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Mean Field Equation on Spheres Mathematical Theory and Applications    2021, 41 (3): 13-37.   Abstract （1764）      PDF（pc） （16655KB）（1161）       Knowledge map    In this expository note, we will introduce the recent progress and open problems concerning mean field type equations on spheres. In particular, some new inequalities of Aubin-Onofri type as well as their close connection to mean field type equations are presented.  Related Articles | Metrics

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Asymptotic Behavior of the Multiscale Stochastic Systems Li Nannan , Xie Longjie Mathematical Theory and Applications    2022, 42 (2): 47-60.   DOI: 10.3969/j.issn.1006-­8074.2022.02.005 Abstract （1907）      PDF（pc） （241KB）（992）       Knowledge map    This paper summarizes the recent progress on the limiting behavior of multiscale stochastic systems with irregular coefficients, focuses on presenting the averaging principle, the normal deviation and the diffusion approximation, in particular, the Smoluchowski-Kramers approximations for the classical stochastic Langevin equation driven by Brownian noise and the Langevin equation driven by L\'evy noise. Unlike the classical equation driven by Brownian noise, there is no noise induced drift in the limit equation of the Langevin euqation driven by L\'evy noise even if the friction is state dependent. Related Articles | Metrics

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An Improved Elastic Net Estimate for Logistic Regression Models Mathematical Theory and Applications    2022, 42 (2): 108-119.   DOI: 10.3969/j.issn.1006­-8074.2022.02.010 Abstract （2468）      PDF（pc） （245KB）（988）       Knowledge map    For improving the application performance of Logistic regression models on classification problems, this paper develops a double adaptive elastic net by combining the adaptive Lasso and adaptive Ridge. The double adaptive elastic net has both the oracle property and the adaptive grouping effect, which ensures that it can effectively estimate parameters and accurately select important variables under certain assumed premises and consequently, makes the established Logistic regression model simple and precise. Simulation and case analysis show that the double adaptive elastic net is suitable for medium or high correlation cases with adaptive grouping effect, and its performance of improving Logistic regression is equal to or better than that of the elastic net and other partial improvement methods. Related Articles | Metrics

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Study on System Benefit Optimization of Airport Pick-up Area Based on Queuing Theory Mathematical Theory and Applications    2020, 40 (4): 118-127.   Abstract （1365）      PDF（pc） （555KB）（922）       Knowledge map     This paper aims to achieve the highest efficiency of boarding in the airport taxi boarding area, and takes into full consideration the time cost of passengers and taxi drivers as well as the construction cost of boarding points, and applies the idea of Queuing Theory to study the optimal number of boarding points in the airport taxi boarding area. Taking Beijing capital airport as an example, this paper establishes a double-end queuing model for taxi and passenger, and respectively solves the number of boarding points that make the queue length reach the shortest, so as to achieve the highest efficiency. In addition, this paper also took the minimum total cost as the optimization objective to verify and optimize the queuing model, and found that the set number of boarding points could not only achieve the highest efficiency, but also achieve the lowest total cost. Finally, by setting the satisfaction weights of taxi drivers and passengers and assigning them to two queuing models, the optimal number of boarding points was obtained to be 7. Related Articles | Metrics

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Entry Timing and Product Differentiation Decision in Continuous Time Circular City Model Zhang Bo, Hu Zhijun Mathematical Theory and Applications    2022, 42 (3): 114-.   DOI: 10.3969/j.issn.1006-8074.2022.03.009 Abstract （1416）      PDF（pc） （310KB）（913）       Knowledge map    This paper investigates enterprises' decision of the location, pricing and entry timing with asymmetric investment costs in a circular city. Using the option game theory, we construct the dynamic game model of duopoly enterprises with horizontal product differentiation in the circular market, analyze the existing sequential equilibrium and preemptive investment equilibrium, and depict the sub-game perfect equilibrium of the dynamic game under the Stackelberg Equilibrium. The study shows that the profit of enterprises increase with the increase of product differentiation; the enterprise with cost advantage always enters the market as a leader; when the cost asymmetry of two enterprises is less than the critical value, the leader's entry timing is controlled by the threat of preemption, and the leader's profits brought by cost advantage will be damaged; the entry timing of the follower is not affected by the degree of cost asymmetry. Related Articles | Metrics

