应用数学学报(英文版)
HOME | ABOUT JOURNAL | EDITORIAL BOARD | FOR AUTHORS | SUBSCRIPTIONS | ADVERTISEMENT | CONTACT US
 
Acta Mathematicae Applicatae
Sinica, Chinese Series
 
   
   
Adv Search »  
 
  Current Issue
 
2021 Vol.37 Issue.3,Published 2021-07-15

ARTICLES
ARTICLES
441 The Analysis of Impact of Brexit on the Post-Brexit EU Using Intervented Multivariate Time Series
Yu TIAN, Shao-pei MA, Rong-xiang RUI, Zhen YU, Mao-zai TIAN
The UK is the most important partner of the EU in terms of economic and other fields due to the geographical proximity. It was one of the largest economies in the EU and its per capita income is higher than the EU average, so it is a net contributor to the EU. With UKs membership of the EU ended on 31 January 2019, there are concerns that the Brexit may have a significant impact on the EU, resulting in social, economic, political, and institutional changes, etc. in EU. While the impact of Brexit on the UK has always been the subject of considerable scholarly interest in recent years, there is relatively little literature on the impact of Brexit on the EU. This paper focuses on the evaluation of the impact of Brexit on the EU economy and other relevant aspects along three dimensions: GDP, PPP, Quarterly GDP growth. Employing powerful quantitative analysis technology that includes vector autoregression model, multivariate time series model with intervention variables, and autoregression integrated moving average, this paper obtains the important and novel evidence about the potential impact of Brexit on the EU economy, pointing out that Brexit is of far-reaching significance to the EU. This analysis uses several statistical models to screen out several key influencing factors, which can be used to predict the total GDP of EU in the next five years. The results show that EU economy will react negatively to "no-deal" Brexit, and its growth rate of economy will slow down significantly in next 5 years. Finally, we put forward relevant policy suggestions on how to deal with the negative impact of Brexit on EU.
2021 Vol. 37 (3): 441-458 [Abstract] ( 6 ) [HTML 1KB] [ PDF 663KB] ( 35 )
459 Asymmetric Information, Heterogeneous Prior Beliefs and Market Regulation
Hong LIU, Ying JIANG, Huai-nian ZHANG
This paper studies the trading behavior of an irrational insider and its influence on the market equilibrium in the presence of market regulation. We find that the market with only one insider with private information is almost close to a strong efficient market, under the condition of market regulation. In the equilibrium, the probability of the insider being caught trading with private information is zero, which shows that the reasonable behavior of the regulator is to essentially give up regulation. But the market efficiency and the irrational trader’s trading intensity all greatly improve because of the existence of the market regulation.
2021 Vol. 37 (3): 459-476 [Abstract] ( 5 ) [HTML 1KB] [ PDF 226KB] ( 22 )
477 Existence and Properties of Solutions for a Class of Fractional Differential Equations
Yong-qiang XU, Shu-hong CHEN, Zhong TAN
In this paper, we consider the initial value problem of a class of fractional differential equations. Firstly, we obtain the existence and uniqueness of the solutions by using Picard’s method of successive approximation. Then we discuss the dependence of the solutions on the initial value.
2021 Vol. 37 (3): 477-484 [Abstract] ( 1 ) [HTML 1KB] [ PDF 131KB] ( 33 )
485 Hosoya and Merrifield-Simmons Indices in Random Polyphenyl Chains
Wei-ling YANG
The Hosoya index of a graph is the total number of matchings in it. And the Merrifield-Simmons index is the total number of independent sets in it. They are typical examples of graph invariants used in mathematical chemistry for quantifying relevant details of molecular structure. In this paper, we obtain explicit analytical expressions for the expectations of the Hosoya index and the Merrifield-Simmons index of a random polyphenyl chain.
2021 Vol. 37 (3): 485-494 [Abstract] ( 2 ) [HTML 1KB] [ PDF 195KB] ( 18 )
495 Least Squares Model Averaging Based on Generalized Cross Validation
Xin-min LI, Guo-hua ZOU, Xin-yu ZHANG, Shang-wei ZHAO
