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Automorphisms of Fano threefolds of rank 2 and degree 28 阶数为 2 和阶数为 28 的法诺三维的自动形变
Annali dell''Universita di Ferrara Pub Date : 2024-06-01 DOI: 10.1007/s11565-024-00525-5
Joseph Malbon
{"title":"Automorphisms of Fano threefolds of rank 2 and degree 28","authors":"Joseph Malbon","doi":"10.1007/s11565-024-00525-5","DOIUrl":"10.1007/s11565-024-00525-5","url":null,"abstract":"<div><p>We describe the automorphism groups of smooth Fano threefolds of rank 2 and degree 28 in the cases where they are finite.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"1083 - 1092"},"PeriodicalIF":0.0,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00525-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409259","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
On the graph (G_P(R)) over commutative ring R 在交换环 R 上的图(G_P(R))上
Annali dell''Universita di Ferrara Pub Date : 2024-05-30 DOI: 10.1007/s11565-024-00533-5
B. Biswas, S. Kar
{"title":"On the graph (G_P(R)) over commutative ring R","authors":"B. Biswas,&nbsp;S. Kar","doi":"10.1007/s11565-024-00533-5","DOIUrl":"10.1007/s11565-024-00533-5","url":null,"abstract":"<div><p>Let <i>R</i> be a commutative ring with identity 1. Then the graph of <i>R</i>, denoted by <span>(G_P(R))</span> which is defined as the vertices are the elements of <i>R</i> and any two distinct elements <i>a</i> and <i>b</i> are adjacent if and only if the corresponding principal ideals <i>aR</i> and <i>bR</i> satisfy the condition: <span>((aR)(bR)=aRbigcap bR)</span>. In this paper, we characterize the class of finite commutative rings with 1 for which the graph <span>(G_P(R))</span> is complete. Here we are able to show that the graph <span>(G_P(R))</span> is a line graph of some graph <i>G</i> if and only if <span>(G_P(R))</span> is complete. For <span>(n=p_1^{r_1}p_2^{r_2}ldots p_{k}^{r_k})</span>, we show that chromatic number of <span>(G_P(mathbb {Z}_n))</span> is equal to the sum of the number of regular elements in <span>(mathbb {Z}_n)</span> and the number of integers <i>i</i> such that <span>({r_{i}}&gt;1)</span>. Moreover, we characterize those <i>n</i> for which the graph <span>(G_P(mathbb {Z}_n))</span> is end-regular.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1621 - 1633"},"PeriodicalIF":0.0,"publicationDate":"2024-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142415052","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
Factors of HOMFLY polynomials HOMFLY 多项式的因数
Annali dell''Universita di Ferrara Pub Date : 2024-05-29 DOI: 10.1007/s11565-024-00530-8
Douglas Blackwell, Damiano Testa
{"title":"Factors of HOMFLY polynomials","authors":"Douglas Blackwell,&nbsp;Damiano Testa","doi":"10.1007/s11565-024-00530-8","DOIUrl":"10.1007/s11565-024-00530-8","url":null,"abstract":"<div><p>We study factorizations of HOMFLY polynomials of certain prime knots and oriented links. We begin with a computer analysis of prime knots with at most 12 crossings, finding 17 non-trivial factorizations. Next, we give an irreducibility criterion for HOMFLY polynomials of oriented links associated to 2-connected plane graphs.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"1155 - 1163"},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00530-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409161","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
Stress intensity factor: new and improved estimates 应力强度因子：新的和改进的估算值
Annali dell''Universita di Ferrara Pub Date : 2024-05-29 DOI: 10.1007/s11565-024-00531-7
Oscar Ascenzi
{"title":"Stress intensity factor: new and improved estimates","authors":"Oscar Ascenzi","doi":"10.1007/s11565-024-00531-7","DOIUrl":"10.1007/s11565-024-00531-7","url":null,"abstract":"<div><p>In this paper we give new estimates from above and from below of the Stress Intensity Factor on an open bounded and convex domain <span>(Omega subseteq mathbb {R}^2)</span>. This analysis is a continuation of the study that we have done in Ascenzi et al. (Appl Math Comput 158:597–617, 2004), Ascenzi (Ann Univ Ferrara Sez VII (NS) 47:41–56, 2001) and Livieri et al. (Acta Mech 176:95–105, 2005) and that started from the paper of Oore and Burns (J Press Vessel Technol 102:204–211, 1980).\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1609 - 1620"},"PeriodicalIF":0.0,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00531-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414933","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
Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron 从牛顿多面体读取平面曲线奇点的对数规范阈值
Annali dell''Universita di Ferrara Pub Date : 2024-05-28 DOI: 10.1007/s11565-024-00524-6
Erik Paemurru
{"title":"Reading the log canonical threshold of a plane curve singularity from its Newton polyhedron","authors":"Erik Paemurru","doi":"10.1007/s11565-024-00524-6","DOIUrl":"10.1007/s11565-024-00524-6","url":null,"abstract":"<div><p>There is a proposition due to Kollár as reported by Kollár (Proceedings of the summer research institute, Santa Cruz, CA, USA, July 9–29, 1995, American Mathematical Society, Providence, 1997) on computing log canonical thresholds of certain hypersurface germs using weighted blowups, which we extend to weighted blowups with non-negative weights. Using this, we show that the log canonical threshold of a convergent complex power series is at most 1/<i>c</i>, where <span>((c, ldots , c))</span> is a point on a facet of its Newton polyhedron. Moreover, in the case <span>(n = 2)</span>, if the power series is weakly normalised with respect to this facet or the point (<i>c</i>, <i>c</i>) belongs to two facets, then we have equality. This generalises a theorem of Varchenko 1982 to non-isolated singularities.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"1069 - 1082"},"PeriodicalIF":0.0,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00524-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414714","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
Rate of convergence of Szász-Durrmeyer type operators involving Hermite polynomials 涉及赫米特多项式的 Szász-Durrmeyer 型算子的收敛率
Annali dell''Universita di Ferrara Pub Date : 2024-05-27 DOI: 10.1007/s11565-024-00527-3
Ajay Kumar
{"title":"Rate of convergence of Szász-Durrmeyer type operators involving Hermite polynomials","authors":"Ajay Kumar","doi":"10.1007/s11565-024-00527-3","DOIUrl":"10.1007/s11565-024-00527-3","url":null,"abstract":"<div><p>This study aims to investigate a generalized version of Szász operators linked with Hermite polynomials in the Durrmeyer framework. Initially, we delve into their approximation properties employing Peetre’s K-functional, along with classical and second-order modulus of continuity. Subsequently, we evaluate the convergence speed using a Lipschitz-type function and establish a Voronovskaya-type approximation theorem. Lastly, we investigate the convergence rate for differentiable functions with bounded variation derivatives.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1527 - 1543"},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414390","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 class of semilinear hypoelliptic Robin problems and Morse theory 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 : 2024-05-27 DOI: 10.1007/s11565-024-00529-1
Kazuaki Taira
{"title":"A class of semilinear hypoelliptic Robin problems and Morse theory","authors":"Kazuaki Taira","doi":"10.1007/s11565-024-00529-1","DOIUrl":"10.1007/s11565-024-00529-1","url":null,"abstract":"<div><p>(1) Background: This paper is devoted to the study of a class of semilinear elliptic boundary value problems with hypoelliptic (degenerate) Robin condition that includes as particular cases the Dirichlet, Neumann and regular Robin problems. (2) Methods: We give a rigorous proof of main theorem, which is based heavily on the theory of linear elliptic boundary value problems in the framework of <span>(L^{p})</span> Sobolev spaces. (3) Results: We extend earlier theorems due to Ambrosetti–Lupo and Struwe to the hypoelliptic Robin case via Morse theory. (4) Conclusions: The main purpose of this paper is to understand the essence of a modern version of the classical Lyapunov–Schmidt procedure through a concrete approach to semilinear hypoelliptic Robin problems.</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1545 - 1605"},"PeriodicalIF":0.0,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414391","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
Commutators and generalized derivations acting on Lie ideals in prime rings 作用于质环中列理想的换元和广义导数
Annali dell''Universita di Ferrara Pub Date : 2024-05-23 DOI: 10.1007/s11565-024-00521-9
Basudeb Dhara
