Research in the Mathematical Sciences最新文献_第5页

On the topology of complex projective hypersurfaces 论复杂投影超曲面的拓扑学

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-27 DOI: 10.1007/s40687-024-00435-0

Laurenţiu G. Maxim

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$$omega $$ -Symplectic algebra and Hamiltonian vector fields $$omega $$ -Symplectic 代数和哈密顿向量场

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-26 DOI: 10.1007/s40687-024-00423-4

Patrícia H. Baptistelli, Maria Elenice R. Hernandes, Eralcilene Moreira Terezio

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Reconstruction of a hypersurface singularity from its moduli algebra 从模代数重构超曲面奇点

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-26 DOI: 10.1007/s40687-024-00432-3

João Hélder Olmedo Rodrigues

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The variance and correlations of the divisor function in $${mathbb {F}}_q [T]$$ , and Hankel matrices $${mathbb {F}}_q [T]$$ 中除数函数的方差和相关性，以及汉克尔矩阵

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-17 DOI: 10.1007/s40687-023-00418-7

Michael Yiasemides

{"title":"The variance and correlations of the divisor function in $${mathbb {F}}_q [T]$$ , and Hankel matrices","authors":"Michael Yiasemides","doi":"10.1007/s40687-023-00418-7","DOIUrl":"https://doi.org/10.1007/s40687-023-00418-7","url":null,"abstract":"We prove an exact formula for the variance of the divisor function over short intervals in ({mathcal {A}}:= {mathbb {F}}_q [T]), where q is a prime power; and for correlations of the form (d(A) d(A+B)), where we average both A and B over certain intervals in ({mathcal {A}}). We also obtain an exact formula for correlations of the form (d(KQ+N) d (N)), where Q is prime and K and N are averaged over certain intervals with ({{,textrm{deg},}}N le {{,textrm{deg},}}Q -1 le {{,textrm{deg},}}K); and we demonstrate that (d(KQ+N)) and d(N) are uncorrelated. We generalize our results to (sigma _z) defined by (sigma _z (A):= sum _{E mid A} |A |^z) for all monics (A in {mathcal {A}}). Our approach is to use the orthogonality relations of additive characters on ({mathbb {F}}_q) to translate the problems to ones involving the ranks of Hankel matrices over ({mathbb {F}}_q). We prove several results regarding the rank and kernel structure of these matrices, thus demonstrating their number-theoretic properties. We also discuss extending our method to other divisor sums, such as those involving (d_k).","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"6 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903881","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

On a new absolute version of Siegel’s lemma 关于西格尔定理的新绝对版本

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-15 DOI: 10.1007/s40687-024-00422-5

引用次数: 0

On Ribet’s lemma for GL $$_2$$ modulo prime powers 关于 GL $_$2$$ 素幂模的里贝特定理

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-14 DOI: 10.1007/s40687-023-00419-6

{"title":"On Ribet’s lemma for GL $$_2$$ modulo prime powers","authors":"","doi":"10.1007/s40687-023-00419-6","DOIUrl":"https://doi.org/10.1007/s40687-023-00419-6","url":null,"abstract":"<h3>Abstract</h3> Let (rho :Grightarrow {{,textrm{GL},}}_2(K)) be a continuous representation of a compact group G over a complete discretely valued field K with ring of integers (mathcal {O}) and uniformiser (pi ) . We prove that ({{,textrm{tr},}}rho ) is reducible modulo (pi ^n) if and only if (rho ) is reducible modulo (pi ^n) . More precisely, there exist characters (chi _1,chi _2 :Grightarrow (mathcal {O}/pi ^nmathcal {O})^times ) such that (det (t - rho (g))equiv (t-chi _1(g))(t-chi _2(g))pmod {pi ^n}) for all (gin G) , if and only if there exists a G-stable lattice (Lambda subseteq K^2) such that (Lambda /pi ^nLambda ) contains a G-invariant, free, rank one (mathcal {O}/pi ^nmathcal {O}) -submodule. Our result applies in the case that (rho ) is not residually multiplicity-free, in which case it answers a question of Bellaïche and Chenevier (J Algebra 410:501–525, 2014, pp. 524). As an application, we prove an optimal version of Ribet’s lemma, which gives a condition for the existence of a G-stable lattice (Lambda ) that realises a non-split extension of (chi _2) by (chi _1) .","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"9 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139750963","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

Extensions of MacMahon’s sums of divisors 麦克马洪除数和的扩展

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-02-05 DOI: 10.1007/s40687-024-00421-6

Tewodros Amdeberhan, George E. Andrews, Roberto Tauraso

引用次数: 0

Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime 洛伦兹-闵科夫斯基时空中洛伦兹达布曲面的奇异特性

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-01-30 DOI: 10.1007/s40687-023-00420-z

Yanlin Li, Xuelian Jiang, Zhigang Wang

引用次数: 0

On Kleinian mock modular forms 关于克莱因模拟模块形式

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2024-01-22 DOI: 10.1007/s40687-023-00410-1

Claudia Alfes, Michael H. Mertens

引用次数: 0

Multi-component separation, inpainting and denoising with recovery guarantees 具有恢复保证的多分量分离、内画和去噪功能

IF 1.2 3区数学

Research in the Mathematical Sciences Pub Date : 2023-12-29 DOI: 10.1007/s40687-023-00416-9

Van Tiep Do

{"title":"Multi-component separation, inpainting and denoising with recovery guarantees","authors":"Van Tiep Do","doi":"10.1007/s40687-023-00416-9","DOIUrl":"https://doi.org/10.1007/s40687-023-00416-9","url":null,"abstract":"In image processing, problems of separation and reconstruction of missing pixels from incomplete digital images have been far more advanced in past decades. Many empirical results have produced very good results; however, providing a theoretical analysis for the success of algorithms is not an easy task, especially, for inpainting and separating multi-component signals. In this paper, we propose two main algorithms based on (l_1) constrained and unconstrained minimization for separating N distinct geometric components and simultaneously filling in the missing part of the observed image. We then present a theoretical guarantee for these algorithms using compressed sensing technique, which is based on a principle that each component can be sparsely represented by a suitably chosen dictionary. Those sparsifying systems are extended to the case of general frames instead of Parseval frames which have been typically used in the past. We finally prove that the method does indeed succeed in separating point singularities from curvilinear singularities and texture as well as inpainting the missing band contained in curvilinear singularities and texture.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"13 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139065637","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