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A Minimum Residual Based Gradient Iterative Method for a Class of Matrix Equations 一类矩阵方程的最小残差梯度迭代法
IF 0.9 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-30 DOI: 10.1007/s10255-024-1100-0
Qing-qing Zheng
{"title":"A Minimum Residual Based Gradient Iterative Method for a Class of Matrix Equations","authors":"Qing-qing Zheng","doi":"10.1007/s10255-024-1100-0","DOIUrl":"10.1007/s10255-024-1100-0","url":null,"abstract":"<div><p>In this paper, we present a minimum residual based gradient iterative method for solving a class of matrix equations including Sylvester matrix equations and general coupled matrix equations. The iterative method uses a negative gradient as steepest direction and seeks for an optimal step size to minimize the residual norm of next iterate. It is shown that the iterative sequence converges unconditionally to the exact solution for any initial guess and that the norm of the residual matrix and error matrix decrease monotonically. Numerical tests are presented to show the efficiency of the proposed method and confirm the theoretical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138496160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Strong Solutions and Large-time Behavior of 2D Tropical Climate Model 二维热带气候模式的全球强解和大时间行为
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1090-3
Dong-juan Niu, Ying Wang
{"title":"Global Strong Solutions and Large-time Behavior of 2D Tropical Climate Model","authors":"Dong-juan Niu,&nbsp;Ying Wang","doi":"10.1007/s10255-023-1090-3","DOIUrl":"10.1007/s10255-023-1090-3","url":null,"abstract":"<div><p>In this paper we mainly deal with the global well-posedness and large-time behavior of the 2D tropical climate model with small initial data. We first establish the global well-posedness of solution in the Besov space, then we obtain the optimal decay rates of solutions by virtue of the frequency decomposition method. Specifically, for the low frequency part, we use the Fourier splitting method of Schonbek and the spectrum analysis method, and for the high frequency part, we use the global energy estimate and the behavior of exponentially decay operator.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors 具有自回归条件异方差误差的时空自回归模型的Bayes估计与模型选择
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1096-x
Bing Su, Fu-kang Zhu, Ju Huang
{"title":"Bayesian Estimation and Model Selection for the Spatiotemporal Autoregressive Model with Autoregressive Conditional Heteroscedasticity Errors","authors":"Bing Su,&nbsp;Fu-kang Zhu,&nbsp;Ju Huang","doi":"10.1007/s10255-023-1096-x","DOIUrl":"10.1007/s10255-023-1096-x","url":null,"abstract":"<div><p>The spatial and spatiotemporal autoregressive conditional heteroscedasticity (STARCH) models receive increasing attention. In this paper, we introduce a spatiotemporal autoregressive (STAR) model with STARCH errors, which can capture the spatiotemporal dependence in mean and variance simultaneously. The Bayesian estimation and model selection are considered for our model. By Monte Carlo simulations, it is shown that the Bayesian estimator performs better than the corresponding maximum-likelihood estimator, and the Bayesian model selection can select out the true model in most times. Finally, two empirical examples are given to illustrate the superiority of our models in fitting those data.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Contact Extension and Symplectification 接触延伸与同情
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1093-0
Qi-huai Liu, An Xie, Chao Wang
{"title":"Contact Extension and Symplectification","authors":"Qi-huai Liu,&nbsp;An Xie,&nbsp;Chao Wang","doi":"10.1007/s10255-023-1093-0","DOIUrl":"10.1007/s10255-023-1093-0","url":null,"abstract":"<div><p>This paper mainly studies the contact extension of conservative or dissipative systems, including some old and new results for wholeness. Then extension of contact system is corresponding to the symplectification of contact Hamiltonian system. This is a reciprocal process and the relation between symplectic system and contact system has been discussed. We have an interesting discovery that by adding a pure variable <i>p</i>, the slope of the tangent of the orbit, every differential system can be regarded as an independent subsystem of contact Hamiltonian system defined on the projection space of contact phase space.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909298","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Injective Δ+2 Coloring of Planar Graph Without Short Cycles 无短环平面图的Δ+2染色
