Table of Content

15 August 2020, Volume 37 Issue 4 Previous Issue   

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The Early Transmission Characteristics of Corona Virus Disease 2019 Based on the Reaction Diffusion Equation in Wuhan GUO Zun-guang, LI Ming-tao, CHANG Li-li, ZHANG Juan, LIANG Juan, XING Guo-rong, ZHANG Wei, SUN Gui-quan 2020, 37 (4):  391-402.  doi: 10.3969/j.issn.1005-3085.2020.04.001 Abstract ( 1182 )   PDF (7723KB) ( 270 )   Save The paper researches the early transmission characteristics of Corona Virus Disease 2019 in Wuhan based on the SEIR (Susceptible-Exposed-Infectious-Removed) spatial reaction diffusion model. In terms of the open data published by China CDC and Wuhan Health Committee, the least square formula of reaction diffusion equation is proposed, then the parameter estimation of the infection rate is calculated by the least square method and the optimal values of model parameters are obtained. The model simulates the spatial transmission of the infected and potential patients from December 8, 2019 to January 5, 2020 showing that the disease will develop from single point outbreak to multi-point infection. In the meantime, the number of patients in fixed space will increase with the spread. Furthermore, the sensitivity analysis of diffusion rate and infection rate reveals that the cumulative number of the infected will increase with the increase of infection rate and diffusion rate, the sensitivity of infection rate is greater than that of diffusion rate. Therefore, for the emergent infectious diseases, timely source cutting-off of infection and effective reduction of infection rate are good measures to the prevention and control to further spread of infectious diseases. For example, the measures of early discovery, early isolation and home isolation, social distance increasing and masks wearing in the outside can effectively reduce the number of the infected. Related Articles | Metrics

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Mathematical Model and Analysis of Residential Land Leasing for Non-center Districts in Shanghai CHENG Jing 2020, 37 (4):  403-414.  doi: 10.3969/j.issn.1005-3085.2020.04.002 Abstract ( 515 )   PDF (1037KB) ( 247 )   Save At present, the house prices in China are rising, and land leasing is the main factor influencing house prices. Through the interviews with the officials of the departments of planning and land authority of some districts in Shanghai, this paper proposes the basic hypotheses for the mathematical model of residential land leasing, and presents the mathematical model of residential land leasing for non-center districts in Shanghai. Based on the data of residential land leasing, gross domestic product (GDP), tenure of district mayor, subway stations, highways, key high schools, parks and industrial parks of non-center districts in Shanghai from 2004 to 2015, the location of each piece of residential land and the distances of each piece of residential land to the city center, the district center, the nearest subway station, the nearest entrance or exit of highway, the nearest university, the nearest key high school, the nearest park and the nearest industrial park obtained using ArcGIS, the influencing factors of residential land leasing by the district government of non-center districts in Shanghai are analyzed, and how these factors affect residential land prices and decisions on residential land leasing made by the district government is analyzed. It is shown that the factors, such as the residential land area, floor area ratio, modes of leasing, whether the residential land used for resettlement houses, the distances between the residential land and the city center, the district center, the nearest subway, the nearest university, the nearest park and the nearest industrial park, affect the decisions on residential land leasing made by the district government and residential land prices. Related Articles | Metrics

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Detection Methods of Hanging String Fracture Based on the Acceleration Signals NIE Jing-xin 2020, 37 (4):  415-422.  doi: 10.3969/j.issn.1005-3085.2020.04.003 Abstract ( 348 )   PDF (756KB) ( 204 )   Save In high speed railway catenary system, hanging strings are impacted by vehicle pantograph and external environment day after day, they are prone to fracture faults. In this paper, we propose an $\mathrm{L}_{1/2}$-LR model of hanging string fault detection based on the dynamic simulation model of pantograph catenary system. Firstly, we generated the acceleration data of contact wire and messenger wire under the multaneous action of pulsating wind and pantograph. Secondly, EEMD (Ensemble Empirical Mode Decomposition) is used to calculate their features, such as energy entropy, singular entropy, average entropy. As a result, an $\mathrm{L}_{1/2}$-LR model is established by the features. The experimental results show that the accuracy of the detection model is 97.25% under the condition of fluctuating wind and pantograph. As $\mathrm{L}_{1/2}$-LR model has variable selection effect, it is found that detecting whether hanging string is broken with high accuracy and calculation efficiency only by collecting vertical acceleration and horizontal acceleration at the middle position of catenary carrier cables. Related Articles | Metrics

