Pub Date : 2022-02-28DOI: 10.1007/s10013-022-00552-9
Farid Chabane, S. Abbas, Maamar Benbachir, M. Benchohra, G. N’Guérékata
{"title":"Existence of Concave Positive Solutions for Nonlinear Fractional Differential Equation with p-Laplacian Operator","authors":"Farid Chabane, S. Abbas, Maamar Benbachir, M. Benchohra, G. N’Guérékata","doi":"10.1007/s10013-022-00552-9","DOIUrl":"https://doi.org/10.1007/s10013-022-00552-9","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"51 1","pages":"505-543"},"PeriodicalIF":0.8,"publicationDate":"2022-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46999873","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 : 2022-02-23DOI: 10.1007/s10013-022-00604-0
Camilla Felisetti, C. Fontanari
{"title":"On Generalized Nefness and Bigness in Adjunction Theory","authors":"Camilla Felisetti, C. Fontanari","doi":"10.1007/s10013-022-00604-0","DOIUrl":"https://doi.org/10.1007/s10013-022-00604-0","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"1 1","pages":"1-9"},"PeriodicalIF":0.8,"publicationDate":"2022-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48811392","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 : 2022-02-22DOI: 10.1007/s10013-021-00543-2
J. Hauenstein, L. Matusevich, C. Peterson, Samantha N. Sherman
{"title":"Binomiality Testing and Computing Sparse Polynomials via Witness Sets","authors":"J. Hauenstein, L. Matusevich, C. Peterson, Samantha N. Sherman","doi":"10.1007/s10013-021-00543-2","DOIUrl":"https://doi.org/10.1007/s10013-021-00543-2","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"50 1","pages":"653 - 678"},"PeriodicalIF":0.8,"publicationDate":"2022-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42601494","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 : 2022-01-26DOI: 10.1007/s10013-021-00544-1
P. K. Anh, T. N. Hai
{"title":"On Regularized Forward-Backward Dynamical Systems Associated with Structured Monotone Inclusions","authors":"P. K. Anh, T. N. Hai","doi":"10.1007/s10013-021-00544-1","DOIUrl":"https://doi.org/10.1007/s10013-021-00544-1","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"51 1","pages":"545-562"},"PeriodicalIF":0.8,"publicationDate":"2022-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43876034","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 : 2022-01-10DOI: 10.1007/s10013-022-00590-3
M. Hess, G. Rozza
{"title":"Model Reduction Using Sparse Polynomial Interpolation for the Incompressible Navier–Stokes Equations","authors":"M. Hess, G. Rozza","doi":"10.1007/s10013-022-00590-3","DOIUrl":"https://doi.org/10.1007/s10013-022-00590-3","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"51 1","pages":"199-211"},"PeriodicalIF":0.8,"publicationDate":"2022-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46998115","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 : 2022-01-06DOI: 10.1007/s10013-021-00542-3
Najia Merrachi, R. Tribak
{"title":"A Class of Retractable and Coretractable Modules","authors":"Najia Merrachi, R. Tribak","doi":"10.1007/s10013-021-00542-3","DOIUrl":"https://doi.org/10.1007/s10013-021-00542-3","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"51 1","pages":"489-504"},"PeriodicalIF":0.8,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42944082","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 : 2022-01-05DOI: 10.1007/s10013-022-00596-x
P. Kunkel, V. Mehrmann
{"title":"Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries","authors":"P. Kunkel, V. Mehrmann","doi":"10.1007/s10013-022-00596-x","DOIUrl":"https://doi.org/10.1007/s10013-022-00596-x","url":null,"abstract":"","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"51 1","pages":"177-198"},"PeriodicalIF":0.8,"publicationDate":"2022-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44798783","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 : 2022-01-01Epub Date: 2021-06-12DOI: 10.1007/s10013-021-00509-4
Karl Kunisch, Philip Trautmann
In this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg-Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033-2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.
{"title":"An Inverse Problem Involving a Viscous Eikonal Equation with Applications in Electrophysiology.","authors":"Karl Kunisch, Philip Trautmann","doi":"10.1007/s10013-021-00509-4","DOIUrl":"https://doi.org/10.1007/s10013-021-00509-4","url":null,"abstract":"<p><p>In this work we discuss the reconstruction of cardiac activation instants based on a viscous Eikonal equation from boundary observations. The problem is formulated as a least squares problem and solved by a projected version of the Levenberg-Marquardt method. Moreover, we analyze the well-posedness of the state equation and derive the gradient of the least squares functional with respect to the activation instants. In the numerical examples we also conduct an experiment in which the location of the activation sites and the activation instants are reconstructed jointly based on an adapted version of the shape gradient method from (J. Math. Biol. 79, 2033-2068, 2019). We are able to reconstruct the activation instants as well as the locations of the activations with high accuracy relative to the noise level.</p>","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"50 1","pages":"301-317"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s10013-021-00509-4","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39583097","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-01-01Epub Date: 2022-05-10DOI: 10.1007/s10013-022-00560-9
Simone Deparis, Paola Gervasio
The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes method is conservative across the interface. If hp-fem discretizations are employed, we prove that both the total force and total work generated by the numerical solution at the interface of the decomposition vanish in an optimal way when the mesh size tends to zero, i.e., like , where p is the local polynomial degree and h the mesh-size. This is the same as the error decay in the H1-broken norm. We observe that the conservation properties of a method are intrinsic to the method itself because they depend on the way the interface conditions are enforced rather then on the problem we are called to approximate. For this reason, in this paper, we focus on second-order elliptic PDEs, although we use the terminology (of forces and works) proper of linear elasticity. Two and three dimensional numerical experiments corroborate the theoretical findings, also by comparing Internodes with Mortar and WACA methods.
{"title":"Conservation of Forces and Total Work at the Interface Using the Internodes Method.","authors":"Simone Deparis, Paola Gervasio","doi":"10.1007/s10013-022-00560-9","DOIUrl":"https://doi.org/10.1007/s10013-022-00560-9","url":null,"abstract":"<p><p>The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes method is conservative across the interface. If <i>hp</i>-fem discretizations are employed, we prove that both the total force and total work generated by the numerical solution at the interface of the decomposition vanish in an optimal way when the mesh size tends to zero, i.e., like <math><mi>O</mi> <mo>(</mo> <msup><mrow><mi>h</mi></mrow> <mrow><mi>p</mi></mrow> </msup> <mo>)</mo></math> , where <i>p</i> is the local polynomial degree and <i>h</i> the mesh-size. This is the same as the error decay in the <i>H</i> <sup>1</sup>-broken norm. We observe that the conservation properties of a method are intrinsic to the method itself because they depend on the way the interface conditions are enforced rather then on the problem we are called to approximate. For this reason, in this paper, we focus on second-order elliptic PDEs, although we use the terminology (of forces and works) proper of linear elasticity. Two and three dimensional numerical experiments corroborate the theoretical findings, also by comparing Internodes with Mortar and WACA methods.</p>","PeriodicalId":45919,"journal":{"name":"Vietnam Journal of Mathematics","volume":"50 4","pages":"901-928"},"PeriodicalIF":0.8,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9550708/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"33516109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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