Table of Content

15 August 2017, Volume 34 Issue 4 Previous Issue    Next Issue

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The Life-cycle Model with Optimal Years of Working and Leisure under Given Survival Schedule ZHU Chang-yan, CAI Dong-han, CHEN Zhong-bin 2017, 34 (4):  331-344.  doi: 10.3969/j.issn.1005-3085.2017.04.001 Abstract ( 99 )   PDF (211KB) ( 213 )   Save In this paper, a life-cycle model with utility from both consumption and leisure which is obtained from retirement is setup to inquire how the individuals optimally chose the retirement age facing the given wage growth rate, longevity and given survival schedule. It is proved that there exists an optimal retirement age under conditions of exponential survival or realistic survival and the retirement age increases with respect to the wage growth rate and the longevity. In the end, the effect of wage growth rate and longevity on the retirement age is presented by numerical simulation. Related Articles | Metrics

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Improved Four-subspace Method and Its Application to Equipment Status Monitoring in Power Plants ZHANG Fan, LING Jun, WEI Xin, MEI Yu, JING Wen-feng 2017, 34 (4):  345-353.  doi: 10.3969/j.issn.1005-3085.2017.04.002 Abstract ( 133 )   PDF (638KB) ( 231 )   Save As a usual status monitoring method, four subspace method is only applicable under the condition that process data follows Gaussian process. However, most of industrial data are non-Gaussian, which makes the application of the four subspace method rather limited. This paper uses a kernel density estimation method to improve the traditional four subspace method, and designs a four subspace status monitoring method based on the kernel density estimation, which is suitable for general distributions. Finally, using the real data of high temperature superheater in some electric power plant, the empirical results show that the improved four subspace method is more universal, and it can significantly improve the status monitoring effect. Related Articles | Metrics

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Rough Dissimilarity Measurement and Its Application in Hierarchical Clustering LI Chun-zhong, ZHENG Yu-bang, WANG Ting 2017, 34 (4):  354-366.  doi: 10.3969/j.issn.1005-3085.2017.04.003 Abstract ( 146 )   PDF (580KB) ( 205 )   Save Local structural feature is important in data analysis procedure. In order to obtain a simple and effective feature detection method for data set's local structures, this paper proposed for detecting local structure a direction consistence measurement, rough dissimilarity, by combing re-sampling and a classical neighborhood selection method. This measurement is a optimized selection method for neighborhood, which considers not only the classical sorting method based on Euclidean distance but also the local structures of the data set. The new dissimilarity measurement can be used in unsupervised learning to construct a hierarchical subgraph clustering, RDClust, because of the advantages of a low computation load and a good direction structure detection performance. The new clustering based on direction consistence measurement has three advantages: 1) It has a low computation load and is an approximately linear method; 2) It needs no assumption for the shape and the distribution of cluster, and can detect local structures of a data set automatically; 3) It has only one parameter which is relatively robust to clustering results. The new clustering based on direction consistence dissimilarity has good performance in testing with synthetic and real data sets. Related Articles | Metrics

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Pricing of Perpetual Corporate Debt with Default Capital Reorganization in Jump-diffusion Model LIN Jian-wei, LI Hui-min 2017, 34 (4):  367-374.  doi: 10.3969/j.issn.1005-3085.2017.04.004 Abstract ( 120 )   PDF (176KB) ( 188 )   Save In order to improve the ability of a company to deal with emergent events and a capital reorganization, based on the default capital reorganization scheme of debt-equity swap, we investigate the pricing problem of the perpetual corporate debt and the optimal capital structure under the framework of a jump-diffusion model with $-1$ jump size. Problems are solved by applying the optimal stopping technique and a structural method. The closed-form formulas for the perpetual corporate debt, the equity and the total value of corporate are obtained by a differential equation method, moreover, the optimal default boundary and the optimal leverage ratio are also given. Finally, a numerical analysis is conducted to reveal the financial phenomenon caused by the jump intensity. Related Articles | Metrics

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Bus Dispatching Optimization Model Considering Satisfaction Degrees JIANG Shao-yi, WANG Bo, YAN Zh 2017, 34 (4):  375-382.  doi: 10.3969/j.issn.1005-3085.2017.04.005 Abstract ( 260 )   PDF (278KB) ( 347 )   Save In this paper, we study the mathematical modelling of bus dispatching problem. Using the historical data of arriving passengers and leaving passengers at different bus stops and various time points, we estimate the expected values of the arriving rate and leaving rate of passengers at different stops. Utilizing the utility function theory, we construct the satisfaction degree indexes, which reflect the satisfaction degrees of passengers when they are waiting for the bus and taking the bus, respectively. Through maxinizing the weighted overall satifaction index and considering different constraints, we construct a mix-integer programming model for the bus dispatching problem. Finally, we discuss possible solution methods. Related Articles | Metrics

