Pub Date : 2021-01-01DOI: 10.4310/amsa.2021.v6.n2.a3
Chin-Tien Wu, Pingrui Huang
{"title":"Stopping criteria based on a posteriori error estimations for iterative solvers of convection-diffusion equations","authors":"Chin-Tien Wu, Pingrui Huang","doi":"10.4310/amsa.2021.v6.n2.a3","DOIUrl":"https://doi.org/10.4310/amsa.2021.v6.n2.a3","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4310/amsa.2021.v6.n2.a1
M. Khalid, S. K. Fareeha, S. Mariam
Delay Differential Equations DDEs have great importance in real life phenomena. Among them is a special type of equation known as Pantograph Delay Differential Equation PDDE. Such kind of equations cannot be solved using ordinary methods, and hence, it becomes a challenge when the complexity increases, especially if one wants to study Fractional Pantograph Delay Differential Equation (FPDDE). In this work, FPDDEs with a general Delay term is solved numerically by an iteration method called Perturbation Iteration Algorithm (PIA). It is based on the Taylor series and elim-inates the non-linear terms easily. Iterative results are discussed in detail in both tabular and graphical forms. A graphical interpre-tation of the variability of the Delay term is also provided for a deeper understanding of its range.
{"title":"Computational solution of fractional pantograph equation with varying delay term","authors":"M. Khalid, S. K. Fareeha, S. Mariam","doi":"10.4310/amsa.2021.v6.n2.a1","DOIUrl":"https://doi.org/10.4310/amsa.2021.v6.n2.a1","url":null,"abstract":"Delay Differential Equations DDEs have great importance in real life phenomena. Among them is a special type of equation known as Pantograph Delay Differential Equation PDDE. Such kind of equations cannot be solved using ordinary methods, and hence, it becomes a challenge when the complexity increases, especially if one wants to study Fractional Pantograph Delay Differential Equation (FPDDE). In this work, FPDDEs with a general Delay term is solved numerically by an iteration method called Perturbation Iteration Algorithm (PIA). It is based on the Taylor series and elim-inates the non-linear terms easily. Iterative results are discussed in detail in both tabular and graphical forms. A graphical interpre-tation of the variability of the Delay term is also provided for a deeper understanding of its range.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4310/amsa.2020.v5.n1.a3
Te-Sheng Lin, C-Y. He, Wei-Fan Hu
A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the differential equations for the Fourier coefficients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O ( NM log 2 N ) arith-metic operations.
{"title":"Fast spectral solver for Poisson equation in an annular domain","authors":"Te-Sheng Lin, C-Y. He, Wei-Fan Hu","doi":"10.4310/amsa.2020.v5.n1.a3","DOIUrl":"https://doi.org/10.4310/amsa.2020.v5.n1.a3","url":null,"abstract":"A simple and efficient spectral method is formulated to solve Poisson equation in an annular domain. The solver relies on the Fourier expansion, where the differential equations for the Fourier coefficients are solved using an ultraspherical spectral method. For a domain with N grid points in the polar direction and M grid points in the radial direction, the solver only requires O ( NM log 2 N ) arith-metic operations.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392425","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4310/amsa.2020.v5.n2.a1
K. Kanagarajan, E. Elsayed, S. Harikrishnan
{"title":"A study on random differential equations of arbitrary order","authors":"K. Kanagarajan, E. Elsayed, S. Harikrishnan","doi":"10.4310/amsa.2020.v5.n2.a1","DOIUrl":"https://doi.org/10.4310/amsa.2020.v5.n2.a1","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392444","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-01DOI: 10.4310/amsa.2020.v5.n2.a5
T. Lai, Shih-Wei Liao, S. P. Wong, Huanzhong Xu
In the decade since the global financial crisis and the Great Recession that followed, the financial technology – or FinTech – revolution has transformed financial markets and services through the automation of trading and risk management, among other things. The “ABCD” of cutting-edge FinTech are AI (Artificial intelligence), Blockchains, Cloud computing and big Data. We first review these technologies of modern FinTech and some of the underlying mathematical foundations. We then describe new statistical models and stochastic optimization methods in FinTech and investment science.
