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STOCHASTIC MAXIMUM PRINCIPLE FOR MIXED REGULAR-SINGULAR CONTROL PROBLEMS OF FORWARD-BACKWARD SYSTEMS

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Journal of Systems Science & Complexity 2013年第6期26卷 886-901页

作者： ZHANG Feng school of Mathematics and Quantitative economics Shandong University of Finance and Economics

This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion *** control problem is difficult to solve with the classical method of spike *** authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control *** optimality conditions are also investigated.

关键词： Forward-backward system maximum principle relaxed control singular control.

Evaluation matrix with the speed feature based on double inspiriting control lines

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Journal of Systems Engineering and Electronics 2013年第6期24卷 962-970页

作者： Weiwei Liu Chunsheng Shi Jing Li school of economics and Management Harbin Engineering University school of economics and Management Harbin Institute of Technology

Methods of the comprehensive evaluation have been studied for many years. However, the change speed of evaluated objects was rarely considered by the existing evaluation methods. An evaluation matrix is proposed to remedy this deficiency. Firstly, the change speed state （CSS） of the evaluated objects is analyzed based on double inspiriting control lines （DICLs）, and a matrix of the CSS is constructed. Then, 72 elements in the matrix are analyzed, and formulas describing each CSS are given. The efficiency of the proposed evaluation matrix is proved when the CSS merges with the change speed trend （CST） in the dynamic comprehensive evaluation. Finally, a computing example shows that the proposed evaluation matrix is feasible in the dynamic comprehensive evaluation with the speed feature.

关键词： double inspiriting control lines (DICLs) change speed state (CSS) change speed trend (CST) evaluation matrix

COMPARISONS OF LOW CARBON POLICIES IN SUPPLY CHAIN COORDINATION

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Journal of Systems Science and Systems Engineering 2014年第3期23卷 343-362页

作者： Lei YANG Chenshi ZHENG Minghui XU school of economics and Commerce South China University of Technology school of economics and Management Wuhan University

This paper investigates the influence of low-carbon policies on channel coordination for a two-echelon supply chain consisting of one supplier and one retailer. Four different models are considered： the basic model, the carbon emission model, the carbon emission trading model and the carbon tax model. We find that the government policy on all carbon emission models is not universal among the firms as well as the customers. The carbon emission trading policy is always better than the carbon emission policy and the carbon tax policy when the allocated carbon emission quotas are greater than the carbon emissions. The carbon emission trading policy is proved to be an effective mechanism which can motivate the supply chain to reduce carbon emissions. Under certain conditions, the supply chain prefers the carbon emission trading policy with higher carbon price to other policies. In the framework of Stackelberg game with the supplier as the leader, for each carbon policy, the paper presents coordination mechanism with the all-unit wholesale quantity discount contract （AWQD）. We analyze and compare the influence of low-carbon policies on channel coordination for the foul＂ low-carbon policies. Numerical experiments are conducted to examine our findings.

关键词： Carbon emission low-carbon policy carbon quotas supply chain coordination quantitydiscount

THE EFFECTS OF MARKET DEPTH ON THE ARRIVAL RATE OF ORDERS

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Journal of Systems Science & Complexity 2014年第6期27卷 1192-1203页

作者： ZHANG Qiang LIU Shancun QIU Wanhua school of economics and Management Beijing University of Chemical Technology school of economics and Management Beihang University

This paper presents a model to describe the dynamic trading process in limit order *** studying the dynamic pattern of execution probabilities of limit orders with both time and the depth of limit order book,the authors conclude with the following properties:Arrival rates of market buy orders increase as the depth of buy queue in the book increases and decrease as the depth of sell queue increases,and vice versa;similar regularities for the arrival rate of market sell orders;both the arrival rate of market buy order and market sell orders increase as the depth of both sides in the book increases by the same ***,the authors describe more detailed temporary and permanent effects of the market depth on the arrival rates of orders.

关键词： Arrival rate limit order market market depth private value.