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Two Units Cold Standby Repairable System with a Replaceable Repair Facility and Delay Repair WEI Ying-yuan, TANG Ying-hui 2020, 37 (4):  423-441.  doi: 10.3969/j.issn.1005-3085.2020.04.004 Abstract ( 371 )   PDF (478KB) ( 226 )   Save This paper considers a two-dissimilar units cold standby repairable system with a replaceable repair facility and delay repair. By using Markov renewal process theory and total probability decomposition technique, we obtain the reliability indices of system, including the steady state availability, the mean time to the first failure, the steady state failure frequency and the probability of system for repair. Furthermore, by introducing the ``generalized busy period" of the repair facility, we derive both the steady state unavailability and the steady state replaceable frequency of the repair facility. Finally, we present a special case and study the influence of delay repair time and the failure rate of repair facility on several reliability index. In engineering applications, it is very interesting to the steady state reliability quantitative indicators. It is hoped that the results obtained in this paper will provide useful information for optimization design and replacement maintenance of the system. Related Articles | Metrics

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A System of Reaction-diffusion Equations in the Unstirred Chemostat with Internal Storage and External Inhibitor LI Shuang-fei, WANG Zhi-guo, CAO Yi 2020, 37 (4):  442-458.  doi: 10.3969/j.issn.1005-3085.2020.04.005 Abstract ( 226 )   PDF (218KB) ( 266 )   Save A system of reaction-diffusion equations in the unstirred chemostat with internal storage and external inhibitor is considered in this paper. Firstly, in order to overcome the ratio singularity, the sharp priori estimates for positive solutions of the system are established by the maximum principle, and then a special cone smaller than the usual positive cone is constructed. Secondly, the sufficient conditions for the existence of the model coexistence solution are studied by the monotone method and the topological degree theory on the special cone. It turns out that there exists at least one positive solution when the principal eigenvalues of the corresponding nonlinear eigenvalue problems are both positive or negative. Related Articles | Metrics

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The Variational Iteration Solution for Nonlinear Soliton in Dusty Plasma XU Jian-zhong, WANG Wei-gang, MO Jia-qi 2020, 37 (4):  459-468.  doi: 10.3969/j.issn.1005-3085.2020.04.006 Abstract ( 316 )   PDF (190KB) ( 462 )   Save Under the global climate warming condition, the dusty plasma diffusing phenomenon may bring a huge havoc. In this paper a class of generalized nonlinear solitary wave model of atmosphere dusty plasma diffusion was considered. Firstly, at typical non-disturbed situation, the analytic expression of solitary wave solution was obtained by using the undetermined coefficient method. Then from the method of generalized variation iteration, the variation multiplier was solved and the generalized variation iteration was constructed. Then we found out various iteration solutions of solitary waves. Further, the solitary wave of corresponding model for generalized nonlinear dusty plasma was obtained using a transform of travelling waves. Finally, from the homologous variation theory for the function sequence of obtained approximate solution, it is an uniformly convergent sequence on the corresponding argument area. Thus the limiting function from iteration solutions is the exact solution to the low frequency vibrated nonlinear equation for dusty plasma and the corresponding approximate solution is an approximate analytic solution. It can be further obtained dependent physical behaviors by using the analytic operation. For example, from the obtained peak value of the soliton wave, as corresponding measures, it avoid arises super-high density assemble physical behaviors of cause electric discharge spark-over phenomenon. Related Articles | Metrics

