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Time-frequency analysis for the multidimensional Gabor Transform 多维 Gabor 变换的时频分析
Annali dell''Universita di Ferrara Pub Date : 2024-11-05 DOI: 10.1007/s11565-024-00558-w
Ahmed Chana, Abdellatif Akhlidj
{"title":"Time-frequency analysis for the multidimensional Gabor Transform","authors":"Ahmed Chana,&nbsp;Abdellatif Akhlidj","doi":"10.1007/s11565-024-00558-w","DOIUrl":"10.1007/s11565-024-00558-w","url":null,"abstract":"<div><p>The main crux of this paper is to introduce a new integral transform called the multidimensional Hankel–Gabor transform and to give some new results related to this transform as Plancherel’s, Parseval’s, inversion and Calderón’s reproducing formulas. Next, we analyse the concentration of this transform on sets of finite measure and we give uncertainty principle for orthonormal sequences and Donoho–Stark’s type uncertainty principle. Last, we introduce a new class of pseudo-differential operator <span>({mathscr {L}}_{u,v}(sigma ))</span> called localization operator which depend on a symbol <span>(sigma )</span> and two functions <i>u</i> and <i>v</i>, we give a criteria in terms of the symbol <span>(sigma )</span> for its boundedness and compactness, we also show that this operator belongs to the Schatten-Von Neumann classes <span>(S^p)</span> for all <span>(p in [1; +infty ])</span> and we give a trace formula.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"71 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142579493","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}
引用次数: 0
Boolean operators and neural networks 布尔运算符和神经网络
Annali dell''Universita di Ferrara Pub Date : 2024-08-22 DOI: 10.1007/s11565-024-00541-5
Sara Marziali
{"title":"Boolean operators and neural networks","authors":"Sara Marziali","doi":"10.1007/s11565-024-00541-5","DOIUrl":"10.1007/s11565-024-00541-5","url":null,"abstract":"<div><p>We compute the homogeneous ideals of varieties, in a projective space of tensors, associated to different choices of the Boolean operators that describe the decision process in small neural networks. We prove that, starting with networks with three nodes, the varieties associated to different Boolean operators are all distinct.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1767 - 1783"},"PeriodicalIF":0.0,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00541-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412967","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}
引用次数: 0
Stability problems with generalized Navier–Stokes–Voigt theories 广义纳维-斯托克斯-沃伊特理论的稳定性问题
Annali dell''Universita di Ferrara Pub Date : 2024-07-30 DOI: 10.1007/s11565-024-00540-6
Brian Straughan
{"title":"Stability problems with generalized Navier–Stokes–Voigt theories","authors":"Brian Straughan","doi":"10.1007/s11565-024-00540-6","DOIUrl":"10.1007/s11565-024-00540-6","url":null,"abstract":"<div><p>We investigate some hydrodynamic stability problems in the context of the Navier–Stokes–Voigt equations. It is pointed out that one should regard the usual set of equations known as the Navier–Stokes–Voigt equations as being the Navier–Stokes equations to which a regularizing term has been added. We investigate other models which have features very similar to the Navier–Stokes–Voigt equations, but which arise from proper continuum thermodynamic approaches, including employing an objective time derivative rather than simply the Laplacian of the partial time derivative of the velocity field. It is shown that in some cases, particularly those connected to straightforward thermal convection studies, the linear theory of the more physically based models reduces to that of the classical Navier–Stokes–Voigt theory. However, these are special problems and we also display other problems where the generalized theories based on continuum mechanics principles lead to very different results from what one finds with traditional Navier–Stokes–Voigt theory. Finally, two further models pertaining to Navier–Stokes–Voigt theory which were introduced by Oskolkov are investigated.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1747 - 1766"},"PeriodicalIF":0.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415156","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}
引用次数: 0
A note on Cline’s formula for some generalized inverses in a ring 克莱因关于环中某些广义倒数公式的说明
Annali dell''Universita di Ferrara Pub Date : 2024-07-13 DOI: 10.1007/s11565-024-00539-z
Soufiane Hadji
{"title":"A note on Cline’s formula for some generalized inverses in a ring","authors":"Soufiane Hadji","doi":"10.1007/s11565-024-00539-z","DOIUrl":"10.1007/s11565-024-00539-z","url":null,"abstract":"<div><p>In this note, we generalize Cline’s formula for some new generalized inverses such as strong Drazin inverse, generalized strong Drazin inverse, Hirano inverse and generalized Hirano inverse. As a particular case, some recent results on this subject are recovered.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1731 - 1745"},"PeriodicalIF":0.0,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141651062","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}
引用次数: 0
Global and blow-up results for a quasilinear parabolic equation with variable sources and memory terms 具有可变源和记忆项的准线性抛物方程的全局和炸毁结果
Annali dell''Universita di Ferrara Pub Date : 2024-07-08 DOI: 10.1007/s11565-024-00538-0
Touil Nadji, Abita Rahmoune
