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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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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 （1663）      PDF（pc） （902KB）（699）       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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A Modified PRP­HS Hybrid Conjugate Gradient Method with Global Convergence Wang Yun, Huang Jingpin, Shao Hu, Liu Pengjie Mathematical Theory and Applications    2022, 42 (4): 58-.   DOI: 10.3969/j.issn.1006-8074.2022.04.005 Abstract （1664）      PDF（pc） （357KB）（597）       Knowledge map    The conjugate gradient method is one of the most effective methods for solving large-scale unconstrained optimization problems due to its simple structure and low storage capacity. In this paper, using the famous PRP and HS methods and their modified versions, a modified PRP-HS hybrid conjugate gradient method is proposed. The conjugate parameter generated by the proposed method is always nonnegative, and the proposed method can generate descent directions independent of any line search at every iteration. Under general assumptions the global convergence of the proposed method is obtained by using the weak Wolfe line search to calculate step-lengths. A large number of numerical tests and comparisons show that the new method is effective.or the proposed method and its comparisons are executed, and the numerical results show that the new method is effective. 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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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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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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Derivation Algebra and Automorphism Group of the Mirror Heisenberg-Virasoro Algebra Zhao Yufang, Cheng Yongsheng Mathematical Theory and Applications    2022, 42 (4): 36-.   DOI: 10.3969/j.issn.1006-8074.2022.04.003 Abstract （1598）      PDF（pc） （175KB）（346）       Knowledge map    In this paper, we study the derivation algebra and automorphism group of the mirror Heisenberg-Virasoro algebra, determine the outer derivation and the first cohomology group of the mirror Heisenberg-Virasoro algebra with the coefficients in itself. Related Articles | Metrics

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Numerical Simulation Algorithms for Stochastic Differential Equations in Systems Biology Niu Yuanling, Chen Lin, Chen luonan Mathematical Theory and Applications    2023, 43 (4): 76-92.   DOI: 10.3969/j.issn.1006-8074.2023.04.005 Abstract （616）      PDF（pc） （508KB）（336）       Knowledge map    Many phenomena in systems biology, such as the biochemical reaction process, the evolution of ecosystems, the spread of infectious diseases, can be described by stochastic differential equations (SDEs). Considering the influence of randomness, stochastic differential equation models can describe the evolution of variables over time more accurately than deterministic differential equation models. However, the analytical solutions of most stochastic differential equations cannot be obtained. Even though some of them can be obtained, the forms of the solutions are usually extremely complex. One therefore requires proper numerical methods to approximate their solutions on computers. These stochastic differential equation models in systems biology usually have the properties of high dimension, high nonlinearity, and the solutions being located in a specified region. It is difficult to simulate them numerically. This paper reviews the numerical simulation algorithms of several typical models in systems biology (biochemical reaction models, ecosystem models, infectious disease models, population genetics models, cell differentiation models), and briefly introduces their advantages and disadvantages. Related Articles | Metrics

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Stability and Hopf Bifurcation of a Class of Epidemic Models with Stage Structure and Fear Effect Liu Yuying, Yang Wensheng Mathematical Theory and Applications    2022, 42 (4): 79-.   DOI: 10.3969/j.issn.1006-8074.2022.04.007 Abstract （1522）      PDF（pc） （684KB）（333）       Knowledge map    In this paper, we consider the stability and Hopf bifurcation of a class of epidemic models with stage structure and fear effect. Firstly, the long-time behavior of population number under certain conditions is analyzed. Then the local stability of the equilibrium point is discussed by using the linear stability theory, and the influence of the degree of fear on the numbers of the susceptible young population, the susceptible adult population and the infected adult population is investigated when the positive equilibrium point is stable. Finally, the conditions for the existence of Hopf bifurcation are given by using the bifurcation theory, and the feasibility of the conclusion is verified by numerical simulation. Related Articles | Metrics