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1098-8
Ying Chen, Lan Tao, Li Zhang
{"title":"Injective Δ+2 Coloring of Planar Graph Without Short Cycles","authors":"Ying Chen,&nbsp;Lan Tao,&nbsp;Li Zhang","doi":"10.1007/s10255-023-1098-8","DOIUrl":"10.1007/s10255-023-1098-8","url":null,"abstract":"<div><p>A coloring of graph <i>G</i> is an <i>injective coloring</i> if its restriction to the neighborhood of any vertex is injective, which means that any two vertices get different colors if they have a common neighbor. The <i>injective chromatic number</i> χ<sub><i>i</i></sub>(<i>G</i>) of <i>G</i> is the least integer <i>k</i> such that <i>G</i> has an injective <i>k</i>-coloring. In this paper, we prove that (1) if <i>G</i> is a planar graph with girth <i>g</i> ≥ 6 and maximum degree Δ ≥ 7, then <i>χ</i><sub><i>i</i></sub>(<i>G</i>) ≤ Δ + 2; (2) if <i>G</i> is a planar graph with Δ ≥ 24 and without 3,4,7-cycles, then <i>χ</i><sub><i>i</i></sub>(<i>G</i>) ≤ Δ + 2.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909305","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Upwind Mixed Finite Volume Element-fractional Step Method and Convergence Analysis for Three-dimensional Compressible Contamination Treatment from Nuclear Waste 核废料三维可压缩污染处理的迎风混合有限体积元-分步法及收敛分析
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1099-7
Chang-feng Li, Yi-rang Yuan, Huai-ling Song
{"title":"An Upwind Mixed Finite Volume Element-fractional Step Method and Convergence Analysis for Three-dimensional Compressible Contamination Treatment from Nuclear Waste","authors":"Chang-feng Li,&nbsp;Yi-rang Yuan,&nbsp;Huai-ling Song","doi":"10.1007/s10255-023-1099-7","DOIUrl":"10.1007/s10255-023-1099-7","url":null,"abstract":"<div><p>In this paper the authors discuss a numerical simulation problem of three-dimensional compressible contamination treatment from nuclear waste. The mathematical model, a nonlinear convection-diffusion system of four PDEs, determines four major physical unknowns: the pressure, the concentrations of brine and radionuclide, and the temperature. The pressure is solved by a conservative mixed finite volume element method, and the computational accuracy is improved for Darcy velocity. Other unknowns are computed by a composite scheme of upwind approximation and mixed finite volume element. Numerical dispersion and nonphysical oscillation are eliminated, and the convection-dominated diffusion problems are solved well with high order computational accuracy. The mixed finite volume element is conservative locally, and get the objective functions and their adjoint vector functions simultaneously. The conservation nature is an important character in numerical simulation of underground fluid. Fractional step difference is introduced to solve the concentrations of radionuclide factors, and the computational work is shortened significantly by decomposing a three-dimensional problem into three successive one-dimensional problems. By the theory and technique of a priori estimates of differential equations, we derive an optimal order estimates in <i>L</i><sup>2</sup> norm. Finally, numerical examples show the effectiveness and practicability for some actual problems.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909213","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Volatility Modeling based on Doubly Truncated Cauchy Distribution and Bayesian Estimation for Chinese Stock Market 基于双截断柯西分布和贝叶斯估计的中国股市随机波动率建模
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1095-y
Cai-feng Wang, Cong Xie, Zi-yu Ma, Hui-min Zhao