WEAK ORLICZ SPACE AND ITS CONVERGENCE THEOREMS

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Acta Mathematica Scientia 2010年第5期30卷 1492-1500页

作者：刘宁叶永刚 school of economics and Managements Wuhan University Finance school Hubei University of Economics

In this article, a class of weak Orlicz function spaces is defined and their basic properties are discused. In particular, for the sequences in weak Orlicz space, we establish several basic convergence theorems including bounded convergence theorem, control convergence theorem and Vitali-type convergence theorem and so on. Moreover, the conditional compactness of its subsets is also discussed.

关键词： weak Orlicz space convergence theorem conditional compactness

Existence of Solutions of Generalized Quasi-Variational Relation Problems by the Inductive Relations and Some Applications

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Journal of Systems Science & Complexity 2016年第1期29卷 219-227页

作者： YANG Zhe school of economics Shanghai University of Finance and Economics Key Laboratory of Mathematical economics(SUFE) Ministry of Education

By the inductive relations,this paper first obtains some existence theorems of solutions for generalized quasi-variational relation problems,which are different from other *** applications,some existence theorems of solutions for generalized quasi-equilibrium problems and NS-equilibria for noncooperative games under uncertainty are obtained.

关键词： Fixed point theorem generalized quasi-equilibrium problem generalized quasi-variational relation problem inductive relation NS-equilibrium uncertainty

Properties of Phase Transition of Traffic Flow on Urban Expressway Systems with Ramps and Accessory Roads

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Communications in Theoretical Physics 2011年第11期56卷 945-951页

作者：梅超群刘业进 school of Statistics Capital University of Economics and Business school of Urban economics and Public Affair Capital University of Economics and Business

In this paper, we develop a cellular automaton model to describe the phase transition of traffic flow on urban expressway systems with on-off-ramps and accessory roads. The lane changing rules are given in detailed, the numerical results show that the main road and the accessory road both produce phase transitions. These phase transitions will omen be influenced by the number of lanes, lane changing, the ramp flow, the input flow rate, and the geometry structure.

关键词： traffic flow ramp phase transition

Hierarchical hesitant fuzzy K-means clustering algorithm

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Applied Mathematics(A Journal of Chinese Universities) 2014年第1期29卷 1-17页

作者： CHEN Na XU Ze-shui XIA Mei-mei school of economics and Management Southeast University school of Applied Mathematics Nanjing University of Finance and Economics Business school Sichuan University school of economics and Management Tsinghua University

Due to the limitation and hesitation in one＇s knowledge, the membership degree of an element to a given set usually has a few different values, in which the conventional fuzzy sets are invalid. Hesitant fuzzy sets are a powerful tool to treat this case. The present paper focuses on investigating the clustering technique for hesitant fuzzy sets based on the K-means clustering algorithm which takes the results of hierarchical clustering as the initial clusters. Finally, two examples demonstrate the validity of our algorithm.

关键词： 90B50 68T10 62H30 Hesitant fuzzy set hierarchical clustering K-means clustering intuitionisitc fuzzy set

Two 8-node quadrilateral spline elements by B-net method

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Acta Mechanica Sinica 2012年第6期28卷 1620-1629页

作者： Juan Chen Chong-Jun Li school of Mathematics and Quantitative economics Dongbei University of Finance and Economics school of Mathematical Sciences Dalian University of Technology

Isoparametric quadrilateral elements are widely used in the finite element method, but the accuracy of the isoparametric quadrilateral elements will drop obviously deteriorate due to mesh distortions. Spline functions have some properties of simplicity and conformality. Two 8-node quadrilateral elements have been developed using the trian- gular area coordinates and the B-net method, which can ex- actly model the quadratic field for both convex and concave quadrangles. Some appropriate examples are employed to evaluate the performance of the proposed elements. The nu- merical results show that the two spline elements can obtain solutions which are highly accurate and insensitive to mesh distortions.

关键词： Spline finite element B-net method Quadri-lateral element - Bivariate spline interpolation The secondorder completeness