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15 June 2019, Volume 36 Issue 3 Previous Issue    Next Issue

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Hierarchical Clustering Based on Multi-scale Information Fusion LI Chun-zhong, JING Wen-feng, XU Jian 2019, 36 (3):  245-255.  doi: 10.3969/j.issn.1005-3085.2019.03.001 Abstract ( 208 )   PDF (2440KB) ( 387 )   Save In volume rendering and image segmentation, data set often possesses manifold structure. Different parts in such data sets are closely adjacent to each other and local noises exist around the boundaries, which bring great difficulty to traditional clustering algorithms. According to the non-parameter density estimation, this paper proposes a hierarchical clustering algorithm based on multi-scale information fusion. The new algorithm integrates density differences and boundary information to define a kind of similarity measurement based on multi-scale information fusion. With the graph connection of level sets, the new approach obtains a hierarchical analyzing process of the cluster structures, which outputs stable clustering results. The new algorithm is not restricted by shapes and density structures of the data set, and can detect common structural features of the data set automatically without assumption. Meanwhile, the clustering results are stable and the new algorithm is strongly robust to noises. The superiority of the proposed algorithm is demonstrated with its applications to synthetic and real data sets. Related Articles | Metrics

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Study on the Principal Agent Model of the Travelers Transfer to Accept Guidance XIAO Hai-yan 2019, 36 (3):  256-264.  doi: 10.3969/j.issn.1005-3085.2019.03.002 Abstract ( 144 )   PDF (177KB) ( 332 )   Save The key problem for the traffic guidance is to determine the optimal induced path, and shunt vehicles as soon as possible, which can reduce the loss and impact caused by congestion. Currently, the problem facing the induced traffic system is the acceptance rate measuring whether the induced paths meet the traveler's needs. In this paper, we establish the principal-agent model of the manager-traveler by treating the manager as the principal and the traveler as the agent. The impact of the cost coefficient, the incentive coefficient, the risk aversion degree, the effort cost coefficient and the uncertainty of the output on the results are also discussed. A numerical experiment was carried out to analyze the impact on the acceptance rate of route guidance. The study shows that managers should make as many travelers in the region accept route guidance as possible with low cost and pertinence so as to achieve a high efficiency of the policy and to improve the acceptance rate of route guidance. Related Articles | Metrics

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Spline Estimation for Heteroscedastic Nonparametric Regression Models under Dependent Errors WU Xin-qian, CHENG Fang, XU Zhen 2019, 36 (3):  265-274.  doi: 10.3969/j.issn.1005-3085.2019.03.003 Abstract ( 185 )   PDF (879KB) ( 540 )   Save These exist non-linear trends, heteroscedasticity and dependent relations in some economic and financial data. The heteroscedastic non-parametric regression models with fixed design and dependent errors have been used in these fields because of its ability to reflect these data characteristics. The spline method is one of the commonly used non-parametric smoothing methods. In order to explore the application of the spline method to this kind of models, we discuss the pointwise consistency of polynomial spline estimators of the mean function and variance function under the $\alpha$-mixing condition, and obtain the pointwise rate of convergence. In addition, we carry out the numerical simulation, and the results show that the proposed spline method is feasible. Related Articles | Metrics

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Information Entropy for a Damped Harmonic Oscillator with Non-Gaussian Noise and External Periodic Force GUO Yong-feng, WEI Fang, XI Bei, TAN Jian-guo 2019, 36 (3):  275-284.  doi: 10.3969/j.issn.1005-3085.2019.03.004 Abstract ( 232 )   PDF (418KB) ( 534 )   Save Damped harmonic oscillators have attracted noticeable attention due to their wide application in solid theory, quantum field theory, quantum mechanics and quantum optics, etc. Information entropy plays an important role in the study of the properties of stochastic dynamical systems. In this paper, we discuss the effects of non-Gaussian noise and external periodic force on the upper bound of the time derivative of information entropy for a damped harmonic oscillator. We transform the non-Gaussian noise into Gaussian noise by using the path integral approximation. The dimension of the Fokker-Planck equation is reduced through the linear transformation. Based on the definition of Shannon's information entropy and Schwartz inequality principle, we obtain the upper bound of the time derivative of information entropy of this system. Finally, we analyz the influence of non-Gaussian noise and system parameters on the upper bound of the time derivative of information entropy. Related Articles | Metrics

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Analysis of Customers' Impatience in an M$^{X}$/M/1 Queue with Multiple Working Vacations ZHANG Xue-mei, YUE De-quan, ZHANG Yu-ying 2019, 36 (3):  285-297.  doi: 10.3969/j.issn.1005-3085.2019.03.005 Abstract ( 165 )   PDF (444KB) ( 325 )   Save We consider an M$^{X}$/M/1 queue with impatient customers and working vacations. Customs arrive in batches; during the vacation, the service is provided at a lower rate and the customer (except customers who are receiving service) may leave the system because the waiting time exceeds the expected waiting time. The model can provide some theoretical guidances for the decision maker of some service systems. Firstly, the steady-state equilibrium equation is established by building the model. Then, using the probability generating function method, the analytic expressions for the mean queue length in the normal and the working vacation are obtained. We further derive the analytic expressions for other performance measures such as: the mean sojourn time of customers; the mean sojourn time of customers arriving in the busy period; the rate of abandonment due to impatience. Finally, some numerical results are presented to demonstrate the effects of some parameters on the performance measures of the system. Related Articles | Metrics

