Annali di Matematica Pura ed Applicata最新文献

Moduli spaces of flat Riemannian metrics on 4-dimensional closed manifolds 四维闭流形上平坦黎曼度量的模空间

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2025-02-26 DOI: 10.1007/s10231-024-01514-3

Karla García, Oscar Palmas

引用次数: 0

Complete Nevanlinna–Pick kernels and the curvature invariant 完成奈万林纳-匹克核和曲率不变量

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-12-05 DOI: 10.1007/s10231-024-01524-1

Tirthankar Bhattacharyya, Abhay Jindal

引用次数: 0

On random sampling of supersingular elliptic curves 超奇异椭圆曲线的随机抽样

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-12-02 DOI: 10.1007/s10231-024-01528-x

Marzio Mula, Nadir Murru, Federico Pintore

{"title":"On random sampling of supersingular elliptic curves","authors":"Marzio Mula, Nadir Murru, Federico Pintore","doi":"10.1007/s10231-024-01528-x","DOIUrl":"10.1007/s10231-024-01528-x","url":null,"abstract":"<div><p>We consider the problem of sampling random supersingular elliptic curves over finite fields of cryptographic size (SRS problem). The currently best-known method combines the reduction of a suitable complex multiplication (CM) elliptic curve and a random walk over some supersingular isogeny graph. Unfortunately, this method is not suitable when the endomorphism ring of the generated curve needs to be hidden, like in some cryptographic applications. This motivates a stricter version of the SRS problem, requiring that the sampling algorithm gives no information about the endomorphism ring of the output curve (cSRS problem). In this work we formally define the SRS and cSRS problems, which are both of theoretical interest. We discuss the relevance of the two problems for cryptographic applications, and we provide a self-contained survey of the known approaches to solve them. Those for the cSRS problem have exponential complexity in the characteristic of the base finite field (since they require computing and finding roots of polynomials of large degree), leaving the problem open. In the second part of the paper, we propose and analyse some alternative techniques—based either on the Hasse invariant or division polynomials—and we explain the reasons why they do not readily lead to efficient cSRS algorithms, but they may open promising research directions.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1293 - 1335"},"PeriodicalIF":1.0,"publicationDate":"2024-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10231-024-01528-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Liouville-type results for three-dimensional equatorial water waves with surface tension and an interface 具有表面张力和界面的三维赤道水波的liouville型结果

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-29 DOI: 10.1007/s10231-024-01529-w

Yan Bai, Yong Zhang, Zhitao Zhang

引用次数: 0

Global regularity for p(x)-Laplace equations with log-BMO matrix weights in Reifenberg domains Reifenberg域中log-BMO矩阵权值p(x)-Laplace方程的全局正则性

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-25 DOI: 10.1007/s10231-024-01526-z

Sun-Sig Byun, Rui Yang

{"title":"Global regularity for p(x)-Laplace equations with log-BMO matrix weights in Reifenberg domains","authors":"Sun-Sig Byun, Rui Yang","doi":"10.1007/s10231-024-01526-z","DOIUrl":"10.1007/s10231-024-01526-z","url":null,"abstract":"<div><p>We study the boundary-value problem </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} mathrm {{div}}left( |mathbb {M}(x)nabla u(x)|^{p(x)-2}mathbb {M}^2(x)nabla u(x)right) =mathrm {{div}}left( |mathbb {M}(x) F(x)|^{p(x)-2}mathbb {M}^2(x)F(x)right) & ~ text {in}~Omega , u(x)=0& text {on}~partial Omega , end{array}right. } end{aligned}$$</span></div></div><p>which has a degeneracy or singularity arising from the nonnegative matrix weight <span>(mathbb {M}(x))</span>. A global Calderón-Zygmund estimate for the relative weight is established under minimal regularity requirements on the associated operator by proving that <span>( |nabla u(x)|^{p(x)})</span> is as integrable as <span>( |F(x)|^{p(x)})</span> in <span>(L^{gamma }left( Omega , |mathbb {M}(x)|^{ gamma p(x) }dxright) )</span> for every <span>(1<gamma <infty )</span>, under the assumptions that the variable exponent <i>p</i>(<i>x</i>) has a small log-Hölder constant, <span>(mathbb {M}(x))</span> has a small log-BMO semi-norm and that the boundary <span>(partial Omega )</span> of the nonsmooth bounded domain <span>(Omega )</span> is flat in the Reifenberg sense. Our work is a natural extension and outgrowth of the uniformly elliptic problem when the matrix <span>(mathbb {M}(x))</span> is a constant matrix as in [1, 7] to the degenerate or singular one when a coefficient of the nonlinearity might goes to zero or <span>(infty )</span>.</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1229 - 1267"},"PeriodicalIF":1.0,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143930177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Biconservative hypersurfaces with constant scalar curvature in space forms 空间形式中具有常标量曲率的双保守超曲面

