Pub Date : 2023-10-30DOI: 10.1007/s40574-023-00396-2
Edoardo Ballico, Changho Keem
{"title":"On the Hilbert scheme of smooth curves of degree 15 and genus 14 in $$mathbb {P}^5$$","authors":"Edoardo Ballico, Changho Keem","doi":"10.1007/s40574-023-00396-2","DOIUrl":"https://doi.org/10.1007/s40574-023-00396-2","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"3 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136103321","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 : 2023-10-10DOI: 10.1007/s40574-023-00389-1
A. Scagliotti, P. Colli Franzone
Abstract Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require decreasing step-sizes to converge. In this paper we propose a subgradient method with constant step-size for composite convex objectives with $$ell _1$$ ℓ1 -regularization. If the smooth term is strongly convex, we can establish a linear convergence result for the function values. This fact relies on an accurate choice of the element of the subdifferential used for the update, and on proper actions adopted when non-differentiability regions are crossed. Then, we propose an accelerated version of the algorithm, based on conservative inertial dynamics and on an adaptive restart strategy, that is guaranteed to achieve a linear convergence rate in the strongly convex case. Finally, we test the performances of our algorithms on some strongly and non-strongly convex examples.
{"title":"A subgradient method with constant step-size for $$ell _1$$-composite optimization","authors":"A. Scagliotti, P. Colli Franzone","doi":"10.1007/s40574-023-00389-1","DOIUrl":"https://doi.org/10.1007/s40574-023-00389-1","url":null,"abstract":"Abstract Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require decreasing step-sizes to converge. In this paper we propose a subgradient method with constant step-size for composite convex objectives with $$ell _1$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>ℓ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:math> -regularization. If the smooth term is strongly convex, we can establish a linear convergence result for the function values. This fact relies on an accurate choice of the element of the subdifferential used for the update, and on proper actions adopted when non-differentiability regions are crossed. Then, we propose an accelerated version of the algorithm, based on conservative inertial dynamics and on an adaptive restart strategy, that is guaranteed to achieve a linear convergence rate in the strongly convex case. Finally, we test the performances of our algorithms on some strongly and non-strongly convex examples.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136294830","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 : 2023-10-10DOI: 10.1007/s40574-023-00388-2
Bahram Khani-Robati, Samira Mehrangiz
{"title":"On the convergence of sequences of weighted composition operators on certain weighted Hardy spaces","authors":"Bahram Khani-Robati, Samira Mehrangiz","doi":"10.1007/s40574-023-00388-2","DOIUrl":"https://doi.org/10.1007/s40574-023-00388-2","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136295767","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 : 2023-10-05DOI: 10.1007/s40574-023-00391-7
H. A. Abass, M. Aphane
Abstract In this article, we propose a new iterative algorithm for solving split common fixed point problems for finite families of single-valued demicontractive mappings in the setting of real Hilbert spaces. In order to solve this problem, we introduce a Halpern method with with an Armijo-line search for approximating the solution of the aforementioned problems. We establish a strong convergence result of the proposed method and display some numerical examples to illustrate the performance of our main result. Our result complements and generalizes some related results in literature.
{"title":"An algorithmic approach to solving split common fixed point problems for families of demicontractive operators in Hilbert spaces","authors":"H. A. Abass, M. Aphane","doi":"10.1007/s40574-023-00391-7","DOIUrl":"https://doi.org/10.1007/s40574-023-00391-7","url":null,"abstract":"Abstract In this article, we propose a new iterative algorithm for solving split common fixed point problems for finite families of single-valued demicontractive mappings in the setting of real Hilbert spaces. In order to solve this problem, we introduce a Halpern method with with an Armijo-line search for approximating the solution of the aforementioned problems. We establish a strong convergence result of the proposed method and display some numerical examples to illustrate the performance of our main result. Our result complements and generalizes some related results in literature.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134974892","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 : 2023-10-04DOI: 10.1007/s40574-023-00392-6
Giulia Bevilacqua, Chiara Lonati
Abstract We introduce a modified Kirchhoff–Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler–Lagrange equations for a planar version of the Kirchhoff–Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium.