{"title":"Statistical models and stochastic optimization in financial technology and investment science","authors":"T. Lai, Shih-Wei Liao, S. P. Wong, Huanzhong Xu","doi":"10.4310/amsa.2020.v5.n2.a5","DOIUrl":"https://doi.org/10.4310/amsa.2020.v5.n2.a5","url":null,"abstract":"In the decade since the global financial crisis and the Great Recession that followed, the financial technology – or FinTech – revolution has transformed financial markets and services through the automation of trading and risk management, among other things. The “ABCD” of cutting-edge FinTech are AI (Artificial intelligence), Blockchains, Cloud computing and big Data. We first review these technologies of modern FinTech and some of the underlying mathematical foundations. We then describe new statistical models and stochastic optimization methods in FinTech and investment science.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-05-18DOI: 10.4310/amsa.2019.v4.n2.a5
W. Miller, Shahabeddin M. Aslmarand, P. Alsing, V. Rana
We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information distance formula of Rokhlin and Rajski. We then define an analogous information area. We motivate this definition and discuss its properties. We extend this definition to higher-dimensional volumes. We briefly discuss the potential utility for these geometric measures in quantum information processing.
{"title":"Geometric measures of information for quantum state characterization","authors":"W. Miller, Shahabeddin M. Aslmarand, P. Alsing, V. Rana","doi":"10.4310/amsa.2019.v4.n2.a5","DOIUrl":"https://doi.org/10.4310/amsa.2019.v4.n2.a5","url":null,"abstract":"We analyze the geometry of a joint distribution over a set of discrete random variables. We briefly review Shannon's entropy, conditional entropy, mutual information and conditional mutual information. We review the entropic information distance formula of Rokhlin and Rajski. We then define an analogous information area. We motivate this definition and discuss its properties. We extend this definition to higher-dimensional volumes. We briefly discuss the potential utility for these geometric measures in quantum information processing.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49105964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/amsa.2019.v4.n2.a4
Chueh-Hsin Chang, Ching-Hao Yu, T. Sheu
Camassa-Holm (CH) equation for modeling shallow water wave will be analyzed through direct scattering analysis. Thanks to this analysis in spectral domain, some physically meaningful wave propagation features that can by no means be obtained from the analysis in the space-time domain are exhibited. To broaden our understanding of the CH equation, in this article the study underlying the scattering analysis is performed in spectral domain and the solution of CH equation is computed by the finite difference method in time domain. We aim to get some missing details in the space-time analysis. The detailed wave transmission and reflection in the CH equation, subject to the chosen initial condition, shall be theoretically enlightened.
{"title":"Space-time analysis and beyond: toward a better understanding of Camassa–Holm equation","authors":"Chueh-Hsin Chang, Ching-Hao Yu, T. Sheu","doi":"10.4310/amsa.2019.v4.n2.a4","DOIUrl":"https://doi.org/10.4310/amsa.2019.v4.n2.a4","url":null,"abstract":"Camassa-Holm (CH) equation for modeling shallow water wave will be analyzed through direct scattering analysis. Thanks to this analysis in spectral domain, some physically meaningful wave propagation features that can by no means be obtained from the analysis in the space-time domain are exhibited. To broaden our understanding of the CH equation, in this article the study underlying the scattering analysis is performed in spectral domain and the solution of CH equation is computed by the finite difference method in time domain. We aim to get some missing details in the space-time analysis. The detailed wave transmission and reflection in the CH equation, subject to the chosen initial condition, shall be theoretically enlightened.","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/AMSA.2019.V4.N1.A2
Yueh-Cheng Kuo, Shih-Feng Shieh, Y. You
{"title":"The classification of symplectic matrices and pairs","authors":"Yueh-Cheng Kuo, Shih-Feng Shieh, Y. You","doi":"10.4310/AMSA.2019.V4.N1.A2","DOIUrl":"https://doi.org/10.4310/AMSA.2019.V4.N1.A2","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-01-01DOI: 10.4310/AMSA.2019.V4.N1.A3
Tsung-Ming Huang, Wen-Wei Lin, Weichung Wang
{"title":"Matrix representations of discrete differential operators and operations in electromagnetism","authors":"Tsung-Ming Huang, Wen-Wei Lin, Weichung Wang","doi":"10.4310/AMSA.2019.V4.N1.A3","DOIUrl":"https://doi.org/10.4310/AMSA.2019.V4.N1.A3","url":null,"abstract":"","PeriodicalId":42896,"journal":{"name":"Annals of Mathematical Sciences and Applications","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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