Frequentist model averaging has received much attention from econometricians and statisticians in recent years. A key problem with frequentist model average estimators is the choice of weights. This paper develops a new approach of choosing weights based on an approximation of generalized cross validation. The resultant least squares model average estimators are proved to be asymptotically optimal in the sense of achieving the lowest possible squared errors. Especially, the optimality is built under both discrete and continuous weigh sets. Compared with the existing approach based on Mallows criterion, the conditions required for the asymptotic optimality of the proposed method are more reasonable. Simulation studies and real data application show good performance of the proposed estimators.
2021 Vol. 37 (3): 495-509 [Abstract] ( 3 ) [HTML 1KB] [ PDF 295KB] ( 29 )
510 The Minimum Stretch Spanning Tree Problem for Typical Graphs
Lan LIN, Yi-xun LIN
With applications in communication networks, the minimum stretch spanning tree problem is to find a spanning tree T of a graph G such that the maximum distance in T between two adjacent vertices is minimized. The problem has been proved NP-hard and fixed-parameter polynomial algorithms have been obtained for some special families of graphs. In this paper, we concentrate on the optimality characterizations for typical classes of graphs. We determine the exact formulae for the complete k-partite graphs, split graphs, generalized convex graphs, and several planar grids, including rectangular grids, triangular grids, and triangulated-rectangular grids.
2021 Vol. 37 (3): 510-522 [Abstract] ( 5 ) [HTML 1KB] [ PDF 193KB] ( 26 )
523 Stabilization and Synchronization of Discrete-time Fractional Chaotic Systems with Non-identical Dimensions
Samir BENDOUKHA
This paper investigates the stabilization and synchronization of two fractional chaotic maps proposed recently, namely the 2D fractional Hénon map and the 3D fractional generalized Hénon map. We show that although these maps have non–identical dimensions, their synchronization is still possible. The proposed controllers are evaluated experimentally in the case of non–identical orders or time–varying orders. Numerical methods are used to illustrate the results.
2021 Vol. 37 (3): 523-538 [Abstract] ( 0 ) [HTML 1KB] [ PDF 803KB] ( 19 )
539 Precise Large Deviations for Sums of Claim-size Vectors in a Two-dimensional Size-dependent Renewal Risk Model
Ke-ang FU, Xin-mei SHEN, Hui-jie LI
Consider a two-dimensional renewal risk model, in which the claim sizes {Xk; k ≥ 1} form a sequence of i.i.d. copies of a non-negative random vector whose two components are dependent. Suppose that the claim sizes and inter-arrival times form a sequence of i.i.d. random pairs, with each pair obeying a dependence structure via the conditional distribution of the inter-arrival time given the subsequent claim size being large. Then a precise large-deviation formula of the aggregate amount of claims is obtained.
2021 Vol. 37 (3): 539-547 [Abstract] ( 5 ) [HTML 1KB] [ PDF 143KB] ( 23 )
548 How Fast Does It Diverge? Discrete Hedging Error with Transaction Costs
Lan WU, Shuo WU
In the present paper, we focus on the diverging behavior of discrecte hedging error with transaction costs. We added the hedging cost to the error directly. The main idea is to divide the hedging error into two parts: the pure hedging error and transaction cost of rebalance. The later part will be diverged when hedging number n goes to infinity. Firstly we show an upper bound of diverging part, which is O(√n) of rebalancing number n, then we prove both the upper bound and the lower bound of discrete hedging error with transaction costs are of √n order, finally we give an approximation of hedging error to determine the coefficient in front of √n. The main technique in the proof is Itô’s formula, L’Hopital’s rule and three important lemmas in [Yuri, Kabanov, Mher, Safarian. Markets with Transaction Costs. Springer-Verlag, Berlin, Heidelberg, 2009]. The numerical result support our theoretical conclusion.
2021 Vol. 37 (3): 548-572 [Abstract] ( 2 ) [HTML 1KB] [ PDF 223KB] ( 15 )
573 Approximate Controllability of Second-order Semilinear Evolution Systems with Finite Delay
Xiao-feng SU, Xian-long FU
