Annali dell''Universita di Ferrara最新文献

{"title":"Study of the existence and uniqueness of solutions for a class of Kirchhoff-type variational inequalities involving using Young measures","authors":"Mouad Allalou,&nbsp;Abderrahmane Raji,&nbsp;Khalid Hilal","doi":"10.1007/s11565-024-00493-w","DOIUrl":"10.1007/s11565-024-00493-w","url":null,"abstract":"<div><p>This paper is devoted to discussing the existence of solutions for a class of Kirchhoff-type variational inequalities: <span>(-mathcal {M}biggl (displaystyle int _{Omega }mathcal {A}(z,nabla u )mathrm {~d}zbiggl )~displaystyle int _{Omega }mathcal {G}(z,nabla u).(nabla vartheta -nabla u)mathrm {~d}z ge displaystyle int _{Omega }Phi (z,u)(vartheta -u)mathrm {~d}z )</span>, for <span>(upsilon )</span> belonging to the following convex set <span>(mathcal {S}_{psi , theta })</span>. By employing Young measure theory in conjunction with a theorem formulated by Kinderlehrer and Stampacchia, we attain the intended result.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1301 - 1320"},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140260963","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}

{"title":"A minimal and non-alternative realisation of the Cayley plane","authors":"Daniele Corradetti,&nbsp;Alessio Marrani,&nbsp;Francesco Zucconi","doi":"10.1007/s11565-024-00498-5","DOIUrl":"10.1007/s11565-024-00498-5","url":null,"abstract":"<div><p>The compact 16-dimensional Moufang plane, also known as the Cayley plane, has traditionally been defined through the lens of octonionic geometry. In this study, we present a novel approach, demonstrating that the Cayley plane can be defined in an equally clean, straightforward and more economic way using two different division and composition algebras: the paraoctonions and the Okubo algebra. The result is quite surprising since paraoctonions and Okubo algebra possess a weaker algebraic structure than the octonions, since they are non-alternative and do not satisfy the Moufang identities. Intriguingly, the real Okubo algebra has <span>(text {SU}left( 3right) )</span> as automorphism group, which is a classical Lie group, while octonions and paraoctonions have an exceptional Lie group of type <span>(text {G}_{2})</span>. This is remarkable, given that the projective plane defined over the real Okubo algebra is nevertheless isomorphic and isometric to the octonionic projective plane which is at the very heart of the geometric realisations of all types of exceptional Lie groups. Despite its historical ties with octonionic geometry, our research underscores the real Okubo algebra as the weakest algebraic structure allowing the definition of the compact 16-dimensional Moufang plane.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"681 - 730"},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00498-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410210","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}

{"title":"A theorem of existence of solution for the nonlocal formulation of the problem of microwave heating","authors":"Giovanni Cimatti","doi":"10.1007/s11565-024-00491-y","DOIUrl":"10.1007/s11565-024-00491-y","url":null,"abstract":"<div><p>Microwave electromagnetic heating are widely used in many industrial processes. The mathematics involved is based on the Maxwell’s equations coupled with the heat equation. The thermal conductivity is strongly dependent on the temperature, itself an unknown of the system of P.D.E. We propose here a model which simplifies this coupling using a nonlocal term as the source of heating. We prove that the corresponding mathematical initial-boundary value problem has solutions using the Schauder’s fixed point theorem.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 2","pages":"533 - 545"},"PeriodicalIF":0.0,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00491-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140423327","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}

{"title":"On the Futaki invariant of Fano threefolds","authors":"Lars Martin Sektnan,&nbsp;Carl Tipler","doi":"10.1007/s11565-024-00503-x","DOIUrl":"10.1007/s11565-024-00503-x","url":null,"abstract":"<div><p>We study the zero locus of the Futaki invariant on <i>K</i>-polystable Fano threefolds, seen as a map from the Kähler cone to the dual of the Lie algebra of the reduced automorphism group. We show that, apart from families 3.9, 3.13, 3.19, 3.20, 4.2, 4.4, 4.7 and 5.3 of the Iskovskikh–Mori–Mukai classification of Fano threefolds, the Futaki invariant of such manifolds vanishes identically on their Kähler cone. In all cases, when the Picard rank is greater or equal to two, we exhibit explicit 2-dimensional differentiable families of Kähler classes containing the anti-canonical class and on which the Futaki invariant is identically zero. As a corollary, we deduce the existence of non Kähler–Einstein cscK metrics on all such Fano threefolds.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"811 - 837"},"PeriodicalIF":0.0,"publicationDate":"2024-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00503-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413356","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}