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A Nonconforming Finite Element Method for the Linearly Elastic Flexural Shell SHEN Xiao-qin, BAI Lin, YANG Qian, LI Hao-ming, WANG Tian-tian 2017, 34 (4):  383-392.  doi: 10.3969/j.issn.1005-3085.2017.04.006 Abstract ( 133 )   PDF (537KB) ( 247 )   Save In this paper, we construct a Galerkin nonconforming finite element method for the linear elastic flexural shell model proposed by Ciarlet-Lods-Miara. First, we discretize the integral domain with Delaunay triangulation. We approximate the first two component of the displacement by the first-order Lagrangian polynomial, whereas we approximate the third component of the displacement, i.e., the normal displacement, by the nonconforming Morley element. Secondly, we discuss the existence, uniqueness, and a priori error estimate of the numerical solution. Finally, we run numerical experiments for the conical shell with special boundary conditions. We derive the displacements of the conical middle surface under the different meshes. We analyze the numerical results which show that the finite element method is convergent and effective. Related Articles | Metrics

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Robust Mean Square Stability for Stochastic Differential Delay Systems with Nonlinear Perturbation CHAI Shuang-long, LI Shu-yong 2017, 34 (4):  393-408.  doi: 10.3969/j.issn.1005-3085.2017.04.007 Abstract ( 113 )   PDF (546KB) ( 200 )   Save This paper is concerned with the robust mean square stability for stochastic differential systems with multiple time-varying delays and nonlinear perturbation in memory state feedback controller. By establishing a Lyapunov-Krasovskii functional, using the It$\hat{\rm o}$ formula, introducing appropriate free-weighting matrices, making use of an integral inequality and an analytical technique, based on the linear matrix inequality (LMI) and Schur complement theorem, the robust mean square asymptotically stability and the robust mean square  exponentially stability for the system are obtained. In addition, the corresponding state feedback controllers are constructed. The results are dependent on delays and stochastic perturbation, and extend the existing results. Related Articles | Metrics

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Global Dynamics for a Two-patch SIS Model with Time Delay and Transport-related Infection LIU Jun-li, JIA Ying, ZHANG Tai-lei 2017, 34 (4):  409-423.  doi: 10.3969/j.issn.1005-3085.2017.04.008 Abstract ( 132 )   PDF (268KB) ( 287 )   Save We formulate a delayed SIS model to describe the effect of transport-related infec-tion. The basic reproduction number is obtained. By the linearization method and comparison principle, it is proved that the disease-free equilibrium is globally asymptotically stable and the disease always dies out if the basic reproduction number is less than unity. While there exists a unique endemic equilibrium which is globally attractive and the disease persists if the basic reproduction number is greater than unity. The simulation results show the influence of travel rates on the disease spread. The dependence of the basic reproduction number on the travel rates during travel is also analyzed. Related Articles | Metrics

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Global Dynamics of a Chronic Virus Infection Model with Bell-shaped Proliferation Rate of Specific Immune Cells LI Jia, LI Jian-quan, LI Yi-qun 2017, 34 (4):  424-436.  doi: 10.3969/j.issn.1005-3085.2017.04.009 Abstract ( 91 )   PDF (385KB) ( 290 )   Save The specific immune response plays a very important role in controlling the viral infection within host. A chronic virus infection model with bell-shaped proliferation rate of specific immune cells is proposed and investigated in this paper, where the bell-shaped expansion implies that the proliferation rate of immune cells could decrease when the virus load is sufficiently large. The impairment of virus on immune response is also incorporated in the model. For the model, the net reproduction number of the immune response with virus impairment is found, and the local dynamical behaviors are demonstrated completely. In order to determine the global dynamics, the center manifold theory is applied for some critical situations, and we also construct the suitable Dulac function to rule out the existence of perio-dic solutions. The obtained results in this paper show that the backward bifurcation may occur under certain conditions, which reflects the dependence of dynamics of the model on the initial conditions. Finally, the numerical simulation also suggests that both eventual monotonicity and sustained oscillation of viral population and immune response are possible for the model. Related Articles | Metrics

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The Homotopic Mapping Solution to the Sea-air Oscillator System for the EI Ni$\tilde{\rm n}$o-southern Oscillation SHI Juan-rong, LIN Wan-tao, MO Jia-qi 2017, 34 (4):  437-448.  doi: 10.3969/j.issn.1005-3085.2017.04.010 Abstract ( 65 )   PDF (138KB) ( 198 )   Save The EI Ni$\tilde{\rm n}$o-southern oscillation is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The aim of this paper is to create an asymptotic method of solve nonlinear equation for the EI Ni$\tilde{\rm n}$o-southern oscillation system. Firstly, the solution to corresponding initial value problem is got by using the characteristic value theory for the linear homogeneous ordinary differential system. And this solution is a zero-th order approximation of solution to the original system. Then, the arbitrary order iterative solutions for the original system are structured with the help of homotopic mapping relational expressions successively. Finally, based on a class of oscillator for the EI Ni$\tilde{\rm n}$o-southern oscillation system, employing the homotopic mapping method, the asymptotic solution to corresponding problem is studied. And there is proved this asymptotic solution is a uniformly valid. The results is that the homotopic mapping method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillator for the EI Ni$\tilde{\rm n}$o-southern oscillation system. Related Articles | Metrics