Pub Date : 2022-08-19DOI: 10.1142/s021953052240005x
H. Feichtinger
{"title":"Translation and modulation invariant banach spaces of tempered distributions satisfy the metric approximation property","authors":"H. Feichtinger","doi":"10.1142/s021953052240005x","DOIUrl":"https://doi.org/10.1142/s021953052240005x","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44574322","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-12DOI: 10.1142/s0219530522400024
Paolo Piersanti, Kristen L. White, B. Dragnea, R. Temam
. In this paper we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable space. Secondly, we show the existence and uniqueness of the solution for the proposed model. Thirdly, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics. Finally, we establish the existence of solutions for the corresponding time-dependent obstacle problem.
{"title":"A three-dimensional discrete model for approximating the deformation of a viral capsid subjected to lying over a flat surface in the static and time-dependent case","authors":"Paolo Piersanti, Kristen L. White, B. Dragnea, R. Temam","doi":"10.1142/s0219530522400024","DOIUrl":"https://doi.org/10.1142/s0219530522400024","url":null,"abstract":". In this paper we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of one vertex only. First, we set up the model in the form of a set of variational inequalities posed over a non-empty, closed and convex subset of a suitable space. Secondly, we show the existence and uniqueness of the solution for the proposed model. Thirdly, we numerically test this model and we observe that the outputs of the numerical experiments comply with physics. Finally, we establish the existence of solutions for the corresponding time-dependent obstacle problem.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47956383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-08-12DOI: 10.1142/s0219530522500130
Mingyang Gu, Song Li, Junhong Lin
{"title":"Compressed Data Separation via Unconstrained l1-Split Analysis","authors":"Mingyang Gu, Song Li, Junhong Lin","doi":"10.1142/s0219530522500130","DOIUrl":"https://doi.org/10.1142/s0219530522500130","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44038476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-26DOI: 10.1142/s0219530523500045
Jos'e M. Maz'on, J. Toledo
In this paper we study a nonlocal Cahn-Hilliard model (CHE) in the framework of random walk spaces, which includes as particular cases, the CHE on locally finite weighted connected graphs, the CHE determined by finite Markov chains or the Cahn-Hilliard Equations driven by convolution integrable kernels. We consider different transitions for the phase and the chemical potential, and a large class of potentials including obstacle ones. We prove existence and uniqueness of solutions in $L^1$ of the Cahn-Hilliard Equation. We also show that the Cahn-Hilliard equation is the gradient flow of the Ginzburg-Landau free energy functional on an appropriate Hilbert space. We finally study the asymptotic behaviour of the solutions.
{"title":"Cahn-Hilliard Equations on Random Walk Spaces","authors":"Jos'e M. Maz'on, J. Toledo","doi":"10.1142/s0219530523500045","DOIUrl":"https://doi.org/10.1142/s0219530523500045","url":null,"abstract":"In this paper we study a nonlocal Cahn-Hilliard model (CHE) in the framework of random walk spaces, which includes as particular cases, the CHE on locally finite weighted connected graphs, the CHE determined by finite Markov chains or the Cahn-Hilliard Equations driven by convolution integrable kernels. We consider different transitions for the phase and the chemical potential, and a large class of potentials including obstacle ones. We prove existence and uniqueness of solutions in $L^1$ of the Cahn-Hilliard Equation. We also show that the Cahn-Hilliard equation is the gradient flow of the Ginzburg-Landau free energy functional on an appropriate Hilbert space. We finally study the asymptotic behaviour of the solutions.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48778058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.1142/s0219530522500117
Brahim Alouini, H. Hajaiej
{"title":"Dynamics of dipolar quantum droplets in an extended Gross-Pitaevskii equation in the presence of time-dependent harmonic trapping potential and a damping term","authors":"Brahim Alouini, H. Hajaiej","doi":"10.1142/s0219530522500117","DOIUrl":"https://doi.org/10.1142/s0219530522500117","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43266915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.1142/s0219530522500099
Aksel Bergfeldt, W. Staubach
{"title":"On the regularity of multilinear Schrödinger integral operators","authors":"Aksel Bergfeldt, W. Staubach","doi":"10.1142/s0219530522500099","DOIUrl":"https://doi.org/10.1142/s0219530522500099","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"63880996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-22DOI: 10.1142/s0219530522500105
Yuesheng Xu
{"title":"Sparse Regularization with the ℓ0 Norm","authors":"Yuesheng Xu","doi":"10.1142/s0219530522500105","DOIUrl":"https://doi.org/10.1142/s0219530522500105","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47565031","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-31DOI: 10.1142/s0219530522400073
P. Degond, A. Diez, Adam R. Walczak
