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2022, Vol. 42 No. 4   Published date: 28 December 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

  2022, 42(4): 1. doi: 10.3969/j.issn.1006­8074.2022.04.001

  Abstract ( 2237 )   PDF (234KB) ( 441 )   　　

  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.

• The Complete Weight Enumerators for Some Three­weight Linear Codes

  Tan Ting, Zhu Canze, Liao Qunying

  2022, 42(4): 19. doi: 10.3969/j.issn.1006-8074.2022.04.002

  Abstract ( 2725 )   PDF (243KB) ( 453 )   　　

  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].

• Derivation Algebra and Automorphism Group of the Mirror Heisenberg-Virasoro Algebra

  Zhao Yufang, Cheng Yongsheng

  2022, 42(4): 36. doi: 10.3969/j.issn.1006-8074.2022.04.003

  Abstract ( 1598 )   PDF (175KB) ( 346 )   　　

  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.

• Constructing Evans Triangles with a Quadratic Equation

  Li Juan, Guan Huanhuan, Yuan Pingzhi

  2022, 42(4): 45. doi: 10.3969/j.issn.1006-8074.2022.04.004

  Abstract ( 1549 )   PDF (176KB) ( 258 )   　　

  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. 

  
  

• A Modified PRP­HS Hybrid Conjugate Gradient Method with Global Convergence

  Wang Yun, Huang Jingpin, Shao Hu, Liu Pengjie

  2022, 42(4): 58. doi: 10.3969/j.issn.1006-8074.2022.04.005

  Abstract ( 1664 )   PDF (357KB) ( 597 )   　　

  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.

• Constructing Cospectral Graphs by Improved GM-switching

  Song Wanwei, Hou Yaoping

  2022, 42(4): 71. doi: 10.3969/j.issn.1006-8074.2022.04.006

  Abstract ( 1582 )   PDF (349KB) ( 243 )   　　

  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.

• Stability and Hopf Bifurcation of a Class of Epidemic Models with Stage Structure and Fear Effect

  Liu Yuying, Yang Wensheng

  2022, 42(4): 79. doi: 10.3969/j.issn.1006-8074.2022.04.007

  Abstract ( 1522 )   PDF (684KB) ( 333 )   　　

  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.

• 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

  2022, 42(4): 93. doi: 10.3969/j.issn.1006-8074.2022.04.008

  Abstract ( 1663 )   PDF (902KB) ( 699 )   　　

  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.

• Parallel Machine Scheduling Problem with Workload-dependent Maintenance Duration

  Zhou Ju, Cheng Zhenmin

  2022, 42(4): 105. doi: 10.3969/j.issn.1006-8074.2022.04.009

  Abstract ( 1555 )   PDF (182KB) ( 273 )   　　

  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. 

• 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

  2022, 42(4): 115. doi: 10.3969/j.issn.1006-8074.2022.04.010

  Abstract ( 1786 )   PDF (6927KB) ( 886 )   　　

  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