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-21 DOI: 10.1007/s10231-024-01527-y

Yu Fu, Min-Chun Hong, Dan Yang, Xin Zhan

引用次数: 0

Existence of solutions to Hamilton systems for the curl–curl operator with subcritical nonlinearities 具有次临界非线性的旋旋算子Hamilton系统解的存在性

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-20 DOI: 10.1007/s10231-024-01525-0

Zhijie Chen, Zhen Song, Zhaoji Zhang

{"title":"Existence of solutions to Hamilton systems for the curl–curl operator with subcritical nonlinearities","authors":"Zhijie Chen, Zhen Song, Zhaoji Zhang","doi":"10.1007/s10231-024-01525-0","DOIUrl":"10.1007/s10231-024-01525-0","url":null,"abstract":"<div><p>This paper is concerned with the following Hamilton system for the curl–curl operator </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll} nabla times (nabla times U_1)=f_2(x,U_2) quad & hbox {in};Omega , nabla times (nabla times U_2)=f_1(x,U_1) quad & hbox {in};Omega , nu times U_1=nu times U_2=0 & hbox {on};partial Omega end{array}right. } end{aligned}$$</span></div></div><p>in a simply connected bounded Lipschitz domain <span>(Omega subset {mathbb {R}}^3)</span> with connected boundary, where <span>(nabla times )</span> denotes the curl operator in <span>({mathbb {R}}^3)</span> and <span>(nu :partial Omega rightarrow {mathbb {R}}^3)</span> is the exterior normal. By using some variational approaches inspired by Szulkin and Weth (J Funct Anal 257(12):3802–3822, 2009) and Bartsch and Mederski (Arch Ration Mech Anal 215(1):283–306, 2015), we show that there exists a ground state solution for the above system if <span>(f_1)</span> and <span>(f_2)</span> are both subcritical and satisfy some other growth conditions and convexity conditions. Furthermore, if the nonlinearities are both even, we establish the existence of infinitely many solutions. Finally, we prove the existence of two types of cylindrically symmetric solutions under some symmetry conditions on the domain and the nonlinearities.\u0000</p></div>","PeriodicalId":8265,"journal":{"name":"Annali di Matematica Pura ed Applicata","volume":"204 3","pages":"1199 - 1227"},"PeriodicalIF":1.0,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143929990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Depth formula for modules of finite reducing projective dimension 有限降射影维数模的深度公式

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-20 DOI: 10.1007/s10231-024-01509-0

Olgur Celikbas, Toshinori Kobayashi, Brian Laverty, Hiroki Matsui

引用次数: 0

Regularity and pointwise convergence of solutions of the Schrödinger operator with radial initial data on Damek-Ricci spaces Damek-Ricci空间上具有径向初始数据的Schrödinger算子解的正则性和点收敛性

IF 1 3区数学

Annali di Matematica Pura ed Applicata Pub Date : 2024-11-19 DOI: 10.1007/s10231-024-01523-2

Utsav Dewan

引用次数: 0

Antiassociative magmas Antiassociative岩浆