Swarmalators are systems of agents which are both self-propelled particles and oscillators. Each particle is endowed with a phase which modulates its interaction force with the other particles. In return, relative positions modulate phase synchronization between interacting particles. In the present model, there is no force reciprocity: when a particle attracts another one, the latter repels the former. This results in a pursuit behavior. In this paper, we derive a hydrodynamic model of this swarmalator system and show that it has explicit doubly-periodic travelling-wave solutions in two space dimensions. These special solutions enjoy non-trivial topology quantified by the index of the phase vector along a period in either dimension. Stability of these solutions is studied by investigating the conditions for hyperbolicity of the model. Numerical solutions of both the particle and hydrodynamic models are shown. They confirm the consistency of the hydrodynamic model with the particle one for small times or large phase-noise but also reveal the emergence of intriguing patterns in the case of small phase-noise. 1 ar X iv :2 20 5. 15 73 9v 1 [ m at hph ] 3 1 M ay 2 02 2
Swarmalator是一种既有自推进粒子又有振荡器的药剂系统。每个粒子都具有一个相位，该相位调节其与其他粒子的相互作用力。作为回报，相对位置调节相互作用粒子之间的相位同步。在目前的模型中，不存在力的互易性：当一个粒子吸引另一个粒子时，后者会排斥前者。这导致了一种追求行为。在本文中，我们导出了该群翼系统的流体动力学模型，并证明了它在两个空间维度上具有显式的双周期行波解。这些特殊的解决方案具有非平凡的拓扑结构，该拓扑结构通过沿任一维度的周期的相位矢量的索引来量化。通过研究模型的双曲性条件，研究了这些解的稳定性。给出了粒子模型和流体动力学模型的数值解。它们证实了小时间或大相位噪声的流体动力学模型与粒子模型的一致性，但也揭示了在小相位噪声的情况下出现的有趣模式。1 ar X iv：2 20 5。15 73 9v 1[m at hph]3 2年5月1日
{"title":"Topological states and continuum model for swarmalators without force reciprocity","authors":"P. Degond, A. Diez, Adam R. Walczak","doi":"10.1142/s0219530522400073","DOIUrl":"https://doi.org/10.1142/s0219530522400073","url":null,"abstract":"Swarmalators are systems of agents which are both self-propelled particles and oscillators. Each particle is endowed with a phase which modulates its interaction force with the other particles. In return, relative positions modulate phase synchronization between interacting particles. In the present model, there is no force reciprocity: when a particle attracts another one, the latter repels the former. This results in a pursuit behavior. In this paper, we derive a hydrodynamic model of this swarmalator system and show that it has explicit doubly-periodic travelling-wave solutions in two space dimensions. These special solutions enjoy non-trivial topology quantified by the index of the phase vector along a period in either dimension. Stability of these solutions is studied by investigating the conditions for hyperbolicity of the model. Numerical solutions of both the particle and hydrodynamic models are shown. They confirm the consistency of the hydrodynamic model with the particle one for small times or large phase-noise but also reveal the emergence of intriguing patterns in the case of small phase-noise. 1 ar X iv :2 20 5. 15 73 9v 1 [ m at hph ] 3 1 M ay 2 02 2","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44336573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-05-31DOI: 10.1142/s0219530522500087
H. Volkmer
{"title":"Asymptotic Expansion of the Generalized Hypergeometric Function pFq(z) as z→∞ for p< q","authors":"H. Volkmer","doi":"10.1142/s0219530522500087","DOIUrl":"https://doi.org/10.1142/s0219530522500087","url":null,"abstract":"","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47905836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-26DOI: 10.1142/s0219530522500166
Yirui Zhao, Dachun Yang, Yangyang Zhang
In this paper, the authors introduce a class of mixed-norm Herz spaces, [Formula: see text], which is a natural generalization of mixed-norm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz–Thorin interpolation theorem on [Formula: see text]. Applying these Riesz–Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy–Littlewood maximal operator and the Fefferman–Stein vector-valued maximal inequality on [Formula: see text]. As applications, the authors develop various real-variable theory of Hardy spaces associated with [Formula: see text] by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of [Formula: see text] and the non-trivial constructions of auxiliary functions in the Riesz–Thorin interpolation theorem.
{"title":"Mixed-norm Herz spaces and their applications in related Hardy spaces","authors":"Yirui Zhao, Dachun Yang, Yangyang Zhang","doi":"10.1142/s0219530522500166","DOIUrl":"https://doi.org/10.1142/s0219530522500166","url":null,"abstract":"In this paper, the authors introduce a class of mixed-norm Herz spaces, [Formula: see text], which is a natural generalization of mixed-norm Lebesgue spaces and some special cases of which naturally appear in the study of the summability of Fourier transforms on mixed-norm Lebesgue spaces. The authors also give their dual spaces and obtain the Riesz–Thorin interpolation theorem on [Formula: see text]. Applying these Riesz–Thorin interpolation theorem and using some ideas from the extrapolation theorem, the authors establish both the boundedness of the Hardy–Littlewood maximal operator and the Fefferman–Stein vector-valued maximal inequality on [Formula: see text]. As applications, the authors develop various real-variable theory of Hardy spaces associated with [Formula: see text] by using the existing results of Hardy spaces associated with ball quasi-Banach function spaces. These results strongly depend on the duality of [Formula: see text] and the non-trivial constructions of auxiliary functions in the Riesz–Thorin interpolation theorem.","PeriodicalId":55519,"journal":{"name":"Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":2.2,"publicationDate":"2022-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45294678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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