{"title":"Power central values with generalized derivations on Lie ideals of prime rings","authors":"Mohammad Aslam Siddeeque,&nbsp;Ali Ahmed Abdullah,&nbsp;Nazim Khan","doi":"10.1007/s11565-024-00497-6","DOIUrl":"10.1007/s11565-024-00497-6","url":null,"abstract":"<div><p>Throughout the work, <span>(Re )</span> is a prime ring which is non-commutative in structure with characteristic different from two, where the center of <span>(Re )</span> is <span>({mathcal {Z}}(Re ))</span>. The rings <span>(Q_r)</span> and <span>({mathcal {C}})</span> are Utumi ring of quotients and extended centroid of <span>(Re )</span> respectively. Consider <span>({mathcal {P}})</span> to be a Lie ideal of <span>(Re )</span> which is non-central. Assume, the generalized derivation defined on <span>(Re )</span> be <span>({mathcal {K}})</span> with associated derivation <span>(mu )</span>. If <span>({mathcal {K}})</span> satisfies certain typical power central functional identities along with an annihilator, then we have established the following: For instance, <span>(0 ne e in Re )</span> with <span>(e({mathcal {K}}(t)t)^m in {mathcal {C}})</span> for every <span>(~t in {mathcal {P}} )</span> and <span>(m&gt;0)</span> a fixed integer. Then one of the following conditions hold: </p><dl><dt><dfn>(i):</dfn></dt><dd>\u0000 <p><span>({mathcal {K}}(t)=qt)</span>, <span>(q=a+b)</span> with <span>(a, b in Q_r)</span>, <span>(b in {mathcal {C}})</span> and <span>(e=beta ea)</span>, where <span>(beta =-b^ {-1})</span>, provided <span>({mathcal {K}})</span> is an inner generalized derivation;</p>\u0000 </dd><dt><dfn>(ii):</dfn></dt><dd>\u0000 <p>there exist <span>(a, b in Q_r)</span> and if <span>(b in {mathcal {C}})</span> then <span>(eq^m in {mathcal {C}}~text {where}~q=a+b)</span>, provided <span>({mathcal {K}})</span> is an inner generalized derivation and <span>(Re )</span> satisfies <span>(s_4)</span>;</p>\u0000 </dd><dt><dfn>(iii):</dfn></dt><dd>\u0000 <p>there exists <span>(a in Q_r)</span> with <span>(ea=0)</span>, provided <span>({mathcal {K}})</span> is not an inner generalized derivation;</p>\u0000 </dd><dt><dfn>(iv):</dfn></dt><dd>\u0000 <p>there exists <span>(a in Q_r)</span> with <span>(ea^m in {mathcal {C}})</span>, provided <span>({mathcal {K}})</span> is not an inner generalized derivation and <span>(Re )</span> satisfies <span>(s_4)</span>.</p>\u0000 </dd></dl></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1285 - 1299"},"PeriodicalIF":0.0,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140440457","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}

{"title":"Completions of the affine 3-space into del Pezzo fibrations","authors":"Adrien Dubouloz,&nbsp;Takashi Kishimoto,&nbsp;Masaru Nagaoka","doi":"10.1007/s11565-024-00499-4","DOIUrl":"10.1007/s11565-024-00499-4","url":null,"abstract":"<div><p>We give constructions of completions of the affine 3-space into total spaces of del Pezzo fibrations of every degree other than 7 over the projective line. We show in particular that every del Pezzo surface other than <span>({mathbb {P}}^{2})</span> blown-up in one or two points can appear as a closed fiber of a del Pezzo fibration <span>(pi :Xrightarrow {mathbb {P}}^{1})</span> whose total space <i>X</i> is a <span>({mathbb {Q}})</span>-factorial threefold with terminal singularities which contains <span>({mathbb {A}}^{3})</span> as the complement of the union of a closed fiber of <span>(pi )</span> and a prime divisor <span>(B_{h})</span> horizontal for <span>(pi )</span>. For such completions, we also give a complete description of integral curves that can appear as general fibers of the induced morphism <span>(bar{pi }:B_{h}rightarrow {mathbb {P}}^{1})</span>.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"731 - 759"},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140513302","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}

