Table of Content

  

20 November 2019
Volume 54 Issue 11

A blindly public verifiable outsourcing scheme for matrix multiplication

ZHENG Jing-zhu, YANG Hai-ning, SU Ye, QIN Jing

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  1-11.  doi:10.6040/j.issn.1671-9352.0.2019.142

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An outsourcing scheme for matrix multiplication in verifiable database is proposed. This scheme supports the blindly public verification, and protects identity privacy and data privacy for clients. This can prevent the servers malicious behavior. The security analysis proof shows that the proposed scheme is adaptive chosen-message security in the random oracle model. The scheme uses the amortized model to reduce the computational overhead. In addition, the resulos of simulated experiment show that the computational overhead of our scheme is smaller than the existing schemes.

Elliptic curve scalar multiplication algorithm based on bronze ratio addition chain

LIU Shuang-gen, LI Dan-dan, LI Xiao

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  12-19.  doi:10.6040/j.issn.1671-9352.0.2019.028

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A new efficient and secure elliptic curve scalar multiplication algorithm is proposed. There is an new addition chain based on generalized Fibonacci sequences, which is called bronze ratio addition chain(BRAC). Each iteration of this algorithm executes fixed “3P1+P₂” operation, which can resist the simple power analysis naturally. BRAC has a shorter chain length, combined with the new projection coordinates can improve efficiency of the previous ones. The experimental results show that the new algorithm is 31.73% faster than golden ratio addition chain(GRAC).

Equilibrium strategies of dual-channel supply chain considering the retailers social comparison behavior

WU Zheng-xiang, LI Bao-ku

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  20-34.  doi:10.6040/j.issn.1671-9352.0.2018.666

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Equilibrium strategies of one-to-one dual-channel supply chain that the retailer with social comparison behavior is investigated. According to the relationship of horizontal competition and vertical trading between the seller and the manufacturer, the retailers social comparison behavior is divided into horizontal and vertical social comparison behavior. The equilibrium strategies of dual-channel supply chain that the retailer with horizontal competitive preference were discussed, and the results show that both the preference of behind aversion and ahead seeking of the retailer can reduce his bargaining power with manufacturer; and the manufacturer can control the price competition between channels by using his pricing power. In addition, the equilibrium strategies of dual-channel supply chain that the retailer with both horizontal and vertical social comparison behavior were analyzed, and the findings indicate that in the manufacturer dominant market, the influence direction of retailers behind aversion preference on the equilibrium strategies of dual-channel supply chain is not affected by the retailers disadvantageous inequity aversion preference; however, under the retailer-dominated market, the influence direction of retailers ahead seeking preference on the equilibrium strategies of dual-channel supply will be changed by the higher advantageous inequity aversion preference of the retailer.

Decision-making and coordination of green supply chain with risk aversion under government subsidies

ZHANG Ke-yong, LI Chun-xia, YAO Jian-ming, LI Jiang-xin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  35-51.  doi:10.6040/j.issn.1671-9352.0.2018.598

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In the green supply chain, both the government green subsidy and the member risk aversion characteristics are considered, the decentralized decision model and the centralized decision model are established. Through the analysis of the model, the risk aversion characteristics of the manufacturer will adversely affect the development of the green supply chain is found, but the implementation of the government subsidy policy could effectively reduce the negative effects. The more a retailers is afraid of risk, the more conductive to the improvement of product green degree. Both the government subsidy ratio and the member risk aversion will affect the member decision variable value and utility value and the intensity of the two influences is different. The incentives of government subsidy policies can weaken the negative effects of member risk aversion on their own utility, and promote the overall utility and social welfare of the supply chain to be higher than the risk-neutral situation of members. By comparing the coordination process of the three kinds of contracts for the green supply chain system, it is concluded that the revenue sharing-cost sharing contract is better than the single traditional contract coordination and verified by numerical simulation.

Dynamic analysis of Bertrand game model about taxation of government and subsidy

CAO Hui-rong , ZHOU Wei, CHU Tong, ZHOU Jie

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  52-62.  doi:10.6040/j.issn.1671-9352.0.2018.530

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In the context of government implements both subsidy and taxation policies, a dynamics Bertrand game model is established based on bounded rationality. The local asymptotic stability of equilibrium points of the system is analyzed using Jury conditions, the evolution process of the system after equilibrium point instability is discussed by numerical simulation method. It is found that enterprise profit is optimal in Nash equilibrium. The high speed of price adjustment or the low share of government subsidies make the system chaotic, and the profits of enterprises will increase negatively. In order to ensure that enterprises are in the profit mode, the state feedback and parameter adjustment control strategy are adopted to keep the system in Nash equilibrium for a long time. In addition, by analyzing the internal structure of the attraction basin, it is found that the high adjustment speed makes the system bifurcate globally, and the choice of initial decision-making appears unpredictable.