{"title":"Effects of surface tension and elasticity on critical points of the Kirchhoff–Plateau problem","authors":"Giulia Bevilacqua, Chiara Lonati","doi":"10.1007/s40574-023-00392-6","DOIUrl":"https://doi.org/10.1007/s40574-023-00392-6","url":null,"abstract":"Abstract We introduce a modified Kirchhoff–Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of minimizers. Indeed, choosing three different geometrical shapes for the cross-section, we derive Euler–Lagrange equations for a planar version of the Kirchhoff–Plateau problem. We show that in the physical range of the parameters, there exists a unique critical point satisfying the imposed constraints. Finally, we analyze the effects of the surface tension on the shape of the cross-sections at the equilibrium.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135592152","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 : 2023-10-03DOI: 10.1007/s40574-023-00393-5
Fausto Ferrari, Nicolò Forcillo
In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework of Carnot groups.
{"title":"Alt–Caffarelli–Friedman monotonicity formula and mean value properties in Carnot groups with applications","authors":"Fausto Ferrari, Nicolò Forcillo","doi":"10.1007/s40574-023-00393-5","DOIUrl":"https://doi.org/10.1007/s40574-023-00393-5","url":null,"abstract":"In this paper we provide a different approach to the Alt-Caffarelli-Friedman monotonicity formula, reducing the problem to test the monotone increasing behavior of the mean value of a function involving the norm of the gradient. In particular, we show that our argument holds in the general framework of Carnot groups.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135738735","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 : 2023-09-24DOI: 10.1007/s40574-023-00386-4
Javid Ahmad Ganie, Altaf Ahmad Bhat, Shahid Ahmed Wani
{"title":"Natural transform of two variables in q-calculus with applications","authors":"Javid Ahmad Ganie, Altaf Ahmad Bhat, Shahid Ahmed Wani","doi":"10.1007/s40574-023-00386-4","DOIUrl":"https://doi.org/10.1007/s40574-023-00386-4","url":null,"abstract":"","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135926140","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 : 2023-09-18DOI: 10.1007/s40574-023-00387-3
E. Macca, G. Russo
Abstract In this work we compute the numerical solution of the Exner model of sedimentation when a train of waves is imposed at the inflow boundary (E. Macca in Shock-Capturing methods: Well-Balanced Approximate Taylor and Semi-Implicit schemes. PhD thesis, Universit‘a degli Studi di Palermo, Palermo, (2022) and Major Revision, (2023)). The numerical solver is a second order finite-volume scheme, with semi-implicit time discretization based on Implicit-Explicit (IMEX) schemes, which guarantees better stability properties than explicit ones, still at a lower cost than fully implicit schemes. We show the effect of spurious reflected waves generated at the outflow edge of the computational domain, propose two remedies, and show how such spurious effects can be reduced by suitable non-reflecting boundary conditions.
{"title":"Boundary effects on wave trains in the Exner model of sedimental transport","authors":"E. Macca, G. Russo","doi":"10.1007/s40574-023-00387-3","DOIUrl":"https://doi.org/10.1007/s40574-023-00387-3","url":null,"abstract":"Abstract In this work we compute the numerical solution of the Exner model of sedimentation when a train of waves is imposed at the inflow boundary (E. Macca in Shock-Capturing methods: Well-Balanced Approximate Taylor and Semi-Implicit schemes. PhD thesis, Universit‘a degli Studi di Palermo, Palermo, (2022) and Major Revision, (2023)). The numerical solver is a second order finite-volume scheme, with semi-implicit time discretization based on Implicit-Explicit (IMEX) schemes, which guarantees better stability properties than explicit ones, still at a lower cost than fully implicit schemes. We show the effect of spurious reflected waves generated at the outflow edge of the computational domain, propose two remedies, and show how such spurious effects can be reduced by suitable non-reflecting boundary conditions.","PeriodicalId":214688,"journal":{"name":"Bollettino dell'Unione Matematica Italiana","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135202363","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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