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Oscillation of Second Order Quasilinear Neutral Delay Differential Equations LI Wen-juan, LI Shu-hai, TANG Huo 2020, 37 (4):  469-477.  doi: 10.3969/j.issn.1005-3085.2020.04.007 Abstract ( 403 )   PDF (151KB) ( 215 )   Save In this paper, we mainly study the oscillation of a class of second order quasilinear neutral delay differential equations. By use of the generalized Riccati transformation, integral averaging technique and an inequality due to Hardy-Littlewood-Polya, some new oscillation criteria are established for the equations above. Compare with other existing results, the results extend and improve some known results in the cited literature. Related Articles | Metrics

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A Discontinuous Galerkin Finite Element Method for the Fourth-order Cahn-Hilliard Equation ZOU Le-qiang, LIU Li-jie, WEI Lei-lei 2020, 37 (4):  478-486.  doi: 10.3969/j.issn.1005-3085.2020.04.008 Abstract ( 573 )   PDF (181KB) ( 614 )   Save The Cahn-Hilliard equation which is a very important fourth-order diffusion model has profound physical background and rich theoretical connotation, and its numerical methods are of important scientific significance and engineering application value. In this paper, we develop and analyze the Discontinuous Galerkin (DG) finite element method for the fourth-order Cahn-Hilliard equation in one dimension. The method, which is different from the traditional local discontinuous Galerkin (LDG) method, can be applied without introducing any auxiliary variables or rewriting the original equation into a larger system and reduce the amount of computation and storage. We prove stability and convergence by choosing interface numerical fluxes carefully. Some numerical tests is provided to illustrate the accuracy and capability of the scheme. Related Articles | Metrics

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Two-agent Scheduling to Minimize Makespan and Total Completion Time on a Serial-batching Machine HE Cheng, HAN Xin-xin 2020, 37 (4):  487-494.  doi: 10.3969/j.issn.1005-3085.2020.04.009 Abstract ( 281 )   PDF (123KB) ( 238 )   Save This paper studies the two-agent scheduling on a serial-batching machine to minimize the makespan of agent $A$ and the total completion time of agent $B$ simultaneously. Under the serial-batching setting, the jobs are processed in batches and the processing time of a batch is equal to the sum of processing times of jobs in the batch, but jobs of different agents cannot be processed in a common batch and the cost function of an agent depends on its jobs only. Moreover, when a new batch starts, a constant setup time is required for the machine. According to the capacity of a batch, the serial-batching model is divided into the unbounded model and the bounded model. In the paper, we present a polynomial-time algorithm for the bounded model and the unbounded model, respectively. Related Articles | Metrics

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Global Stability for a Heroin Model with Infection Age and Treat Age LIU Jun-li 2020, 37 (4):  495-510.  doi: 10.3969/j.issn.1005-3085.2020.04.010 Abstract ( 256 )   PDF (154KB) ( 266 )   Save In this paper, a new model for the dynamics of heroin is formulated that incorporates both the infection age of drug users not in treatment and the treat age of drug users in treatment. We derive the basic reproduction number. By using the fluctuation lemma and Lyapunov functional, we show that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable, whereas if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable. Related Articles | Metrics

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Numerical Investigation on Nonlinear Ion-acoustic Waves in a Nonextensive Plasma: Fractional Model ZHAO Mei-mei 2020, 37 (4):  511-520.  doi: 10.3969/j.issn.1005-3085.2020.04.011 Abstract ( 393 )   PDF (182KB) ( 581 )   Save The paper is intended to study the nonlinear behavior of planar ion-acoustic waves  in an unmagnetized plasma consisting of positive ions, non-extensive electrons, positrons, and stationary negatively charged dust grains. In the basic fluid eq-uations, Jumarie's modified Riemann-Liouville fractional derivative is adopted as the time derivative for the first time. Combined with the reductive perturbation method, a Korteweg-de Vries (KdV) equation is derived for the motions of ion-acoustic waves. The Chebyshev-Legendre-Galerkin (CLG) pseudospectral method is applied to solve this KdV equation numerically for analyzing how the plasma parameters influence the soliton structures of ion-acoustic waves. It concludes that increasing the order of fractional derivatives can increase the amplitude of solitary waves, which enables a better understanding of nonlinear wave phenomena in both astrophysical environments and laboratory plasma experiments. Related Articles | Metrics