Dynamic analysis of game model considering advertising spillover effect

LU Zheng-yu, ZHOU Wei, YU Huan-huan, ZHAO Na

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  63-70.  doi:10.6040/j.issn.1671-9352.0.2019.159

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Based on the bounded rationality, the dynamic adjustment game model of bounded rationality is established by introducing the parameters of advertising spillover effect, adjustment speed and advertising promotion effect. Firstly, the stability of the system is discussed based on the eigenvalues of Jacobi matrix and Jury criterion. Secondly, the dynamic evolution process of the system under the parameters of advertising spillover effect and adjustment speed is analyzed by the bifurcation diagram of single and double parameters, the maximum Lyapunov index diagram and the attractor basin. The results show that when the adjustment speed of advertising spillover effect is slower, the system will be in a more stable state, and will be in a stable state. In addition, when the adjustment speed increases, the system appears chaos from period and attractor coexistence, which indicates that the market will be chaotic.

Bipolar fuzzy prime ideals in negative non-involutive residuated lattices

LIU Chun-hui

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  71-80.  doi:10.6040/j.issn.1671-9352.0.2019.245

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The problem of bipolar fuzzy ideals is further studied in negative non-involutive residuated lattices. The concept of bipolar fuzzy prime ideal(BF-prime ideal for short)is introduced and its properties are investigated. Some equivalent characterizations of BF-prime ideal are obtained. The BF-prime ideal theorem in a prelinearity negative non-involutive residuated lattice is established. It is proved that the NRL-homomorphism image and the inverse image of a BF-prime ideal are also BF-prime ideals. This work further expands the way for revealing the structural characteristics of negative non-involutive residuated lattices.

MV-algebra valued metric-based fuzzy rough sets

XIONG Xing-guo, LU Ling-xia

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  81-89.  doi:10.6040/j.issn.1671-9352.0.2018.674

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MV-algebra valued metric-based fuzzy rough set model is defined. The interrelations between -hemimetrics and the standard real valued hemimetrics are investigated. It is shown that -hemimetrics and -similarities are equivalent to each other. The properties of fuzzy rough approximation operators and the related definable sets are studied.

Open remote neighborhoods of topological systems and their applications

FENG Dan-dan, WU Hong-bo

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  90-96.  doi:10.6040/j.issn.1671-9352.0.2018.532

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The concept of open remote neighborhood is proposed in topological system, and its properties with applications are studied. At first, the concept of open remote neighborhood is proposed in topological system, and its basic properties are discussed. Furthermore, a method of determining topological system is given by open remote neighborhood systems. The definition of continuous of mapping at a fixed point between topological systems is defined by open remote neighborhood systems, by which the equivalent form of continuous mapping between topological systems is given. At last, the equivalent forms of some separations of topological systems are given by using the open remote neighborhood systems.

On the (α,O)-migrative of 2-uninorms over overlap functions

SONG Yi-fan, ZHAO Bin

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  97-107.  doi:10.6040/j.issn.1671-9352.0.2019.411

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Based on the concept of (α,O)-migrative of uninorms over overlap functions, the notion of (α,O)-migrative of 2-uninorms over overlap functions is introduced, the equivalent characterizations of(0,O)-migrative and(1,O)-migrative are given. Furthermore,(α,O)-migrative of 2-uninorm U² over overlap function O when the 2-uninorm U² belongs to five common types of 2-uninorms are discussed, respectively, in particular, when U 2∈U 2_k, U 20,k, U 20,1, U 21,0, the structure of overlap functions under the migrativity functional equation is characterized.

Representation of the number operator in continuous-time Guichardet-Fock space

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  108-114.  doi:10.6040/j.issn.1671-9352.0.2019.513

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The paper considers the representation of the number operator N in continuous-time Guichardet-Fock space L2(Γ;η). Firstly, the gradient-Skorohod integral representation of N is given by using modified stochastic gradient SymbolQC@ and non-adaptive Skorohod integral δ:N=δSymbolQC@. Secondly, the representation of Bochner integral is given: N=∫_R+SymbolQC@^*sSymbolQC@sds in the sense of the inner product, by means of the family of isometric operator {SymbolQC@^*sSymbolQC@_s; s∈R₊}. Meanwhile, the spectrum of N is just the nonnegative integral N, and for any n≥0, the closed subspace L2(Γ⁽ⁿ⁾;η) of Guichardet-Fock space L2(Γ;η) is just the eigenspace corresponding to the eigenvalue n, and N has the spectrum representation: N=∑^∞_n=1nJ_n, where J_n:L2(Γ;η)→L2(Γ⁽ⁿ⁾;η), is the orthogonal projection.

An image restoration algorithm based on variable exponential fractional order total variation and integer order total variation

WANG Ying-mei, WANG Zhen-dong, LI Gong-sheng

JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE). 2019, 54(11):  115-126.  doi:10.6040/j.issn.1671-9352.0.2019.358

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This paper proposes a new variational image restoration algorithm based on variable exponential total variation(TV)and integer order TV. The energy functional of the variational problem is mainly composed of three parts: a fractional order TV regularization term of variable exponent p(x), an integer order TV regularization term and a data fidelity term. The exponential p(x) in this model is a function which related to the gradient information of the image. As the combination of the fractional order derivative and integral derivative, the proposed method can effectively remove the noise of the image, protect the image boundary, and also better retain the image texture details. At the same time, this method can greatly eliminate the staircase effect and the speckle effect. To solve the model, using the variational method, the optimization problem can be simply transformed into a gradient descent flow. Finally, to validate the effectiveness of our proposed method, we give the experiments with simulated data and real data. The experimental results show that this method can effectively remove noise, keep boundary and texture details and is robust to noise. And it has certain practical application value.