Table of Content

15 February 2016, Volume 33 Issue 1 Previous Issue    Next Issue

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A Game between Insurer and Reinsurer under the Heston Model WANG Su-xin, RONG Xi-min, ZHAO Hui 2016, 33 (1):  1-16.  doi: 10.3969/j.issn.1005-3085.2016.01.001 Abstract ( 24 )   PDF (228KB) ( 3 )   Save This paper considers an optimal investment problem for both insurer and reinsurer. The insurer is allowed to purchase proportional reinsurance and both the insurer and reinsurer are allowed to invest in a risk-free asset and a risky asset whose price process satisfies the Heston's stochastic volatility model. Firstly, we establish the objective function in the sense of maximizing the exponential utility of both the insurer and reinsurer on terminal wealth; Secondly, by solving the Hamilton-Jacobi-Bellman system, the closed-form expressions for the optimal reinsurance and investment strategies and the optimal value function are obtained; Finally, some numerical illustrations and sensitivity analysis for the proposed theoretical results are provided. Related Articles | Metrics

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Optimal Design and Analysis of Maintenance Service Contract PENG Yi, WU Jin-biao 2016, 33 (1):  17-24.  doi: 10.3969/j.issn.1005-3085.2016.01.002 Abstract ( 18 )   PDF (165KB) ( 6 )   Save In this paper, we study a maintenance model with a given type of service contract. In order to study the optimal designing of machine maintenance contracts, this paper develops a multi-server queueing model to obtain the expected net incomes by each machine and the agent. Using a non-cooperative game formulation, we achieve the agent's optimal pricing strategy, the length of warranty and the number of repairmen. We find that the optimal length of warranty and the number of repairmen are independent of the warranty price functions. Furthermore, for fixed lifetime of the unit, the number of customers hardly affects the optimal length of warranty. Related Articles | Metrics

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A Generalized Eigenvalue Approach to Analyzing T-SPH$/M/1/N$ Queue with State-dependent Service Rate ZHANG Hong-bo, YANG Xian-li, FENG Ping-hua 2016, 33 (1):  25-35.  doi: 10.3969/j.issn.1005-3085.2016.01.003 Abstract ( 20 )   PDF (205KB) ( 2 )   Save In this paper, we analyze a finite T-SPH$/M/1/N$ queue model with state-dependent service rate, where T-SPH denotes the continuous time phase type distribution defined on a birth and death process with countable number of states. The queue system investigated can be described by a quasi-birth-and-death (QBD) process with infinite levels and finite number of phases. By analyzing the QBD process with the method of generalized eigenvalues, we derive the analytic expression of the stationary queue length distribution of the queue model. Meanwhile, to explain the validity of our method, we also present several numerical examples to illustrate the effect of the varying parameters on the system performance. Related Articles | Metrics

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Research on Magic Squares in Trend Free Plans MA Hai-nan, CHEN Xue-ping 2016, 33 (1):  36-44.  doi: 10.3969/j.issn.1005-3085.2016.01.004 Abstract ( 23 )   PDF (164KB) ( 3 )   Save There are always trend disturbances in design of experiment, which arise from the time trend or the space trend. In this paper, several applications of magic squares and perfect magic squares in trend free plans are discussed. Firstly, based on the combinational properties of magic squares, a class of plans which keep the estimations of design factors and trend disturbance factors independent are obtained. Moreover, by using perfect magic squares, the trend free plans with more factors are provided. Finally, some construction methods of such trend free plans are developed by magic squares and perfect magic squares. Meanwhile, the results between concentric magic squares and cross validation are also proved. Related Articles | Metrics

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Node Placement Method by Bubble Simulation and Mesh Generation in Three-dimensional Region SHA Xin-chi, NIE Yu-feng, ZHANG Wei-wei 2016, 33 (1):  45-51.  doi: 10.3969/j.issn.1005-3085.2016.01.005 Abstract ( 26 )   PDF (785KB) ( 4 )   Save This paper studies how to generate high-quality node sets and use the nodes to generate the mesh in the three-dimensional region. According to the geometric description of the boundary region and the desired node-spacing function, the node placement method by bubble simulation is used on the surface and inside the area to layout the nodes successively. After the placement of the nodes distribution is finished, the bubble-type local mesh generate method and the Delaunay mesh method can be used to generate the mesh on the area surface and inside the area, respectively. Then quality of the bubble distribution is measured according to the quality of the Delaunay mesh. Numerical examples show that uniform node sets and non-uniform node sets generated by this method have high quality, and non-uniformly node sets obtained by this method have good gradualness. Related Articles | Metrics

