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The Nonparametric Empirical Likelihood Goodness-of-fit Test for Integrated Diffusion Processes Liu Zaiming, Tang Mingtian, Wang Yunyan Mathematical Theory and Applications    2022, 42 (3): 1-.   DOI: 10.3969/j.issn.1006-8074.2022.03.001 Abstract （2904）      PDF（pc） （320KB）（375）       Knowledge map    This paper is devoted to the nonparametric goodness-of-fit test for integrated diffusion processes. Firstly, a nonparametric test is constructed for testing whether the drift function of a integrated diffusion process is of a known parametric form with unknown parameters. Secondly, a test statistic for goodness-of-fit test is obtained by applying the empirical likelihood technique. And finally, the asymptotic distribution of the test statistic is established, and then the proposed test method is applied to an example to verify its effectiveness. Related Articles | Metrics

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The Complete Weight Enumerators for Some Three­weight Linear Codes Tan Ting, Zhu Canze, Liao Qunying Mathematical Theory and Applications    2022, 42 (4): 19-.   DOI: 10.3969/j.issn.1006-8074.2022.04.002 Abstract （2725）      PDF（pc） （243KB）（453）       Knowledge map    In this paper, for an odd prime $p$, some $p$-element three-weight linear codes are constructed by defining set, and the complete weight enumerators of those codes are determined by using Weil sums over the finite field $\mathbb{F}_p$. Furthermore, it is proved that those codes are minimal under certain conditions, and thus suitable for secret sharing schemes. Especially, a class of those codes with parameters $[p^2-1,3,p^2-p-1]$ are obtained, which are optimal with respect to the Griesmer bound. Our results can be regarded as improvements to some results of Jian et al. in [1]. 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 （2478）      PDF（pc） （245KB）（990）       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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Multiplicity of P-cyclic Symmetric Closed Characteristics on Compact Star-shaped P-cyclic Symmetric Hypersurfaces in R2n Li Yangyang , Liu Hui Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006-­8074.2022.02.001 Online available: 21 April 2022

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Existence and Uniqueness of Global Solutions for a Class of Double Damped $\sigma$-evolution Equations Liu Mei, He Xinhai, Yang Han, Ming Sen Mathematical Theory and Applications    2022, 42 (4): 1-.   DOI: 10.3969/j.issn.1006­8074.2022.04.001 Abstract （2237）      PDF（pc） （234KB）（441）       Knowledge map    This paper studies the Cauchy problem for a class of double damped $\sigma$-evolution equations with different power nonlinearities. The $(L^{m}\cap L^{2})-L^{2}$ estimates of solution to the corresponding linear problem is established by using the Fourier transform, and then the influence of the exponential of the nonlinear term on the existence of the global solution is studied by employing the global iterative method in the case of small initial value. Moreover, the conditions that the index $p$ should satisfy for the existence of global solution are given. Related Articles | Metrics

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Extrapolated CSCS Iterations of Large Continuous Sylvester Equations Liu Zhongyun, Zhang Fang Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006-8074.2022.02.011 Online available: 23 January 2022

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Prediction of Mortality of Elderly Population with an Improved AE-LSTM Model Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006-8074.2022.03.008 Accepted: 28 September 2022

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Research on the SIR Model of Two New Coronaviruses with Time Delay in Parallel Propagation  Jin Wei, Liao Xinyuan, She Zhifeng Mathematical Theory and Applications    2022, 42 (2): 99-107.   DOI: 10.3969/j.issn.1006-­8074.2022.02.009 Abstract （2022）      PDF（pc） （278KB）（487）       Knowledge map    In this paper a SIR model for the parallel propagation of two new coronaviruses with time delay is studied. Firstly, the existence and uniqueness of the global positive solution of the system is proved. Secondly, the sufficient conditions for persistence and extinction of the new coronavirus and the variant new coronavirus are obtained by constructing a appropriate Lyapunov function. Finally, the relevant conclusions are verified by numerical simulations. Related Articles | Metrics