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Fast Modeling of Ultrasonic Transducer Sound Field and Optimization Design of Acoustic Hologram Mathematical Theory and Applications    2020, 40 (3): 121-128.   Abstract （1203）      PDF（pc） （855KB）（893）       Knowledge map    In this paper, in order to improve the speed of finite element simulation software such as COMSOL to simulate the three-dimensional (3D) sound field of ultrasonic transducer (UT), the fast modelling method for the sound field of UT is developed based on the angular spectrum method (ASM). In addition, the control method for the sound field of UT is proposed by combining the ASM with Gerchberg-Saxton iterative algorithm. Based on the calculated phase difference, the acoustic hologram of UT can be fabricated by using the 3D printing technology to accurately control the sound field of UT. Related Articles | Metrics

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Research on Optimization of Airport Security Check Process  Based on Multi-stage M/M/s Queuing Model Fang Qiulian, Chen Siqi, Chen Weirong, Dong Shangyi, Yan Pengwei Mathematical Theory and Applications    2022, 42 (4): 115-.   DOI: 10.3969/j.issn.1006-8074.2022.04.010 Abstract （1780）      PDF（pc） （6927KB）（883）       Knowledge map    Concering the extremely long queues that customers often encounter during the airport security check process, this paper studies the optimization of the airport security check process. Firstly, the airport security check process is divided into four stages: identity verification, preparation for machine scanning, machine scanning, and manual scanning, and is modeled as a multi-stage queuing system $M/M/s$. Then with the data provided in Question D of ICM 2017 empirical analysis is performed and the model is futher optimized from the perspective of queue size and queuing mechanism. The results of empirical analysis show that when $s$ is equal to 3, the average waiting time of customers in the system is reduced significantly, and the system reliability is improved significantly; In addition, the multi-angle sensitivity analysis shows that the model has good robustness. Finally, based on the analysis results, some suggestion Related Articles | Metrics

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Construction of Cross-border E-commerce Development Indices and Empirical Analysis Mathematical Theory and Applications    2019, 39 (3-4): 113-120.   Abstract （779）      PDF（pc） （713KB）（823）       Knowledge map    Related Articles | Metrics

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Quasi-Monte Carlo Method for a Class of Stochastic Optimal Control Problems Zhou Hongmin, Luo Xianbing, Ye Changlun Mathematical Theory and Applications    2022, 42 (3): 71-.   DOI: 10.3969/j.issn.1006-8074.2022.03.006 Abstract （1553）      PDF（pc） （305KB）（801）       Knowledge map    In this paper, a gradient projection optimization method is applied to solve a class of stochastic optimal control problems. The Monte Carlo method is a common method to deal with stochastic optimal control problems, but it has a notoriously slow convergence rate. We choose the Quasi-Monte Carlo method with faster convergence.  In order to make the random sampling dimensions and time discrete points independent, we use the Karhunen-Lo${\grave{\rm e}}$ve truncation for the Brown motion. Sobol sequences of  the Quasi-Monte Carlo method are used for sampling. The error of numerical approximation is presented, and the effectiveness of the method is verified by numerical experiments. Related Articles | Metrics