{"title":"Geometric endomorphisms of the Hesse moduli space of elliptic curves","authors":"Fabrizio Catanese,&nbsp;Edoardo Sernesi","doi":"10.1007/s11565-024-00502-y","DOIUrl":"10.1007/s11565-024-00502-y","url":null,"abstract":"<div><p>We consider the geometric map <span>( {mathfrak {C}})</span>, called Cayleyan, associating to a plane cubic <i>E</i> the adjoint of its dual curve. We show that <span>( {mathfrak {C}})</span> and the classical Hessian map <span>( {mathfrak {H}})</span> generate a free semigroup. We begin the investigation of the geometry and dynamics of these maps, and of the <b>geometrically special elliptic curves</b>: these are the elliptic curves isomorphic to cubics in the Hesse pencil which are fixed by some endomorphism belonging to the semigroup <span>({{mathcal {W}}}(mathfrak {H}, mathfrak {C}))</span> generated by <span>( mathfrak {H}, mathfrak {C})</span>. We point out then how the dynamic behaviours of <span>( {mathfrak {H}})</span> and <span>( {mathfrak {C}})</span> differ drastically. Firstly, concerning the number of real periodic points: for <span>( {mathfrak {H}})</span> these are infinitely many, for <span>( {mathfrak {C}})</span> they are just 4. Secondly, the Julia set of <span>( {mathfrak {H}})</span> is the whole projective line, unlike what happens for all elements of <span>({{mathcal {W}}}(mathfrak {H}, mathfrak {C}))</span> which are not iterates of <span>( {mathfrak {H}})</span>.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"781 - 810"},"PeriodicalIF":0.0,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412871","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}

{"title":"Gorenstein curve singularities of genus three","authors":"Luca Battistella","doi":"10.1007/s11565-024-00495-8","DOIUrl":"10.1007/s11565-024-00495-8","url":null,"abstract":"<div><p>We classify the analytic germs of isolated Gorenstein curve singularities of genus three, and relate them to the connected components of strata of abelian differentials.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"655 - 680"},"PeriodicalIF":0.0,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00495-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140491362","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}

{"title":"Integral operator frames on Hilbert (C^{*})-modules","authors":"Nadia Assila,&nbsp;Hatim Labrigui,&nbsp;Abdeslam Touri,&nbsp;Mohamed Rossafi","doi":"10.1007/s11565-024-00501-z","DOIUrl":"10.1007/s11565-024-00501-z","url":null,"abstract":"<div><p>Introduced by Duffin and Schaefer as a part of their work on nonhamonic Fourier series in 1952, the theory of frames has undergone a very interesting evolution in recent decades following the multiplicity of work carried out in this field. In this work, we introduce a new concept that of integral operator frame for the set of all adjointable operators on a Hilbert <span>(C^{*})</span>-modules <span>({mathcal {H}})</span> and we give some new properties relating for some construction of integral operator frame, also we establish some new results. Some illustrative examples are provided to advocate the usability of our results.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1271 - 1284"},"PeriodicalIF":0.0,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139961114","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}

{"title":"Some remarks about deformation theory and formality conjecture","authors":"Huachen Chen,&nbsp;Laura Pertusi,&nbsp;Xiaolei Zhao","doi":"10.1007/s11565-024-00500-0","DOIUrl":"10.1007/s11565-024-00500-0","url":null,"abstract":"<div><p>Using the algebraic criterion proved by Bandiera, Manetti and Meazzini, we show the formality conjecture for universally gluable objects with linearly reductive automorphism groups in the bounded derived category of a K3 surface. As an application, we prove the formality conjecture for polystable objects in the Kuznetsov components of Gushel–Mukai threefolds and quartic double solids.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"761 - 779"},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00500-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139850330","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}