Table of Content

15 June 2020, Volume 37 Issue 3 Previous Issue   

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Deep Learning Methods for Fastener Identification and Location of High Speed Railway Catenary Support Devices ZHANG Cheng 2020, 37 (3):  261-268.  doi: 10.3969/j.issn.1005-3085.2020.03.001 Abstract ( 551 )   PDF (663KB) ( 255 )   Save The 4C detection system of high-speed railway can obtain a large number of pictures of high-speed railway catenary. How to use artificial intelligence technologies to detect the looseness, dropping, deformation and other faults of catenary support devices is an urgent technical problem to be solved. Because the fasteners occupy a very small part of the whole images, a feasible solution to the problem is to identify and locate the fasteners first, then segment them, and finally identify the fault type of the segmented fasteners. Aiming at the problem of fastener identification and location, we propose an improved Faster R-CNN algorithm, which can accurately identify and locate various fasteners. The specific improvement strategy is to introduce an attention mechanism based on the SE model into the deep network, extract effective features from each channel, and use GA-RPN instead of RPN in the Faster R-CNN. The experimental results show that the method proposed in this paper has a recognition accuracy of more than 93.4%. Related Articles | Metrics

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Linear Bayesian Estimation under Constraint Conditions LIN Pan-pan, ZHANG Feng-yue, WANG Li-chun 2020, 37 (3):  269-280.  doi: 10.3969/j.issn.1005-3085.2020.03.002 Abstract ( 453 )   PDF (214KB) ( 275 )   Save In this paper, a linear Bayesian estimator is derived for the regression parameters in a linear model with equality constraints. The superiority of the linear Bayesian estimator over the constrained least square estimator is proved in terms of the mean square error matrix criterion. Monte Carlo simulations and a numerical example are employed to investigate the superiorities of the proposed linear Bayesian estimator. Related Articles | Metrics

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Existence, Uniqueness and Stability of Positive Solutions for a Kind of Predator-prey Model YANG Meng-na, LI Yan-ling 2020, 37 (3):  281-294.  doi: 10.3969/j.issn.1005-3085.2020.03.003 Abstract ( 347 )   PDF (1703KB) ( 359 )   Save In this paper, the positive solution of the steady-state system for the predator-prey model with a non-monotonous growth rate is studied. Firstly, through calculating the fixed point index of compact maps in cone, the sufficient conditions for the existence of any possible positive solutions are obtained. Secondly, by the perturbation theory and the topological degree theory, the influence of the parameter on the uniqueness and linear stability of positive solutions is discussed. Finally, some numerical simulations are carried out to complement the existence theorem of positive solutions in one dimension and two dimensions, respectively. That is, the predator and prey can co-exist under certain conditions. Related Articles | Metrics

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On the Strong Roman Domination Number of Some Special Graphs XU Jia-xue, WANG Zhi-ping 2020, 37 (3):  295-302.  doi: 10.3969/j.issn.1005-3085.2020.03.004 Abstract ( 259 )   PDF (359KB) ( 301 )   Save The determination of the domination number of a graph is a NP-complete problem. It is of great theoretical significance to investigate the exact values or better upper and lower bounds of the domination number of a graph. Strong Roman domination number, which is an important kind of domination number, not only is widely applied in protein structure research, circuit diagram design and computer programming, but also has prominent applications in scientific fields such as logic, linguistics, communication network and artificial intelligence. In this paper, the methods of mathematical induction and classification discussion are mainly used to deeply investigate the relationship between the strong Roman domination number and the order of a graph. We show that the strong Roman domination number of some special graphs such as windmill graph, complete bipartite graph, and thorn graph of complete graph is not greater than the six sevenths of the order of the graph. Related Articles | Metrics

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The Non-stationary State Solution of Non-linear Drift Fokker-Planck Equation with Non-Gaussian Noise and its Application YAO Ting, GUO Yong-feng, FAN Shun-hou, WEI Fang 2020, 37 (3):  303-313.  doi: 10.3969/j.issn.1005-3085.2020.03.005 Abstract ( 352 )   PDF (1648KB) ( 301 )   Save Non-Gaussian noise widely exists in many kinds of nonlinear systems. The study about the non-stationary state evolution behavior of the system driven by non-Gaussian noise can help us to understand its inherent evolution mechanism more deeply. In this paper, we investigate the non-stationary state evolution problem of the non-linear dynamical system driven by both non-Gaussian noise and Gaussian white noise. First, the non-linear dynamical system is linearized in the initial area by using the $\Omega$-expansion of the Green function. Then, we obtain the expression for the approximate non-stationary state solution through the eigenvalue and eigenvector theory. Finally, taking the Logistic model as an example, we examine the influences of the non-Gaussian noise intensity, the correlation time and the deviation parameter on the non-stationary state solution and its mean. The results show that when the Logistic model is used to describe the growth of product output, the non-stationary state solution can better reflect the evolution behavior of the product output near the unstable point. Related Articles | Metrics

