical structures on a hyperbolic space

JIANG Yan, WU Feng, ZHANG Liang

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2021, 56(11):  105-110.  doi:10.6040/j.issn.1671-9352.0.2021.156

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Hyperbolic space is a Riemannian manifold with constant negative sectional curvature. In particular, an odd-dimensional hyperbolic space H 2n+1 with sectional curvature -1 can be endowed with the classical Kenmotsu structure. In this paper, we prove that on H 2n+1 there exists no non-trivial Kenmotsu statistical structure with constant φ-curvature based on the classical Kenmotsu structure.