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Study of Period Functions Li Chengzhi Mathematical Theory and Applications    2023, 43 (1): 1-31.   DOI: 10.3969/j.issn.1006-8074.2023.01.001 Abstract （1971）      PDF（pc） （485KB）（512）       Knowledge map    In this survey article we first briefly introduce some concepts related to the period function of a planar smooth (or analytic) vector field, and its isochronicity, monotonicity, and the number of critical periods. Then, we introduce some important results in this field, especially about the isochronous centers, the period functions associated to the elliptic and hyperelliptic Hamiltonian functions, and the period functions of quadratic integrable systems. Besides these results we list some conjectures and problems in Section 6, which may provide topics for further studies. Related Articles | Metrics

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Finite­time Flocking Analysis of a Class of Complex Coupling Systems Wang Chuxiang, Liu Yicheng, Ru Lining Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006­-8074.2022.02.002 Online available: 21 April 2022

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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 （1918）      PDF（pc） （241KB）（997）       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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Subharmonic Bifurcations and Chaos of the Buckled Beam Subjected to Parametrical Excitations Zhang Dongmei, Li Feng Mathematical Theory and Applications    2022, 42 (2): 25-34.   DOI: 10.3969/j.issn.1006-­8074.2022.02.003 Abstract （1893）      PDF（pc） （348KB）（513）       Knowledge map    This paper presents a new particle dynamic system based on the C-S model, studies the sufficient condition of flocking in finite time, and analyzes the factors of convergence time. We show that when the initial values of the agents’ position satisfy some specific conditions, finite-time flocking occurs. Furthermore, the convergence time can be estimated by the agents’ number, that is, there is a power-law relationship between them. When the number of the agents is large, the convergence time will decrease. Related Articles | Metrics

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A compact difference scheme for the time fractional integro-differential equation with Neumann boundary conditions Tang Sheng , Mo Yan , Wang Zhibo Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006-­8074.2022.02.007 Online available: 25 February 2022

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Prediction of Early Summer Rainstorm Days in South China Based on Least Angle Regression on High Correlation Regions Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006-­8074.2022.02.004 Online available: 10 January 2022

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Free Cocycle Infinitesimal Unitary Hopf Algebra on Decorated Rooted Forests Zhang Yi, Cao Jinghan, Wu Xiaoxing Mathematical Theory and Applications    DOI: 10.3969/j.issn.1006­-8074.2022.02.006 Online available: 25 May 2022

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Integer Vectors Arising From Cluster Algebras Fu Changjian, Geng Shengfei, Liu Pin Mathematical Theory and Applications    2022, 42 (1): 1-15.   Abstract （1809）      PDF（pc） （7707KB）（515）       Knowledge map    There are four kinds of integer vectors arising from the structure theory of cluster algebras: $c$-vector, $d$-vector, $f$-vector and $g$-vector, which have played important roles in the study of cluster algebras. This paper is devoted to reviewing the concepts of those vectors and introducing their properties, research problems and research progress. 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 （1794）      PDF（pc） （368KB）（761）       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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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 （1786）      PDF（pc） （6927KB）（886）       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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Explicit High-order Maximum Principle Preserving Schemes for the Conservative Allen--Cahn Equation Mathematical Theory and Applications    2021, 41 (3): 96-110.   Abstract （1775）      PDF（pc） （11270KB）（331）       Knowledge map    Compared with the well-known classical Allen--Cahn equation, the modified Allen--Cahn equation, equipped with a nonlocal Lagrange multiplier, enforces the mass conservation for modeling phase transitions. In this paper, a class of up to eighth-order maximum principle preserving schemes are proposed for solving the modified conservative Allen--Cahn equation. Based on the second-order finite-difference space discretization, we investigate the high-order integrating factor two-step Runge--Kutta maximum principle preserving schemes. We prove that the schemes can preserve the maximum principle and mass of the conservative Allen--Cahn equation and give the convergence analysis of proposed schemes. Finally, two- and three-dimensional numerical tests are carried out to verify the theoretical results and demonstrate the performance of proposed schemes. Related Articles | Metrics

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Mean Field Equation on Spheres Mathematical Theory and Applications    2021, 41 (3): 13-37.   Abstract （1768）      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