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Research on Algorithm of Minimum Edge Covering Problem on Hypergraphs Mathematical Theory and Applications    2021, 41 (4): 109-.   Abstract （1322）      PDF（pc） （1350KB）（793）       Knowledge map    In this paper, the minimum edge covering problem of general hypergraphs and a class of special hypergraphs is investigated. The minimum edge covering problem of hypergraphs is a NP-hard problem. We design a layering algorithm to solve the problem, which the approximate ratio is reached $f$ and the time complexity is $O(km)$; then we provide two tight examples. The minimum edge covering problem of the special hypergraphs is solvable in polynomial time, and the strategy to solve the problem is: a corresponding root tree is firstly constructed, and then the tree traverses from down to up according to the level of each node with the dynamic programming, which based on the particularity of the root tree; MEC algorithm is designed for the minimum edge covering of special hypergraphs and the time complexity is $O({m^3})$. Related Articles | Metrics

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The Extremal Value of Exponential Inverse Forgotten Index of a Tree Zeng Mingyao , Deng Hanyuan Mathematical Theory and Applications    2022, 42 (3): 61-.   DOI: 10.3969/j.issn.1006-8074.2022.03.005 Abstract （1782）      PDF（pc） （368KB）（757）       Knowledge map    For a simple graph $G$ with edge set $E(G)$, the exponential inverse forgotten index of $G$ is defined as ~$e^{\frac{1}{\mathcal{F}}}(G)=\sum_{uv\in E(G)}e^{\left(\frac{1}{{d_G^2(u)}}+\frac{1}{{d_G^2(v)}}\right)}$, where $d_G(u)$ is the degree of the vertex $u$ in $G$. In this paper, firstly, we give the minimum value of exponential inverse forgotten index of a tree and determine its corresponding extremal graph. Then, we investigate the maximum value of the exponential inverse forgotten index and describe the structural characteristics of the extremal graph.  Related Articles | Metrics

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The Generalized 3­connectivity of Cayley Graphs Generated by Unicyclic Graphs Wang Yanna, Zhou Bo Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006­-8074.2022.02.008 Online available: 23 January 2022

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Quantitative Trading Strategies of Shanghai and Shenzhen 300Index Futures Based on SVM Zhang Jian, Wang Bo Mathematical Theory and Applications    2017, 37 (2): 112-121.   Abstract （1418）      PDF（pc） （1789KB）（720）       Knowledge map    Based on the theory of support vector machine,aquantitative trading model of Shanghai and Shenzhen 300 stock index futures is established.Differing from the regression forecasting method,the model firstly makes use of the advantage of support vector machine in classification in nonlinear systems to transform a complex time series regression prediction problem into a two classification problem by converting the price evolution trend into a transaction signal,and then takes the price information and technical indicators as the input vector,introduces the stop-loss mechanism and obtains the quantitative trading strategy upon the dynamic forecasting model.Empirical results show that the price information transaction strategy has better performance than the technical index trading strategy,and overall,the quantitative trading model has achieved good profit effect. Related Articles | Metrics

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Numerical Simulation of the Generalized Fractional Allen - Cahn Phase FielS Equations Mathematical Theory and Applications    Online available: 05 March 2021

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A Mathematical Model for Parameter-Calibration and Imaging of CT System Yang Yunxia Mathematical Theory and Applications    2017, 37 (3-4): 115-121.   Abstract （1355）      PDF（pc） （3704KB）（708）       Knowledge map    Abstract In this paper,firstly,by fitting the CT scan received information with the MATLAB software,a  series of images about the parameter-calibration and imaging of a CT system are obtained.And then,based on the received information and the obtained images,a mathematical model is established for the parameter-calibration and imaging of the CT system. Related Articles | Metrics

