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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
{"title":"Singularity properties of Lorentzian Darboux surfaces in Lorentz–Minkowski spacetime","authors":"Yanlin Li, Xuelian Jiang, Zhigang Wang","doi":"10.1007/s40687-023-00420-z","DOIUrl":"https://doi.org/10.1007/s40687-023-00420-z","url":null,"abstract":"<p>In this paper, by virtue of unfolding theory in singularity theory, we investigate the singularities of five special surfaces generated by a regular curve lying on a spacelike hypersurface in Lorentz–Minkowski 4-space. Using two kinds of extended Lorentzian Darboux frames along the curve as tools, five new invariants are obtained to characterize the singularities of five special surfaces and their geometric meanings are discussed in detail. In addition, some dual relationships between a normal curve of the original curve and five surfaces are revealed under the meanings of Legendrian duality.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139645822","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 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
{"title":"On Kleinian mock modular forms","authors":"Claudia Alfes, Michael H. Mertens","doi":"10.1007/s40687-023-00410-1","DOIUrl":"https://doi.org/10.1007/s40687-023-00410-1","url":null,"abstract":"<p>We give an explicit and computationally efficient construction of harmonic weak Maass forms which map to weight 2 newforms under the <span>(xi )</span>-operator. Our work uses a new non-analytic completion of the Kleinian <span>(zeta )</span>-function from the theory of Abelian functions.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139558888","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
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":"<p>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 <span>(l_1)</span> constrained and unconstrained minimization for separating <i>N</i> 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.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"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
Identification of unbounded electric potentials through asymptotic boundary spectral data 通过渐近边界谱数据识别无界电势
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2023-12-28 DOI: 10.1007/s40687-023-00417-8
Mourad Bellassoued, Yavar Kian, Yosra Mannoubi, Éric Soccorsi
{"title":"Identification of unbounded electric potentials through asymptotic boundary spectral data","authors":"Mourad Bellassoued, Yavar Kian, Yosra Mannoubi, Éric Soccorsi","doi":"10.1007/s40687-023-00417-8","DOIUrl":"https://doi.org/10.1007/s40687-023-00417-8","url":null,"abstract":"<p>We prove that the real-valued electric potential <span>(q in L^{max (2,3 n /5)}(Omega ))</span> of the Dirichlet Laplacian <span>(-Delta +q)</span> acting in a bounded domain <span>(Omega subset mathbb {R}^n)</span>, <span>(n ge 3)</span>, is uniquely determined by the asymptotics of the eigenpairs formed by the eigenvalues and the boundary observation of the normal derivative of the eigenfunctions.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139065603","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
Analyticity of Steklov eigenvalues of nearly hyperspherical domains in $${mathbb {R}}^{d + 1}$$ $${mathbb {R}}^{d + 1}$$ 近超球面域的斯特克洛夫特征值的解析性
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2023-12-22 DOI: 10.1007/s40687-023-00415-w
Chee Han Tan, Robert Viator
{"title":"Analyticity of Steklov eigenvalues of nearly hyperspherical domains in $${mathbb {R}}^{d + 1}$$","authors":"Chee Han Tan, Robert Viator","doi":"10.1007/s40687-023-00415-w","DOIUrl":"https://doi.org/10.1007/s40687-023-00415-w","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138946310","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
Towards the Erdős-Hajnal conjecture for $$P_5$$ -free graphs 实现无 P_5$$ 图的厄尔多斯-哈依纳猜想
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2023-12-19 DOI: 10.1007/s40687-023-00413-y
Pablo Blanco, Matija Bucić
{"title":"Towards the Erdős-Hajnal conjecture for $$P_5$$ -free graphs","authors":"Pablo Blanco, Matija Bucić","doi":"10.1007/s40687-023-00413-y","DOIUrl":"https://doi.org/10.1007/s40687-023-00413-y","url":null,"abstract":"<p>The Erdős-Hajnal conjecture is one of the most classical and well-known problems in extremal and structural combinatorics dating back to 1977. It asserts that in stark contrast to the case of a general <i>n</i>-vertex graph, if one imposes even a little bit of structure on the graph, namely by forbidding a fixed graph <i>H</i> as an induced subgraph, instead of only being able to find a polylogarithmic size clique or an independent set, one can find one of polynomial size. Despite being the focus of considerable attention over the years, the conjecture remains open. In this paper, we improve the best known lower bound of <span>(2^{Omega (sqrt{log n})})</span> on this question, due to Erdős and Hajnal from 1989, in the smallest open case, namely when one forbids a <span>(P_5)</span>, the path on 5 vertices. Namely, we show that any <span>(P_5)</span>-free <i>n</i>-vertex graph contains a clique or an independent set of size at least <span>(2^{Omega (log n)^{2/3}})</span>. We obtain the same improvement for an infinite family of graphs.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138742679","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