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The Limit Properties of the Conditional Mean Growth Rate for a Kind of Bisexual Branching Process SONG Ming-zhu, SHAO Jing 2020, 37 (3):  314-324.  doi: 10.3969/j.issn.1005-3085.2020.03.006 Abstract ( 336 )   PDF (165KB) ( 224 )   Save In this paper, we study the limiting behavior of the conditional mean growth rate for the bisexual Galton-Watson branching process with population-size-dependent mating in random environments. Using the properties of superadditive functions, we obtain the limit properties of the mean growth rate per mating unit, and the upper bound and lower bound of the conditional mean. We introduce two sequences on the conditional mean growth rate, whose limit properties are established by utilizing the properties of the mean growth rate per mating unit. The bisexual Galton-Watson branching process with population-size-dependent mating is rather complex, so our results improve and extend the related known works in the literature. Related Articles | Metrics

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A Set of New Criteria for Nonsingular $H$-matrices CHEN Xi, TUO Qing 2020, 37 (3):  325-334.  doi: 10.3969/j.issn.1005-3085.2020.03.007 Abstract ( 282 )   PDF (168KB) ( 234 )   Save Nonsingular $H$-matrices, as an essential special matrices in the area of matrix theory, has been widely used in many fields such as computational mathematics, statistics, elastic mechanics and neural networks. Therefore, it is important to study its determination criteria. This paper is focused on the direct criteria for nonsingular $H$-matrix. A set of simple and novel practical criteria for nonsingular $H$-matrices are obtained through forming different positive diagonal factors and new parameters. The obtained results improve some recent studies and expand the range of determination criteria for nonsingular $H$-matrices. Three numerical examples illustrate the advantages of the proposed new conditions. Related Articles | Metrics

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Mathematical Modeling for Optimally Allocating the Medical and Health Supplies Reserve in Hainan Province HU Xiao-hua, BAYANMUNKH Bolormaa, ZHANG Zhong-wei 2020, 37 (3):  335-346.  doi: 10.3969/j.issn.1005-3085.2020.03.008 Abstract ( 442 )   PDF (140KB) ( 291 )   Save The Floyd algorithm is applied to calculate the shortest path and the shortest distance between any two of the 18 major towns in Hainan province. We strive to explore how to make an allocation plan to assign the medical and health supplies from the given center locations reserving these goods and materials to all other towns, such that the total ton-kilometre (ton.km) numbers of the freight transport is minimized and achieve an optimal allocation in engineering. We respectively consider three situations, one center location (town)--Qiongzhong; two center locations (towns)--Ledong and Tunchang; three  center locations (towns)- Changjiang, Dingan and Wuzhishan, and establish the optimization models. The relevant parameters in the models are estimated reasonably, and the numerical results are obtained respectively by Lingo mathematical software in three cases. Furthermore, the optimization models are established similarly in the case of an unknown center point position (not in eighteen towns). Related Articles | Metrics

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The Role of Longevity Bond in DC Pension Plan During Both Accumulation and Decumulation Phases ZHANG Xiao-yi 2020, 37 (3):  347-369.  doi: 10.3969/j.issn.1005-3085.2020.03.009 Abstract ( 459 )   PDF (214KB) ( 213 )   Save Longevity risk has attracted increasing attention in financial mathematics and financial engineering area. Longevity bond is defined as a kind of financial instrument to hedge longevity risk. To investigate whether the longevity bond can hedge longevity risk in defined contribution (DC) pension plans effectively, this paper deals with two optimal management problems for a DC pension plan during its accumulation phase and decumulation phase, respectively. For both problems, the scheme aims to maximize the expected constant relative risk aversion (CRRA) utility from the terminal fund by investing its wealth in a financial market consisting of a longevity bond and a risk-free asset. Closed-form optimal investment strategies are derived by using the dynamic programming approach and solving the related HJB equation. Under rational assumptions, the results reveal that the maximal expected utility under the market with a longevity bond is higher than the maximal expected utility under the market with an ordinary bond, in both phases. Related Articles | Metrics

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A Posteriori Error Analysis for Elliptic Variational Inequalities Based on Duality Theory HE Li-min, WANG Juan, HOU Yu-shuang 2020, 37 (3):  370-390.  doi: 10.3969/j.issn.1005-3085.2020.03.010 Abstract ( 353 )   PDF (169KB) ( 441 )   Save In this paper, we provide a relatively complete a posteriori error analysis for the regularization method via duality theory for elliptic variational inequalities. The model problems considered in the paper are a friction contact problem and an obstacle problem, respectively. Choosing a different bounded operator form and a functional form, we perform their dual formations and give an $H^1$-norm a posteriori error estimation based on the regularization method which is usually used in solving non-differentiable minimization problems. A posteriori error estimates, with residual type for an obstacle problem in the general framework, is established by using duality theory in convex analysis. At the same time, we make a particular choice of the dual variable that leads to a residual-based error estimate of the model problem and its efficiency. A posteriori error estimates for numerical solutions are the basis for developing efficient adaptive algorithms, whereas a posteriori estimates for modeling errors are useful for analyzing the effects of uncertainties in problem data on the solution. Related Articles | Metrics