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Noise Induced Chaotic Bursting Li Ji, Li Ping Mathematical Theory and Applications    2023, 43 (1): 44-63.   DOI: 10.3969/j.issn.1006-8074.2023.01.003 Abstract （1280）      PDF（pc） （540KB）（323）       Knowledge map    Periodic or chaotic bursting behavior is commonly observed in neurons and endocrine cells, consisting of recurrent transitions between quiescent states and repetitive spikings, and has been of interest for a long time. Stochastic forcing is known to have non-negligible influence in many cases. In this paper we study the effect of uniformly bounded noise on the spike and burst behavior and explain the mechanism how uniformly bounded noise generates chaotic bursting. Numerical simulation is provided to support the underlying mechanism. Related Articles | Metrics

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Gradient Estimates and Liouville Theorems for $\Delta u + au^{p+1}=0$  Peng Bo, Wang Youde, Wei Guodong Mathematical Theory and Applications    2023, 43 (1): 32-43.   DOI: 10.3969/j.issn.1006-8074.2023.01.002 Abstract （1399）      PDF（pc） （177KB）（304）       Knowledge map    In this paper, we employ Li-Yau's method and delicate analysis techniques to provide a unified and simple approach to the gradient estimate of the positive solution to the nonlinear elliptic equation $\Delta u + au^{p+1}=0$ defined on a complete noncompact Riemannian manifold $(M, g)$ where $a > 0$ and $ p < 4/n $ or $a < 0$ and $p >0$ are two constants. For the case $a>0$, we extend the range of $p$ and improve some results in \cite{J-L, MHL} and supplement the results for the case $\dim(M)= 2$. For the case $a<0$ and $p>0$, we improve or perfect the previous results due to Ma, Huang and Luo \cite{MHL} since one does not need to suppose the positive solutions are bounded. When the Ricci curvature of $(M,g)$ is nonnegative, we also obtain a Liouville-type theorem for the above equation. Related Articles | Metrics

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Progress in Spatio­temporal Dynamics of Vegetation Systems Zhang Hongtao, Sun Guiquan Mathematical Theory and Applications    2023, 43 (2): 1-15.   DOI: 10.3969/j.issn.1006­8074.2023.02.001 Abstract （1193）      PDF（pc） （509KB）（281）       Knowledge map    Vegetation pattern is one of the typical characteristics of ecosystems in arid and semi­arid areas, which can qualitatively describe the spatial distribution structure of vegetation, and can be used as an early indicator of ecosystem improvement and degradation. This paper devotes to summarize the bifurcation phenomena in vegetation system to reveal the formation mechanism of vegetation pattern and provide warning signals of desertification. Firstly, through the Hopf bifurcation theory, the conditions of spatial homogeneous Hopf bifurcation in vegetation model are qualitatively analyzed, and the phenomenon of interannual periodic fluctuation of vegetation biomass is explained. Secondly, the existing vegetation models are analyzed by the Turing bifurcation theory, the regular distribution of vegetation in space and the formation mechanism of pattern are revealed, and the types of these patterns are refined by applying the multiple scale analysis method, and the parameter threshold of the system undergoing pattern phase transition is found. Finally, when the Hopf bifurcation and Turing bifurcation occur at the same time, the system will undergo a Turing-­Hopf bifurcation. By means of the normal form theory of reaction­diffusion equation, the normal form of the Turing­-Hopf bifurcation is derived, and the amplitude equation is obtained by the cylindrical coordinate  transformation to analyze its dynamic behavior, and then more complex spatiotemporal patterns of vegetation are revealed. Related Articles | Metrics