{"title":"Stochastic Volatility Modeling based on Doubly Truncated Cauchy Distribution and Bayesian Estimation for Chinese Stock Market","authors":"Cai-feng Wang,&nbsp;Cong Xie,&nbsp;Zi-yu Ma,&nbsp;Hui-min Zhao","doi":"10.1007/s10255-023-1095-y","DOIUrl":"10.1007/s10255-023-1095-y","url":null,"abstract":"<div><p>In order to measure the uncertainty of financial asset returns in the stock market, this paper presents a new model, called SV-dtC model, a stochastic volatility (SV) model assuming that the stock return has a doubly truncated Cauchy distribution, which takes into account the high peak and fat tail of the empirical distribution simultaneously. Under the Bayesian framework, a prior and posterior analysis for the parameters is made and Markov Chain Monte Carlo (MCMC) is used for computing the posterior estimates of the model parameters and forecasting in the empirical application of Shanghai Stock Exchange Composite Index (SSECI) with respect to the proposed SV-dtC model and two classic SV-N (SV model with Normal distribution) and SV-T (SV model with Student-t distribution) models. The empirical analysis shows that the proposed SV-dtC model has better performance by model checking, including independence test (Projection correlation test), Kolmogorov-Smirnov test(K-S test) and Q-Q plot. Additionally, deviance information criterion (DIC) also shows that the proposed model has a significant improvement in model fit over the others.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Parametric Anisotropic (p, q)-Neumann Problems 参数各向异性（p，q）-Neumann问题
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1087-y
Zhen-hai Liu, Nikolaos S. Papageorgiou
{"title":"Parametric Anisotropic (p, q)-Neumann Problems","authors":"Zhen-hai Liu,&nbsp;Nikolaos S. Papageorgiou","doi":"10.1007/s10255-023-1087-y","DOIUrl":"10.1007/s10255-023-1087-y","url":null,"abstract":"<div><p>We consider a Neumann problem driven by a (<i>p</i>(<i>z</i>), <i>q</i>(<i>z</i>))-Laplacian (anisotropic problem) plus a parametric potential term with λ &gt; 0 being the parameter. The reaction is superlinear but need not satisfy the Ambrosetti-Rabinowitz condition. We prove a bifurcation-type theorem describing the changes in the set of positive solutions as the parameter λ moves on </p><div><figure><div><div><picture><source><img></source></picture></div></div></figure></div><p>.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative 一种新的谱法误差分析多项时间分数阶导数的异常解扩散问题
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1091-2
Bo Tang, Yan-ping Chen, Bin Xie, Xiu-xiu Lin
{"title":"A Novel Error Analysis of Spectral Method for the Anomalous Subdiffusion Problems with Multi-term Time-fractional Derivative","authors":"Bo Tang,&nbsp;Yan-ping Chen,&nbsp;Bin Xie,&nbsp;Xiu-xiu Lin","doi":"10.1007/s10255-023-1091-2","DOIUrl":"10.1007/s10255-023-1091-2","url":null,"abstract":"<div><p>This paper aims to extend a space-time spectral method to address the multi-term time-fractional subdiffusion equations with Caputo derivative. In this method, the Jacobi polynomials are adopted as the basis functions for temporal discretization and the Lagrangian polynomials are used for spatial discretization. An efficient spectral approximation of the weak solution is established. The main work is the demonstration of the well-posedness for the weak problem and the derivation of a posteriori error estimates for the spectral Galerkin approximation. Extensive numerical experiments are presented to perform the validity of a posteriori error estimators, which support our theoretical results.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909299","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation n-D非齐次Burgers方程的非自相似初等波的整体解和相互作用
IF 0.8 4区 数学
Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2023-11-08 DOI: 10.1007/s10255-023-1097-9
Yuan-an Zhao, Gao-wei Cao, Xiao-zhou Yang
{"title":"Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation","authors":"Yuan-an Zhao,&nbsp;Gao-wei Cao,&nbsp;Xiao-zhou Yang","doi":"10.1007/s10255-023-1097-9","DOIUrl":"10.1007/s10255-023-1097-9","url":null,"abstract":"<div><p>We investigate the global structures of the non-selfsimilar solutions for <i>n</i>-dimensional (<i>n</i>-D) non-homogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a (<i>n</i> − 1)-dimensional sphere. We first obtain the expressions of <i>n</i>-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves, we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the <i>n</i>-D shock waves. The asymptotic behaviors with geometric structures are also proved.</p></div>","PeriodicalId":6951,"journal":{"name":"Acta Mathematicae Applicatae Sinica, English Series","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71909224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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