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An Adaptive Online Learning Load Forecasting Combination Algorithm Based On Time Series Decomposition Xie Xiaopeng, Hu Weiming, He Jilong, Wang Li, Xiang Wujing, Luo Xiang, Zheng Zhoushun Mathematical Theory and Applications    2022, 42 (4): 93-.   DOI: 10.3969/j.issn.1006-8074.2022.04.008 Abstract （1660）      PDF（pc） （902KB）（698）       Knowledge map    Since it is troublesome for conventional machine learning methods to extract the main features relevant to the uncertainties and variations of electrical load, in this paper, a recently proposed hidden Markov model based online learning algorithm is used to solve the load forecasting problems, extracting the uncertainties and variations from the load data. By combining with the decomposition algorithm, the variation features can be estimated more precisely and forecasting accuracy can be improved. Based on the hidden Markov model, the proposed algorithm is updated once new samples are received, thus adapting to real-time data; the STL algorithm is implemented to decompose the load data, leading to the separation of components with different trends. The online learning algorithm is then applied to each component of data, composing the hybrid load forecasting algorithm. Validated by three public datasets, it is shown that the proposed algorithm can improve the forecasting accuracy and reduce the relative error up to $27\%$ when compared with the existing technique. Related Articles | Metrics

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Research on the Fuzzy Membership Function Determination Based on Probability Statistics Ma Wanyuan, Geng Xiuli Mathematical Theory and Applications    2016, 36 (3): 93-100.   Abstract （1217）      PDF（pc） （682KB）（698）       Knowledge map    The key of using fuzzy mathematics to solve practical problems is to establish realistic membership function.The commonly used method to compute the fuzzy membership function is fuzzy statistic method, which relies on a large number of survey data and analysis on the function graph,and the calculation with heavy workload and complex process limits the practical application of fuzzy technology.A method for determining the fuzzy membership function based on probability statistics is proposed from the view of statistics.The proposed method is relatively simple and can adapt to much more cases of fuzzy membership function determination. Finally,a real world case is given and membership function curves derived from two methods are compared to verify the proposed method having higher accuracy. Related Articles | Metrics

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Dynamics and Optimal Control of an Antibody Immune HIV Model with a Saturated Proliferation Rate Mathematical Theory and Applications    2021, 41 (2): 1-.   Abstract （930）      PDF（pc） （561KB）（690）       Knowledge map    In this paper, an antibody immune HIV model with a saturated proliferation rate is established, and some conditions of local stability and global stability for the disease-free equilibrium, the no-immune endemic equilibrium and the immune endemic equilibrium are obtained by the linearization method and the Lyapunov function method, respectively. Moreover, motivated by the success of the latest anti-AIDS vaccine in some animal experiments, the dual action of antibody immunity and drug therapy is builded into the above kinetic model, which forms a optimal control problem to minimize the concentration of infected cells and virus and the cost of control. Using the Pontryagin maximum principle, the optimality conditions for the optimal control problem are gotten. After obtaining the parameters of the model , numerical simulation tests are carried out for the double control problem and the single control problem respectively. Experimental results show that the concentration of the infected cells and viruses can quickly reduce under the condition of the effective vaccine, and the immune control effect is almost as well as the effect of the double control by comparing with double control effect, which illustrates the vaccine is fairly effective in controlling AIDS. It can be expected that vaccine will greatly change the current situation of AIDS spread and may even eliminate AIDS eventually, after the vaccine is put into clinical practice. Related Articles | Metrics

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Some Research on Limit Cycles of Li\'enard System Mathematical Theory and Applications    2021, 41 (3): 59-95.   Abstract （1753）      PDF（pc） （24586KB）（684）       Knowledge map    The aim of this paper is to introduce the progress on the research for limit cycles of Li\'enard systems and present some new results. The results focus on four problems: the existence of limit cycles, the uniqueness of limit cycles, the exact number of limit cycles and the upper bound of limit cycles. Finally, we summarize some methods for studying limit cycles of Li\'enard systems. Related Articles | Metrics

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Image Denoising Algorithm Based on Total Variation Ni Nianyong, Sun Bo Mathematical Theory and Applications    2017, 37 (2): 32-37.   Abstract （1372）      PDF（pc） （564KB）（680）       Knowledge map    In this paper we study the image denoising algorithm based on total variation.The corresponding optimization model is solved by the steepest descend method,the difference iterative method and the split Bregman method,respectively.Experiment results show that the difference iterative method convergences rapidly,and achieves better denoising performances. Related Articles | Metrics