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Parallel Machine Scheduling Problem with Workload-dependent Maintenance Duration Zhou Ju, Cheng Zhenmin Mathematical Theory and Applications    2022, 42 (4): 105-.   DOI: 10.3969/j.issn.1006-8074.2022.04.009 Abstract （1555）      PDF（pc） （182KB）（273）       Knowledge map    In this paper a parallel machine scheduling problem with tool changes, where the tool change durations are workload-dependent, is considered. The objective is to minimize the makespan. Firstly, based on the fact that the maintenance duration function is a monotone undiminished function, two properties of the optimal scheduling scheme are obtained: the difference between the numbers of job processed by each machine is at most one, and each machine in its last maintenance interval should process as many jobs as possible. Secondly, for each case that the maintenance duration function is concave, convex, or linear, a corresponding optimal optimal algorithm MNJF, SFF or SLE is presented respectively. Finally, it is proved that the algorithms MNJF, SJF and SLE are all optimal in the corresponding cases, and the algorithm MNJF is also optimal when the maintenance duration function is linear.  Related Articles | Metrics

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Constructing Evans Triangles with a Quadratic Equation Li Juan, Guan Huanhuan, Yuan Pingzhi Mathematical Theory and Applications    2022, 42 (4): 45-.   DOI: 10.3969/j.issn.1006-8074.2022.04.004 Abstract （1549）      PDF（pc） （176KB）（258）       Knowledge map    In this paper, two new classes of primitive Evans triangles are constructed by using the positive integer solutions of the quadratic equation \ $kx^2-ly^2=2$, and the trilateral forms and corresponding Evans ratios of these kinds of Evans triangles are given.  Related Articles | Metrics

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Constructing Cospectral Graphs by Improved GM-switching Song Wanwei, Hou Yaoping Mathematical Theory and Applications    2022, 42 (4): 71-.   DOI: 10.3969/j.issn.1006-8074.2022.04.006 Abstract （1582）      PDF（pc） （349KB）（243）       Knowledge map    Spectral theory of graphs mainly investigates the eigenvalues of the related matrices of graphs. Since there are cospectral graphs which are not isomorphic, it is meaningful to find methods to construct the cospectral graphs. In this paper, a method of constructing cospectral graphs is given, which is an improvement of the well known GM-switching. Related Articles | Metrics

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High-accuracy Randomized Completion Algorithm for the Low Rank Toeplitz Tensor Wen Ruiping, Li Wenwei Mathematical Theory and Applications    2023, 43 (3): 95-110.   DOI: 10.3969/j.issn.1006-8074.2023.03.005 Abstract （751）      PDF（pc） （390KB）（235）       Knowledge map    In this paper, we consider the solution for the completion problem of low rank Toeplitz tensors , and based on the high-accuracy completion algorithm, present a high-accuracy completion algorithm with randomized technique, in which the n-mode tensor is stochastically unfolded and the corresponding singular value decomposition (SVD) is modified in each iteration. Moreover, the convergence of the new algorithm is established. The results of numerical experiments on the Toeplitz tensor and the Toeplitz mean tensor show that the new algorithm is significantly better than the high-accuracy completion algorithm for low rank Toeplitz tensors in terms of computational cost. Related Articles | Metrics

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Existence of Perfect Matchings in General Graphs and Bipartite Graphs with Respect to Distance Signless Laplacian Spectral Radius Yan Zimo, Liu Chang, Li Jianping Mathematical Theory and Applications    2023, 43 (1): 74-84.   DOI: 10.3969/j.issn.1006-8074.2023.01.005 Abstract （1231）      PDF（pc） （277KB）（231）       Knowledge map    Let $\mathcal{D}(G)=(D_{i,j})$ be the distance matrix of a connected graph $G$, where $\mathcal{D}_{i,j}$ equals the distance between the vertices $v_i$ and $v_j$ of $G$. Let $\eta_1(G)$ be the distance signless Laplacian spectral radius of $G$, i.e., the largest eigenvalue of the distance signless Laplacian matrix $\mathcal{Q}(G)=Diag(Tr)+\mathcal{D}(G)$, where $Diag(Tr)$ is a diagonal matrix with $Diag(Tr)_{ii}=\sum_{v_iv_j\in E(G)}\mathcal{D}_{i,j}$. In this paper, we investigate the relationships between the perfect matchings and the distance signless Laplacian spectral radius, and give sufficient conditions for the existence of perfect matchings in general graphs and bipartite graphs with respect to the distance signless Laplacian spectral radius, respectively. Related Articles | Metrics