In this work, we study the approximate controllability for a class of semilinear second-order control systems with finite delay. Sufficient conditions for approximate controllability are established by constructing fundamental solutions and using the resolvent condition and techniques on cosine family of linear operators. To illustrate the applications of the obtained results, an example is provided in the end.
2021 Vol. 37 (3): 573-589 [Abstract] ( 4 ) [HTML 1KB] [ PDF 208KB] ( 21 )
590 Gini Correlation for Feature Screening
Jun-ying ZHANG, Xiao-feng LIU, Ri-quan ZHANG, Hang-WANG
In this paper we propose the Gini correlation screening (GCS) method to select the important variables with ultrahigh dimensional data. The new procedure is based on the Gini correlation coefficient via the covariance between the response and the rank of the predictor variables rather than the Pearson correlation and the Kendall τ correlation coefficient. The new method does not require imposing a specific model structure on regression functions and only needs the condition which the predictors and response have continuous distribution function. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.
2021 Vol. 37 (3): 590-601 [Abstract] ( 1 ) [HTML 1KB] [ PDF 170KB] ( 24 )
602 A Difference Scheme with Intrinsic Parallelism for Fractional Diffusion-wave Equation with Damping
Li-Fei WU, Xiao-Zhong YANG, Min LI
Anomalous diffusion is a widespread physical phenomenon, and numerical methods of fractional diffusion models are of important scientific significance and engineering application value. For time fractional diffusion-wave equation with damping, a difference (ASC-N, alternating segment Crank-Nicolson) scheme with intrinsic parallelism is proposed. Based on alternating technology, the ASC-N scheme is constructed with four kinds of Saul’yev asymmetric schemes and Crank-Nicolson (C-N) scheme. The unconditional stability and convergence are rigorously analyzed. The theoretical analysis and numerical experiments show that the ASC-N scheme is effective for solving time fractional diffusion-wave equation.
2021 Vol. 37 (3): 602-616 [Abstract] ( 0 ) [HTML 1KB] [ PDF 825KB] ( 28 )
617 Exponential Stability for Time-changed Stochastic Differential Equations
Min ZHU, Jun-ping LI, De-zhi LIU
So far there have been few results presented on the exponential stability for time-changed stochastic differential equations. The main aim of this work is to fill this gap. By making use of general Lyapunov methods and time-changed Itô formula, we establish the exponential stability and almost sure exponential stability of solution to time-changed SDEs. Finally, we construct some examples to illustrate the effectiveness of our established theory.
2021 Vol. 37 (3): 617-627 [Abstract] ( 2 ) [HTML 1KB] [ PDF 151KB] ( 18 )
628 On the Second Smallest and the Largest Normalized Laplacian Eigenvalues of a Graph
Xiao-guo TIAN, Li-gong WANG, You LU
Let G be a simple connected graph with order n. Let L(G) and Q(G) be the normalized Laplacian and normalized signless Laplacian matrices of G, respectively. Let λk(G) be the k-th smallest normalized Laplacian eigenvalue of G. Denote by ρ(A) the spectral radius of the matrix A. In this paper, we study the behaviors of λ2(G) and ρ(L(G)) when the graph is perturbed by three operations. We also study the properties of ρ(L(G)) and X for the connected bipartite graphs, where X is a unit eigenvector of L(G) corresponding to ρ(L(G)). Meanwhile we characterize all the simple connected graphs with ρ(L(G)) = ρ(Q(G)).
2021 Vol. 37 (3): 628-644 [Abstract] ( 3 ) [HTML 1KB] [ PDF 190KB] ( 20 )
645 Existence of p-mean Almost Periodic Mild Solution for Fractional Stochastic Neutral Functional Differential Equation
Xiao-ke SUN, Ping HE
A class of fractional stochastic neutral functional differential equation is analyzed in this paper. With the utilization of the fractional calculations, semigroup theory, fixed point technique and stochastic analysis theory, a sufficient condition of the existence for p-mean almost periodic solution is obtained, which are supported by two examples.
2021 Vol. 37 (3): 645-656 [Abstract] ( 1 ) [HTML 1KB] [ PDF 173KB] ( 32 )
Acta Mathematicae Applicatae Sinica, English Serie
      Forthcoming Articles
      Current Issue
      Archive
      Email Alert
      
      Read Articles
      Download Articles
  Copyright 2011 © Editorial Board of Acta Mathematicae Applicatae Sinica
Beijing 100080, P. R. China Tel: 010-82541908, Fax: 010-82541716  Email: amas@amt.ac.cn
京ICP备05002806号-9