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Numerical Simulation of Viscoelastic Flows Using Discontinuous Galerkin Finite Element Method GUO Hong-ping, OUYANG Jie, YANG Guang-hui, ZHOU Wen 2016, 33 (1):  52-62.  doi: 10.3969/j.issn.1005-3085.2016.01.006 Abstract ( 24 )   PDF (1168KB) ( 2 )   Save The traditional finite element method needs to supplement a stabilization scheme to simulate Oldroyd-B viscoelastic flows. To alleviate this issue, a unified discontinuous Galerkin finite element framework based on unstructured grids is proposed in this paper. The system contains two key points: one is using the IPDG (interior penalty discontinuous Galerkin) method to discretize mass and momen-tum equations, and the other is employing the RKDG (Runge-Kutta DG) method to solve the Oldroyd-B constitutive equation. Simulation results reveal the intrinsic characteristics of non-Newtonian viscoelastic fluids and indicate that the approach can effectively overcome the drawback of the traditional finite element method, which redundantly introduces stabilization process in the method. Moreover, these results substantiate that the proposed method is simple to implement, has high accuracy and can be used to simulate complex viscoelastic flows with stress singularity. Related Articles | Metrics

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Newton's Iterative Method for Solving the Matrix Equation $X-A^{T}X^{-1}A=Q$ CHENG Ke-xin, PENG Zhen-yun, DU Dan-dan, XIAO Xian-wei 2016, 33 (1):  63-72.  doi: 10.3969/j.issn.1005-3085.2016.01.007 Abstract ( 27 )   PDF (163KB) ( 3 )   Save Nonlinear matrix equation $X-A^{T}X^{-1}A=Q$ has been widely applied to control theory, dynamic programming, interpolation theory and stochastic filtering. In this paper, an equivalent form of this equation is derived, and the Newton's iterative method is applied to solving this equivalent equation. By defining a class of matrix functions which have the property that the matrix sequence generated by the Newton's method to compute its root is the same as that generated by the Newton's method to solve the nonlinear matrix equation, we prove that the matrix sequence generated by the Newton's method to solve the nonlinear matrix equation is included in the closed ball which has an unique solution to the matrix equation. It is also convergent to the unique solution in that closed ball. The error estimate of the approximate solution with the true solution is derived, and a numerical example to illustrate the efficiency of Newton's method is also given. Related Articles | Metrics

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Hybrid Projective Synchronization of Markovian Jumping Complex Networks with Mode-dependent Time-varying Delays SHAO Hao-yu, HU Ai-hua, HU Man-feng 2016, 33 (1):  73-90.  doi: 10.3969/j.issn.1005-3085.2016.01.008 Abstract ( 25 )   PDF (312KB) ( 3 )   Save Hybrid projective synchronization of complex networks has recently been applied to various areas of engineering, applied mathematics and others. In this paper, the problem of hybrid projective synchronization for a class of Markovian jumping complex networks with mode-dependent time-varying delays is investigated. Linear coupling function and nonlinear coupling function are considered simultaneously for each response system in complex networks. Based on Lyapunov stability theory and linear matrix inequality method, some sufficient conditions for hybrid projective synchronization of complex networks are derived. Numerical simulations are finally demonstrated to illustrate the effectiveness of the developed theory. The results provide theoretical basis for hybrid projective synchronization of complex networks and control of system with mode-dependent time-varying delays. Related Articles | Metrics

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Mean Square Exponential Stability and Periodic Solutions of Stochastic Delay Cellular Neural Networks with Impulses LI Hao, LI Yu 2016, 33 (1):  91-105.  doi: 10.3969/j.issn.1005-3085.2016.01.009 Abstract ( 30 )   PDF (139KB) ( 3 )   Save For a class of stochastic cellular neural networks with discrete delays and impu-lses (SDCNNswI), this paper discusses their exponential stability and the existence of periodic solutions. Firstly, Poincare contraction theory is utilized to derive the conditions to guarantee the existence of periodic solutions of SDCNNswI. Next, Lyapunov function, stochastic analysis theory and Young inequality are develo-ped to derive some theorems. These theorems provide several sufficient conditions to guarantee that the periodic solutions of SDCNNswI are mean square exponentially stable. These sufficient conditions only include the governing parameters of SDCNNswI and can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate the usefulness of the obtained results. Related Articles | Metrics

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Positive Periodic Solutions of First-order Delay Differential Equations WENG Ai-zhi 2016, 33 (1):  106-110.  doi: 10.3969/j.issn.1005-3085.2016.01.010 Abstract ( 23 )   PDF (89KB) ( 2 )   Save In this paper, we study the existence of positive periodic solutions for a particular class of first-order delay differential equations, where the linearized system may be degenerate. It is known that most methods may fail to guarantee the existence of periodic solution under the degenerate case. To alleviate this issue, this paper presents an efficient algorithm based on Schauder's fixed point theorem. Theorems which list the conditions for the existence of periodic solutions are presented. Simulation studies show the correctness of the improved method. Related Articles | Metrics