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Functional Inequalities of q- Analog of Bi-univalent Function Classes Involving a Particular Integral Operator Mai Tingmei, Long Pinhong, Han Huili, He Fuli Mathematical Theory and Applications    2023, 43 (1): 85-99.   DOI: 10.3969/j.issn.1006-8074.2023.01.006 Abstract （1247）      PDF（pc） （213KB）（229）       Knowledge map    In this paper a kind of integral operator $I^{\beta}_{\alpha}f(z)$ related to the parameters $\alpha, \beta$ in an open unit disk is investigated. Firstly, the bi-univalent function classes $\mathfrak{H}_{\Sigma_{q}}^{\alpha,\beta}(\lambda;\phi)$ and $\mathfrak{L}_{\Sigma_{q}}^{\alpha,\beta}(\mu,\lambda;\phi)$ involving this integral operator and the $q$-derivative operator are defined by applying the subordination principle of analytic functions. Then, the upper bounds of the first two coefficients $a_{2}$ and $ a_{3}$ of the two classes of bi-univalent analytic functions are estimated, and the corresponding Fekete-Szegö  inequalites for these classes are obtained. Related Articles | Metrics

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Strong Attractors for Semilinear Reaction-diffusion Equations with Memory Tang Zhipiao, Sun Chunyou, Xie Yongqin Mathematical Theory and Applications    2023, 43 (1): 115-125.   DOI: 10.3969/j.issn.1006-8074.2023.01.008 Abstract （1180）      PDF（pc） （232KB）（210）       Knowledge map    In this paper, we discuss the long time behavior of strong solutions of semilinear reaction diffusion equations with fading memory. First of all, by the regularity of solutions and the control convergence principle, we prove that the semigroup of the solutions is an contractive semigroup on $ H_0^1(\Omega)\times L_\mu^2(\mathbb{R}; D(A))$, which leads to the asymptotic compactness of the semigroup. Then, we show the existence and regularity of global attractor $\mathcal{A}$ on the product space. It is noteworthy that the nonlinearity $f$ satisfies the polynomial growth of arbitrary order and $\mathcal{A}\subset D(A)\times L_\mu^2(\mathbb{R}; D(A))$. Related Articles | Metrics

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The Turán  Number of Disjoint Stars in Hypergraphs Deng Jinghua, Hou Jianfeng, Zeng Qinghou, Zhang Yixiao Mathematical Theory and Applications    2023, 43 (1): 64-73.   DOI: 10.3969/j.issn.1006-8074.2023.01.004 Abstract （1257）      PDF（pc） （165KB）（208）       Knowledge map    Given an $r$-uniform hypergraph $\mathcal{F}$, the { Tur\'{a}n number} of $\mathcal{F}$, denoted by $\mathrm{ex}_{r}(n,\mathcal{F})$, is the maximum number of edges in an $\mathcal{F}$-free $r$-uniform hypergraph on $n$ vertices. For $r\ge 3$, determining $\mathrm{ex}_{r}(n,\mathcal{F})$ is known to be notoriously hard especially when $\mathrm{ex}_{r}(n,\mathcal{F})=o(n^r)$. For a graph $F$, the expansion of $F$, denoted by $F^{+}$, is an $r$-uniform hypergraph by adding $r-2$ new elements to each edge of $F$; and the Berge copy of $F$, denoted by Berge-$F$, is an $r$-uniform hypergraph $\mathcal{H}$ with $V(F) \subseteq V(\mathcal{H})$ satisfying that there is a bijection $f$ from $E(F)$ to $E(\mathcal{H})$ such that $e\subseteq f(e)$ for every $e \in E(F)$. In this paper, we determine the Tur\'{a}n numbers of the expansion, and the family of all Berge copy of disjoint union of stars. Both generalize the results given by Khormali and Palmer [14]. Related Articles | Metrics