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2022, Vol. 42 No. 3   Published date: 30 September 2022
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• The Nonparametric Empirical Likelihood Goodness-of-fit Test for Integrated Diffusion Processes

  Liu Zaiming, Tang Mingtian, Wang Yunyan

  2022, 42(3): 1. doi: 10.3969/j.issn.1006-8074.2022.03.001

  Abstract ( 2967 )   PDF (320KB) ( 407 )   　　

  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.

• Blow up Solutions of the Elastic String Equation with Nonlinear Damping and  Source Terms

  Zhang Zaiyun, Ouyang Qiancheng, Zou Pengcheng, Wang Qiong, Ling Wenjing

  2022, 42(3): 21. doi: 10.3969/j.issn.1006-8074.2022.03.002

  Abstract ( 1584 )   PDF (166KB) ( 371 )   　　

  In this paper, we consider the elastic string equation with nonlinear damping and source terms. Following the ideas of Zhang and Miao [43] the blow up of the solutions with positive initial energy is investigated by the perturbed energy method.

• Almost Periodic Solutions of a Discrete Model via Quasi-uniform Asymptotic Stability

  Fang Lini , N'gbo N'gbo, Xia Yonghui

  2022, 42(3): 33. doi: 10.3969/j.issn.1006-8074.2022.03.003

  Abstract ( 1465 )   PDF (213KB) ( 398 )   　　

  This paper concerns the existence and uniqueness of almost periodic solutions to a discrete system. Because in general, the conditions to guarantee the quasi-uniform asymptotic stability is relatively weaker, we employ the quasi-uniform asymptotic stability to derive the sufficient conditions for the existence of positive almost periodic solutions to the concerned system. The effectiveness of our results are verified by a numerical example.

• Resource Dispatching Conditions in NFV Networks from Binding Number Perspective

  Wu Jianzhang

  2022, 42(3): 46. doi: 10.3969/j.issn.1006-8074.2022.03.004

  Abstract ( 1532 )   PDF (172KB) ( 555 )   　　

  In the resource scheduling network, the availability of resource scheduling is equivalent to the existence of the fractional factor in the corresponding network graph. The study on the existence of fractional factors in specific graph structure can help engineers design and  construct the network with efficient use of resources. A graph $G$ is called an all fractional $(g,f,n',m)$-critical deleted graph if after removing any $n'$ vertices from $G$ the remaining graph is still an all fractional $(g,f,m)$-deleted graph. In this paper, we present two binding number conditions for a graph to be an all fractional $(g,f,n',m)$-critical deleted graph, and illustrate the results are sharp with examples.

• The Extremal Value of Exponential Inverse Forgotten Index of a Tree

  Zeng Mingyao , Deng Hanyuan

  2022, 42(3): 61. doi: 10.3969/j.issn.1006-8074.2022.03.005

  Abstract ( 1854 )   PDF (368KB) ( 819 )   　　

  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. 

  
  

• Quasi-Monte Carlo Method for a Class of Stochastic Optimal Control Problems

  Zhou Hongmin, Luo Xianbing, Ye Changlun

  2022, 42(3): 71. doi: 10.3969/j.issn.1006-8074.2022.03.006

  Abstract ( 1661 )   PDF (305KB) ( 904 )   　　

  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.

• On the Filtered Krylov-Like Sequence Method for Solving Non-Symmetric Eigenvalue Problems

  Tan Xueyuan, Cheng Lan

  2022, 42(3): 85-15. doi: 10.3969/j.issn.1006-8074.2022.03.007

  Abstract ( 1508 )   PDF (371KB) ( 327 )   　　

  The filtered Krylov-like sequence method, which integrates the standard Krylov subspace method with the polynomial filtering technique, is efficient for computing several extreme eigenvalues of symmetric matrices. In this paper, we generalize this method to compute eigenvalues with largest real parts and corresponding eigenvectors of non-symmetric matrices. The filtered Krylov-like sequence method can be expected to show great superiority and robustness over the standard Krylov subspace methods. Numerical experiments are carried out to show competitiveness of the new method.

• Prediction of Mortality of Elderly Population with an Improved AE-LSTM Model

  2022, 42(3): 100. doi: 10.3969/j.issn.1006-8074.2022.03.008

  Abstract ( 2126 )   PDF (1786KB) ( 604 )   　　

  Prediction of mortality of the elderly population is the basis of longevity risk measurement and management, assessment of pension cost and debt. Based on the characteristics of mortality data of the elderly population, an improved AE-LSTM model is proposed to predict the mortality of the elderly population. Firstly, the AE model is used to extract the potential time factor from the mortality data of the elderly population. Then, the potential time factor is used as the input variable of the LSTM model. The mortality prediction value of the elderly population is obtained by decoding the AE model. At the same time, the mortality rate of the elderly aged 60-89 in China mainland from 1994 to 2018 is selected as the sample data for empirical analysis. The results show that the prediction accuracy of the improved AE-LSTM model is significantly higher than that of the traditional CBD model, and the prediction results show strong robustness.

• Entry Timing and Product Differentiation Decision in Continuous Time Circular City Model

  Zhang Bo, Hu Zhijun

  2022, 42(3): 114. doi: 10.3969/j.issn.1006-8074.2022.03.009

  Abstract ( 1487 )   PDF (310KB) ( 1158 )   　　

  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.