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East Asian Journal on Applied Mathematics最新文献

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Extension of the ENO-ET Reconstruction Scheme to Two Space Dimensions on Cartesian Meshes in Conjunction with the ADER Approach 结合ADER方法将ENO-ET重建方案扩展到二维笛卡尔网格
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2022-352.280423
Gino I. Montecinos null, E. Toro
{"title":"Extension of the ENO-ET Reconstruction Scheme to Two Space Dimensions on Cartesian Meshes in Conjunction with the ADER Approach","authors":"Gino I. Montecinos null, E. Toro","doi":"10.4208/eajam.2022-352.280423","DOIUrl":"https://doi.org/10.4208/eajam.2022-352.280423","url":null,"abstract":"","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48517828","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
Approximation Analysis of Convolutional Neural Networks 卷积神经网络的逼近分析
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2022-270.070123
N. Null
{"title":"Approximation Analysis of Convolutional Neural Networks","authors":"N. Null","doi":"10.4208/eajam.2022-270.070123","DOIUrl":"https://doi.org/10.4208/eajam.2022-270.070123","url":null,"abstract":". In its simplest form, convolution neural networks (CNNs) consist of a fully connected two-layer network g composed with a sequence of convolution layers T . Although g is known to have the universal approximation property, it is not known if CNNs, which have the form g ◦ T inherit this property, especially when the kernel size in T is small. In this paper, we show that under suitable conditions, CNNs do inherit the universal approximation property and its sample complexity can be characterized. In addition, we discuss concretely how the nonlinearity of T can improve the approximation power. Finally, we show that when the target function class has a certain compositional form, convolutional networks are far more advantageous compared with fully connected networks, in terms of the number of parameters needed to achieve the desired accuracy.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46746271","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: 18
Bounded Traveling Wave Solutions of a (2+1)-Dimensional Breaking Soliton Equation 一类（2+1）维破缺孤立子方程的有界行波解
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2022-135.041222
Fuli Tian
{"title":"Bounded Traveling Wave Solutions of a (2+1)-Dimensional Breaking Soliton Equation","authors":"Fuli Tian","doi":"10.4208/eajam.2022-135.041222","DOIUrl":"https://doi.org/10.4208/eajam.2022-135.041222","url":null,"abstract":". We qualitatively analyze the bounded traveling wave solutions of a (2 + 1)- dimensional generalized breaking soliton (gBS) equation by using the theory of planar dynamical systems. We present the global phase diagrams of the dynamical system corresponding to the (2 + 1)-dimensional gBS equation under different parameters. The conditions for the existence of bounded traveling wave solutions are successfully derived. We find the relationship between the waveform of bounded traveling wave solutions and the dissipation coefficient β . When the absolute value of the dissipation coefficient β is greater than a critical value, we find that the equation has a kink profile solitary wave solution, while the solution has oscillatory and damped property if | β | is less than the critical value. In addition, we give the exact bell profile solitary wave solution and kink profile solitary wave solution by using undetermined coefficient method. The approximate oscillatory damped solution is given constructively. Through error analysis, we find that the approximate oscillatory damped solution is meaningful. Finally, we present the graphical analysis of the influence of dissipation coefficient β on oscillatory damped solution in order to better understand their dynamical behaviors.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45474019","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
Faster Deterministic Pseudoinverse-Free Block Extension of Motzkin Method for Large Consistent Linear Systems 大型一致线性系统的Motzkin方法的快速确定性伪逆块扩展
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2022-203.140123
J. Zhang
{"title":"Faster Deterministic Pseudoinverse-Free Block Extension of Motzkin Method for Large Consistent Linear Systems","authors":"J. Zhang","doi":"10.4208/eajam.2022-203.140123","DOIUrl":"https://doi.org/10.4208/eajam.2022-203.140123","url":null,"abstract":". Recently, a fast deterministic block Kaczmarz (FDBK) method which uses a greedy criterion of the row selections and contains pseudoinverse-free computation is presented. In this work, we introduce a maximum residual rule into FDBK and develop a new block Kaczmarz method which is also considered as a fast deterministic pseudoinverse-free block extension of Motzkin (FBEM) method. In addition, we prove that FBEM converges linearly to the unique least-norm solution of the linear systems. Furthermore, by incorporating the Polyak momentum technique into the FBEM iteration method, we establish an accelerated variant of FBEM (mFBEM) and show its global linear convergence. Numerical examples using artificial and real datasets demonstrate the effectiveness of FBEM as well as mFBEM.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47592828","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
Regularized Numerical Methods for the Nonlinear Schrödinger Equation with Singular Nonlinearity 奇异非线性非线性Schrödinger方程的正则化数值方法
4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2022-295.300123
Weizhu Bao, Yue Feng and Ying Ma
{"title":"Regularized Numerical Methods for the Nonlinear Schrödinger Equation with Singular Nonlinearity","authors":"Weizhu Bao, Yue Feng and Ying Ma","doi":"10.4208/eajam.2022-295.300123","DOIUrl":"https://doi.org/10.4208/eajam.2022-295.300123","url":null,"abstract":"","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135104473","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: 1