{"title":"Commutators and generalized derivations acting on Lie ideals in prime rings","authors":"Basudeb Dhara","doi":"10.1007/s11565-024-00521-9","DOIUrl":"10.1007/s11565-024-00521-9","url":null,"abstract":"<div><p>Let <i>R</i> be a prime ring of char <span>((R)ne 2, 3)</span> and <i>L</i> a noncentral Lie ideal of <i>R</i>. Let <i>U</i> be the Utumi quotient ring of <i>R</i> and <span>(C=Z(U))</span> be the extended centroid of <i>R</i>. Suppose that <i>F</i>, <i>G</i>, <i>H</i> are three generalized derivations of <i>R</i> such that </p><div><div><span>$$[F(u),u]G(u)+u[H(u),u]=0$$</span></div></div><p>for all <span>(uin L)</span>. Then either <i>R</i> satisfies standard polynomial <span>(s_4(x_1,x_2,x_3,x_4))</span> or one of the following holds: </p><ol>\u0000 <li>\u0000 <span>1.</span>\u0000 \u0000 <p>There exist <span>(alpha , beta in C)</span> such that <span>(F(x)= alpha x)</span> and <span>(H(x)= beta x)</span> for all <span>( xin R)</span>;</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>2.</span>\u0000 \u0000 <p>There exists <span>(beta in C)</span> such that <span>(G(x)=0)</span>, <span>(H(x)=beta x)</span> for all <span>( xin R)</span>;</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>3.</span>\u0000 \u0000 <p>There exist <span>(a,bin U)</span> and <span>(0ne mu in C)</span> such that <span>(F(x)=xa)</span>, <span>(G(x)=mu x)</span>, <span>(H(x)=bx)</span> for all <span>( xin R)</span> with <span>(mu a+bin C)</span>.</p>\u0000 \u0000 </li>\u0000 </ol></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 4","pages":"1509 - 1526"},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141103398","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
The graded ring database for Fano 3-folds and the Bogomolov stability bound 法诺 3 折叠的梯度环数据库和博戈莫洛夫稳定性约束
Annali dell''Universita di Ferrara Pub Date : 2024-05-23 DOI: 10.1007/s11565-024-00518-4
Kaori Suzuki
{"title":"The graded ring database for Fano 3-folds and the Bogomolov stability bound","authors":"Kaori Suzuki","doi":"10.1007/s11565-024-00518-4","DOIUrl":"10.1007/s11565-024-00518-4","url":null,"abstract":"<div><p>My paper (Suzuki 2003) produced some computer routines in Magma (Bosma et al. J Symb Comp 24:235–265, 1997) for the numerical invariants of Fano 3-folds, and used them in particular to determine the maximum value <span>(f=19)</span> of the Fano index. As a byproduct of the research, extensive data associated with all possible sets of singular points of Fano 3-folds with Fano indices greater than or equal to 2 was obtained. Collaborative research with Gavin Brown developed an improved version of the Magma program. The data discussed above was added to the Graded Ring Data Base (Brown et al. 2015) at the University of Kent. Subsequently, GRDB, now located to the University of Warwick, recently modified its interface to accommodate additional conditions, facilitating a more refined selection of Fano manifolds. In this context, we focus on the inequality known as the Bogomolov stability bound. We present a list of candidates for Fano 3-folds that do not satisfy these conditions and propose the conjecture that they do not exist.This result has been independently obtained in Liu and Liu (2023).</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"1023 - 1035"},"PeriodicalIF":0.0,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00518-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141103454","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
Some models for bubbling of (log) Kähler–Einstein metrics 凯勒-爱因斯坦（对数）度量冒泡的一些模型
Annali dell''Universita di Ferrara Pub Date : 2024-05-21 DOI: 10.1007/s11565-024-00520-w
Martin de Borbon, Cristiano Spotti
{"title":"Some models for bubbling of (log) Kähler–Einstein metrics","authors":"Martin de Borbon,&nbsp;Cristiano Spotti","doi":"10.1007/s11565-024-00520-w","DOIUrl":"10.1007/s11565-024-00520-w","url":null,"abstract":"<div><p>We investigate aspects of the metric bubble tree for non-collapsing degenerations of (log) Kähler–Einstein metrics in complex dimensions one and two, and further describe a conjectural higher dimensional picture.\u0000</p></div>","PeriodicalId":35009,"journal":{"name":"Annali dell''Universita di Ferrara","volume":"70 3","pages":"1037 - 1068"},"PeriodicalIF":0.0,"publicationDate":"2024-05-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11565-024-00520-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141115773","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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