{"title":"Global and blow-up results for a quasilinear parabolic equation with variable sources and memory terms","authors":"Touil Nadji,&nbsp;Abita Rahmoune","doi":"10.1007/s11565-024-00538-0","DOIUrl":"10.1007/s11565-024-00538-0","url":null,"abstract":"<div><p>The paper presents a general model of quasi-linear parabolic equations with variable exponents for the source and dissipative term types </p><div><div><span>$$begin{aligned} textrm{L}left( tright) left| u_{t}right| ^{mleft( xright) -2}u_{t}-Delta u+int _{0}^{t}g(t-s)Delta u(x,s)textrm{d}s=left| uright| ^{pleft( xright) -2}u. end{aligned}$$</span></div></div><p>When <span>(p(x)ge m(x)ge 2)</span>, the matrix <span>(textrm{L}(t))</span> is both positive definite and bounded, while the function <i>g</i> is continuously differentiable and decays over time. The paper shows that the blow-up result occurs at two different finite times and provides an upper bound for the blow-up time. Finally, it establishes that the energy function decays globally for solutions, with both positive and negative initial energy.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1697 - 1729"},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141668596","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}
引用次数: 0
Characterization of ((alpha ,beta )) biderivations in triangular algebras 三角代数中$$(alpha,beta)$$双分维的特征
Annali dell''Universita di Ferrara Pub Date : 2024-07-02 DOI: 10.1007/s11565-024-00536-2
Wasim Ahmed, Mohd Shuaib Akhtar, Muzibur Rahman Mozumder
{"title":"Characterization of ((alpha ,beta )) biderivations in triangular algebras","authors":"Wasim Ahmed,&nbsp;Mohd Shuaib Akhtar,&nbsp;Muzibur Rahman Mozumder","doi":"10.1007/s11565-024-00536-2","DOIUrl":"10.1007/s11565-024-00536-2","url":null,"abstract":"<div><p>In this paper we have define <span>((alpha ,beta ))</span>-biderivation on triangular algebra <span>(mathcal {A})</span> and characterize some result on triangular algebras. Apart from that, in Theorem 3.5, we show that any map on <span>(mathcal {A} times mathcal {A} rightarrow mathcal {A})</span> becomes <span>((alpha ,alpha ))</span>-biderivation after imposing certain conditions.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1687 - 1696"},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141686933","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}
引用次数: 0
Publisher Correction to: A class of semilinear hypoelliptic Robin problems and Morse theory 出版商更正为：一类半线性次椭圆罗宾问题和莫尔斯理论
Annali dell''Universita di Ferrara Pub Date : 2024-06-28 DOI: 10.1007/s11565-024-00537-1
Kazuaki Taira
{"title":"Publisher Correction to: A class of semilinear hypoelliptic Robin problems and Morse theory","authors":"Kazuaki Taira","doi":"10.1007/s11565-024-00537-1","DOIUrl":"10.1007/s11565-024-00537-1","url":null,"abstract":"","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1607 - 1607"},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414692","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}
引用次数: 0
On the birational geometry of ({mathbb {Q}})-Fano threefolds of large Fano index, I 论大法诺指数的（{mathbb {Q}})-Fano threefolds of large Fano index, I
Annali dell''Universita di Ferrara Pub Date : 2024-06-20 DOI: 10.1007/s11565-024-00515-7
Yuri Prokhorov
{"title":"On the birational geometry of ({mathbb {Q}})-Fano threefolds of large Fano index, I","authors":"Yuri Prokhorov","doi":"10.1007/s11565-024-00515-7","DOIUrl":"10.1007/s11565-024-00515-7","url":null,"abstract":"<div><p>We investigate the rationality problem for <span>({mathbb {Q}})</span>-Fano threefolds of Fano index <span>(ge 2)</span>.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"955 - 985"},"PeriodicalIF":0.0,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412641","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}
引用次数: 0
Bounds on tree distribution in number theory 数论中的树分布界限
Annali dell''Universita di Ferrara Pub Date : 2024-06-17 DOI: 10.1007/s11565-024-00535-3
Roberto Conti, Pierluigi Contucci, Vitalii Iudelevich
{"title":"Bounds on tree distribution in number theory","authors":"Roberto Conti,&nbsp;Pierluigi Contucci,&nbsp;Vitalii Iudelevich","doi":"10.1007/s11565-024-00535-3","DOIUrl":"10.1007/s11565-024-00535-3","url":null,"abstract":"<div><p>By recursively applying the prime decomposition to the exponents, every natural number determines a rooted planar tree in a canonical way. In particular, trees with only one edge correspond to prime numbers. In this work we investigate the occurrence and the distribution of patterns of trees associated to the natural numbers. Bounds from above and below are proven for certain natural quantities. It is proved that the distance between two consecutive occurrences of the same configuration of trees is unbounded. For any <i>k</i>, there is at least one configuration of trees arising from <i>k</i> consecutive integers that occurs infinitely many times. Dirichlet theorem about primes in arithmetic progressions is generalized to any planar rooted tree. The appearence of equal nonplanar trees associated to <i>k</i> consecutive integers is also investigated. Finally, constraints implied by the repeated occurrence of a given configuration of planar trees are analyzed.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1655 - 1685"},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142412184","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}
引用次数: 0
On K-stability of (mathbb {P}^3) blown up along a quintic elliptic curve 论沿着五元椭圆曲线炸开的 $$mathbb {P}^3$$ 的 K 稳定性
Annali dell''Universita di Ferrara Pub Date : 2024-06-05 DOI: 10.1007/s11565-024-00532-6
Ivan Cheltsov, Piotr Pokora
{"title":"On K-stability of (mathbb {P}^3) blown up along a quintic elliptic curve","authors":"Ivan Cheltsov,&nbsp;Piotr Pokora","doi":"10.1007/s11565-024-00532-6","DOIUrl":"10.1007/s11565-024-00532-6","url":null,"abstract":"<div><p>In this note, we study K-stability of smooth Fano threefolds that can be obtained by blowing up the three-dimensional projective space along a smooth elliptic curve of degree five.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"1165 - 1192"},"PeriodicalIF":0.0,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00532-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141385755","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}
引用次数: 0
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