A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation Darcy方程最优控制问题的混合虚拟单元方法的先验误差分析
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.070322.210722
Xiuhe Wang, Qiming Wang null, Zhaojie Zhou
{"title":"A Priori Error Analysis of Mixed Virtual Element Methods for Optimal Control Problems Governed by Darcy Equation","authors":"Xiuhe Wang, Qiming Wang null, Zhaojie Zhou","doi":"10.4208/eajam.070322.210722","DOIUrl":"https://doi.org/10.4208/eajam.070322.210722","url":null,"abstract":". A mixed virtual element discretization of optimal control problems governed by the Darcy equation with pointwise control constraint is investigated. A discrete scheme uses virtual element approximations of the state equation and a variational discretization of the control variable. A discrete first-order optimality system is obtained by the first-discretize-then-optimize approach. A priori error estimates of the state, ad-joint, and control variables are derived. Numerical experiments confirm the theoretical results.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48097136","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: 2
Cryptographic Systems Based on an Algebraic Structure 基于代数结构的密码系统
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.240522.200822
Ł. Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka null, Martin Waldoch
{"title":"Cryptographic Systems Based on an Algebraic Structure","authors":"Ł. Matysiak, Monika Chrzaniuk, Maximilian Duda, Marta Hanc, Sebastian Kowalski, Zoja Skotnicka null, Martin Waldoch","doi":"10.4208/eajam.240522.200822","DOIUrl":"https://doi.org/10.4208/eajam.240522.200822","url":null,"abstract":". In this paper cryptographic systems based on the Dedekind and Galois structures are considered. We supplement the created cryptosystems based on the Dedekind structure with programs written in C ++ and discuss the inner structure of Galois in cryptography. It is well-known that such a structure is based on finite fields only. Our results reveals something more internal. The final section contains additional information about square-free and radical factorizations in monoids consisting in searching for a minimal list of counterexamples. As an open problem, we leave creating a program that would generate such a list and how to use such a list to create a cryptosystem","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47443785","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: 1
Time Complexity Analysis of Quantum Difference Methods for Multiscale Transport Equations 多尺度输运方程量子差分方法的时间复杂度分析
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2022-315.200423
Xiaoyang He, Shi Jin null, Yue Yu
{"title":"Time Complexity Analysis of Quantum Difference Methods for Multiscale Transport Equations","authors":"Xiaoyang He, Shi Jin null, Yue Yu","doi":"10.4208/eajam.2022-315.200423","DOIUrl":"https://doi.org/10.4208/eajam.2022-315.200423","url":null,"abstract":". We investigate time complexities of finite difference methods for solving the multiscale transport equation by quantum algorithms. It is found that the time complexity of classical and quantum treatments of the standard explicit scheme scale is O ( 1 /ε ) , where ε is a small scaling parameter. On the other hand, the complexity of the even-odd parity based asymptotic-preserving (AP) schemes do not depend on ε . This indicates that in quantum computing, AP schemes (and probably other multiscale ones) are of great importance for solving multiscale transport and kinetic equations.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41722154","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
The Random Feature Method for Time-Dependent Problems 时变问题的随机特征方法
4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.2023-065.050423
Jing-Run Chen, Wei-Nan E and Yi-Xin Luo
{"title":"The Random Feature Method for Time-Dependent Problems","authors":"Jing-Run Chen, Wei-Nan E and Yi-Xin Luo","doi":"10.4208/eajam.2023-065.050423","DOIUrl":"https://doi.org/10.4208/eajam.2023-065.050423","url":null,"abstract":"","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135624204","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
Framework and Numerical Algorithm for a Phase Field Fracture Model 相场断裂模型的框架与数值算法
IF 1.2 4区 数学
East Asian Journal on Applied Mathematics Pub Date : 2023-06-01 DOI: 10.4208/eajam.280921.270722
S. Karthik, A. Nasedkina, A. null, A. Rajagopal
{"title":"Framework and Numerical Algorithm for a Phase Field Fracture Model","authors":"S. Karthik, A. Nasedkina, A. null, A. Rajagopal","doi":"10.4208/eajam.280921.270722","DOIUrl":"https://doi.org/10.4208/eajam.280921.270722","url":null,"abstract":". A phase field fracture model for quasi-brittle material in 2D is implemented in Abaqus software. The phase field damage variables 0 and 1 define undamaged and damaged regions of the material and simplify crack surface tracking. On the other hand, one has to use a fine spatial discretization for the smooth distribution of the phase field variable regularized by a small length scale parameter, which makes the method computationally expensive. At the fully damaged regions both the stiffness and stress reach zero. The displacements and damage are determined by a staggered approach, and a few standard benchmark fracture problems are used to demonstrate the work of the phase field fracture model under consideration.","PeriodicalId":48932,"journal":{"name":"East Asian Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48733926","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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