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Numerical Simulation of Potential Flow Equation under Continuous Segmental Motion HU Dan-dan, LUO Zhi-qiang 2019, 36 (3):  298-308.  doi: 10.3969/j.issn.1005-3085.2019.03.006 Abstract ( 203 )   PDF (597KB) ( 340 )   Save In order to investigate the wave elevation on the free surface and the nonlinearity of a two dimensional tank with irrotational and inviscid fluid under segmented excitation, we utilize the Crank-Nicolson finite difference method for the potential flow equation. By changing the excitation parameters, we draw the wave height of the free surface under different excitation conditions. As shown in the numerical results, the wave elevation demonstrates the regular periodic beating phenomenon under the single horizontal excitation with different excited frequencies. Under the segmented excitation, the phenomenon of free surface wave beating disappears immediately when the horizontal excitation disappears. When the wave elevation of the free surface is small, the wave on the free surface exhibits the form of standing wave. When the free surface wave elevation is large, the wave crest and trough decrease, and the nonlinear phenomenon occurs. In addition, when the amplitude of the wave becomes larger, the nonlinear phenomenon is more obvious. Related Articles | Metrics

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Stochastic Evolution Equations Driven by Rosenblatt Process in a Hilbert Space with Finite Delay SANG Li-heng, LV Wen-hua, TANG Zheng 2019, 36 (3):  309-321.  doi: 10.3969/j.issn.1005-3085.2019.03.007 Abstract ( 168 )   PDF (198KB) ( 441 )   Save As an important self-similar stochastic process, Rosenblatt process is often used to describe non-Gaussian random phenomena. In order to further characterize stochastic phenomena driven by Rosenblatt process, we study the mild solution for a class of time-dependent stochastic evolution equations with finite delay driven by Rosenblatt process in this paper. An existence and uniqueness theorem for the mild solution to this class of stochastic evolution equations is obtained by means of the Banach fixed point theorem in a real separable Hilbert space with time-dependent, and an example is proposed to illustrate the result. Related Articles | Metrics

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Hopf Bifurcation Control of a Five-dimensional Hyperchaotic System ZHANG Liang 2019, 36 (3):  322-332.  doi: 10.3969/j.issn.1005-3085.2019.03.008 Abstract ( 172 )   PDF (5467KB) ( 349 )   Save In this paper, the five-dimensional hyperchaotic Pan system is studied. According to the high dimensional Hopf bifurcation theory and the Routh-Hurwitz theory, the stability of the non-zero equilibrium point of the system and the stability of the bifurcation solution are analyzed. The Hopf bifurcation and stability control of the system are set up by using the Washout control method. Through analyzing the controlled system, we obtain the corresponding relations between the bifurcation parameter and control parameters, and between the stability parameters and control parameters. These relationships show that by controlling the parameters of the controller, the bifurcation parameter and stability parameter of the system can be adjusted, and the Hopf bifurcation can be delayed and the stability range of the bifurcation solution can be changed. The numerical simulation proves the correctness of theoretical analyses. Related Articles | Metrics

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Global Analysis of an Epidemic Model with Stage-structure ZHANG Feng-qin, ZHAO Tian, LIU Han-wu 2019, 36 (3):  333-343.  doi: 10.3969/j.issn.1005-3085.2019.03.009 Abstract ( 206 )   PDF (201KB) ( 301 )   Save An epidemic model with bilinear incidence and stage structure is established by assuming that the infection can transmit only among adult individuals and that the growth of adult individuals is density-dependent. The basic reproduction numbers of the population growth and the infection transmission are both obtained, the global stability of equilibriums is established by constructing Lyapunov functions, and the theoretical results are verified through numerical simulation. In conclusion, the dynamic behaviors of this model is completely determined by its two basic reproduction numbers, and the basic reproduction numbers of infection transmission can be depressed through decreasing the incidence or increasing the remove rate. Related Articles | Metrics

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Analysis of the Single Working Vacation and Vacation Interruption G-queue with Setup Times ZHOU Zong-hao, ZHOU Zhen-chuan, ZHU Yi-jun, SHI Zhi-yan, BAO Zhi-hui 2019, 36 (3):  344-358.  doi: 10.3969/j.issn.1005-3085.2019.03.010 Abstract ( 185 )   PDF (384KB) ( 309 )   Save This paper considers the single working vacation and vacation interruption G-queue with negative customers and setup times. When a service is completed during a regular busy period, if there is no customer in the system, the server begins a working vacation of random length. There are two ways that the system transfers to the regular service period, one is that there are customers in the queue after the completion of a service during the working vacation. Another is that there are customers in the queue after the completion of a vacation, but the service time before is invalid for the unfinished service. If there is no customer in the system after the completion of a service during the working vacation, the system turns off. The service of the first positive customer must take a setup time from the close-down server. Using the quasi birth death process and matrix-geometric-solution method, the steady-state distribution for the steady probabilities of the system and the queue length distribution are obtained. The mean waiting time of arriving customers in the regular busy period is derived by solving the distribution function. Additionally, we provide the numerical examples to illustrate the effect of the parameters on several performance characteristics mentioned above. Related Articles | Metrics

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Unique Continuation Property for a Class of Seventh-order Shallow Water Wave Equations ZHANG Li, GAO Juan-juan 2019, 36 (3):  359-366.  doi: 10.3969/j.issn.1005-3085.2019.03.011 Abstract ( 190 )   PDF (121KB) ( 552 )   Save The properties of Cauchy problems are closely related with those of the initial values. The unique continuation properties of these problems are one of the important properties of the solution to the integrable system. Considered herein is the Cauchy problem associated with a class of seventh-order shallow water wave equations, which describe the propagation of weakly dispersive nonlinear long waves in the horizontal direction. The purpose here is to investigate the unique continuation property of the solutions to this Cauchy problem. Based on the complex variables technique and Paley-Wiener Theorem, it is proved that, if a sufficiently smooth solution to this Cauchy problem is supported compactly in a nontrivial time interval, then it vanishes identically. Related Articles | Metrics