Estimate for the largest zeros of the D’Arcais polynomials 估计D 'Arcais多项式的最大零
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2023-11-15 DOI: 10.1007/s40687-023-00412-z
Bernhard Heim, Markus Neuhauser
{"title":"Estimate for the largest zeros of the D’Arcais polynomials","authors":"Bernhard Heim, Markus Neuhauser","doi":"10.1007/s40687-023-00412-z","DOIUrl":"https://doi.org/10.1007/s40687-023-00412-z","url":null,"abstract":"<p>The zeros of the <i>n</i>th D’Arcais polynomial, also known in combinatorics as the Nekrasov–Okounkov polynomial, dictate the vanishing properties of the <i>n</i>th Fourier coefficients of all complex powers <i>x</i> of the Dedekind <span>(eta )</span>-function. In this paper, we prove that these coefficients are non-vanishing for <span>(vert x vert &gt; kappa , (n-1))</span> and <span>(kappa approx 9.7225)</span>. Numerical computations imply that 9.72245 is a lower bound for <span>(kappa )</span>. This significantly improves previous results by Kostant, Han, and Heim–Neuhauser. The polynomials studied in this paper include Chebyshev polynomials of the second kind, 1-associated Laguerre polynomials, Hermite polynomials, and polynomials associated with overpartitions and plane partitions.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2023-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527794","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
Operator shifting for noisy elliptic systems 带噪声椭圆系统的算子移位
3区 数学
Research in the Mathematical Sciences Pub Date : 2023-11-12 DOI: 10.1007/s40687-023-00414-x
Philip A. Etter, Lexing Ying
{"title":"Operator shifting for noisy elliptic systems","authors":"Philip A. Etter, Lexing Ying","doi":"10.1007/s40687-023-00414-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00414-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135037343","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: 2
Certain invertible operator-block matrices induced by $$C^{*}$$-algebras and scaled hypercomplex numbers 由$$C^{*}$$ -代数和标度超复数导出的可逆算子块矩阵
3区 数学
Research in the Mathematical Sciences Pub Date : 2023-10-21 DOI: 10.1007/s40687-023-00411-0
Daniel Alpay, Ilwoo Cho
{"title":"Certain invertible operator-block matrices induced by $$C^{*}$$-algebras and scaled hypercomplex numbers","authors":"Daniel Alpay, Ilwoo Cho","doi":"10.1007/s40687-023-00411-0","DOIUrl":"https://doi.org/10.1007/s40687-023-00411-0","url":null,"abstract":"Abstract The main purposes of this paper are (i) to enlarge scaled hypercomplex structures to operator-valued cases, where the operators are taken from a $$C^{*}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msup> <mml:mi>C</mml:mi> <mml:mrow> <mml:mrow /> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> </mml:math> -subalgebra of an operator algebra on a separable Hilbert space, (ii) to characterize the invertibility conditions on the operator-valued scaled-hypercomplex structures of (i), (iii) to study relations between the invertibility of scaled hypercomplex numbers, and that of operator-valued cases of (ii), and (iv) to confirm our invertibility of (ii) and (iii) are equivalent to the general invertibility of $$left( 2times 2right) $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mfenced> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mn>2</mml:mn> </mml:mfenced> </mml:math> -block operator matrices.","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135510833","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
The tension determination problem for an inextensible interface in 2D Stokes flow 二维Stokes流中不可扩展界面的张力确定问题
3区 数学
Research in the Mathematical Sciences Pub Date : 2023-10-20 DOI: 10.1007/s40687-023-00406-x
Po-Chun Kuo, Ming-Chih Lai, Yoichiro Mori, Analise Rodenberg
{"title":"The tension determination problem for an inextensible interface in 2D Stokes flow","authors":"Po-Chun Kuo, Ming-Chih Lai, Yoichiro Mori, Analise Rodenberg","doi":"10.1007/s40687-023-00406-x","DOIUrl":"https://doi.org/10.1007/s40687-023-00406-x","url":null,"abstract":"","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135570031","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: 1
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