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Computational Methods and Function Theory最新文献

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Exponential Iteration and Borel Sets 指数迭代和伯尔集合
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-03-29 DOI: 10.1007/s40315-024-00526-7
David S. Lipham
{"title":"Exponential Iteration and Borel Sets","authors":"David S. Lipham","doi":"10.1007/s40315-024-00526-7","DOIUrl":"https://doi.org/10.1007/s40315-024-00526-7","url":null,"abstract":"<p>We determine the exact Borel class of escaping sets in the exponential family <span>(exp (z)+a)</span>. We also prove that the sets of non-escaping Julia points for many of these functions are topologically equivalent.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"34 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140324512","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Deviations of Meromorphic Minimal Surfaces of Finite Lower Order 论有限下阶单态极小曲面的偏差
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-03-26 DOI: 10.1007/s40315-024-00522-x
{"title":"On Deviations of Meromorphic Minimal Surfaces of Finite Lower Order","authors":"","doi":"10.1007/s40315-024-00522-x","DOIUrl":"https://doi.org/10.1007/s40315-024-00522-x","url":null,"abstract":"<h3>Abstract</h3> <p>This paper is devoted to the development of Beckenbach’s theory of meromorphic minimal surfaces. We get an estimate of the sum of Petrenko’s deviations of the meromorphic minimal surface of finite lower order in term of Valiron’s defect <span> <span>(Delta ({textbf {0}}, S_u))</span> </span>. We also give an example showing that the estimate is sharp.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"32 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Faber Series for $$L^2$$ Holomorphic One-Forms on Riemann Surfaces with Boundary 有边界黎曼曲面上 $$L^2$$ Holomorphic One-Forms 的 Faber 系列
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-03-22 DOI: 10.1007/s40315-024-00529-4
Eric Schippers, Mohammad Shirazi
{"title":"Faber Series for $$L^2$$ Holomorphic One-Forms on Riemann Surfaces with Boundary","authors":"Eric Schippers, Mohammad Shirazi","doi":"10.1007/s40315-024-00529-4","DOIUrl":"https://doi.org/10.1007/s40315-024-00529-4","url":null,"abstract":"<p>Consider a compact surface <span>(mathscr {R})</span> with distinguished points <span>(z_1,ldots ,z_n)</span> and conformal maps <span>(f_k)</span> from the unit disk into non-overlapping quasidisks on <span>(mathscr {R})</span> taking 0 to <span>(z_k)</span>. Let <span>(Sigma )</span> be the Riemann surface obtained by removing the closures of the images of <span>(f_k)</span> from <span>(mathscr {R})</span>. We define forms which are meromorphic on <span>(mathscr {R})</span> with poles only at <span>(z_1,ldots ,z_n)</span>, which we call Faber–Tietz forms. These are analogous to Faber polynomials in the sphere. We show that any <span>(L^2)</span> holomorphic one-form on <span>(Sigma )</span> is uniquely expressible as a series of Faber–Tietz forms. This series converges both in <span>(L^2(Sigma ))</span> and uniformly on compact subsets of <span>(Sigma )</span>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"84 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Nevanlinna Theory on Infinite Graphs 无穷图上的内万林纳理论
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-03-18 DOI: 10.1007/s40315-024-00530-x
Atsushi Atsuji, Hiroshi Kaneko
{"title":"Nevanlinna Theory on Infinite Graphs","authors":"Atsushi Atsuji, Hiroshi Kaneko","doi":"10.1007/s40315-024-00530-x","DOIUrl":"https://doi.org/10.1007/s40315-024-00530-x","url":null,"abstract":"<p>In this paper, we explore a generalization of one-dimensional tropical Nevanlinna theory developed by Halburd &amp; Southall and Laine &amp; Toghe for a scheme on general locally finite graphs. We first give a probabilistic interpretation of a fundamental observation in one-dimensional tropical Nevanlinna theory on the graph with countably infinitely many vertices of degree two, aiming at its extension in terms of one-dimensional Brownian motion. A counterpart of Lemma on the logarithmic derivative in the classical Nevanlinna theory was proved by Halburd and Southall (cf. Int. Math. Res. Not. 2009:887–911, 2009, https://doi.org/10.1093/imrn/rnn150). Taking advantage of the stochastic analytical interpretation, we prove an analogous result to their lemma on the logarithmic derivative on infinite graphs admitting tree structure.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"152 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140167766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Near-Circularity in Capacity and Maximally Convergent Polynomials 容量和最大收敛多项式的近圆性
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-03-13 DOI: 10.1007/s40315-024-00528-5
Hans-Peter Blatt
{"title":"Near-Circularity in Capacity and Maximally Convergent Polynomials","authors":"Hans-Peter Blatt","doi":"10.1007/s40315-024-00528-5","DOIUrl":"https://doi.org/10.1007/s40315-024-00528-5","url":null,"abstract":"<p>If <i>f</i> is a power series with radius <i>R</i> of convergence, <span>(R &gt; 1)</span>, it is well-known that the method of Carathéodory–Fejér constructs polynomial approximations of <i>f</i> on the closed unit disk which show the typical phenomenon of near-circularity on the unit circle. Let <i>E</i> be compact and connected and let <i>f</i> be holomorphic on <i>E</i>. If <span>(left{ p_nright} _{nin mathbb {N}})</span> is a sequence of polynomials converging maximally to <i>f</i> on <i>E</i>, it is shown that the modulus of the error functions <span>(f-p_n)</span> is asymptotically constant in capacity on level lines of the Green’s function <span>(g_Omega (z,infty ))</span> of the complement <span>(Omega )</span> of <i>E</i> in <span>(overline{mathbb {C}})</span> with pole at infinity, thereby reflecting a type of near-circularity, but without gaining knowledge of the winding numbers of the error curves with respect to the point 0.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"30 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
About the Cover: Complex Finite Differences of Higher Order 关于封面高阶复杂有限差分
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-03-06 DOI: 10.1007/s40315-024-00520-z
{"title":"About the Cover: Complex Finite Differences of Higher Order","authors":"","doi":"10.1007/s40315-024-00520-z","DOIUrl":"https://doi.org/10.1007/s40315-024-00520-z","url":null,"abstract":"<p>In his recent work, Bengt Fornberg describes the construction of finite difference schemes (FDS) for accurate numerical computation of higher order derivatives of analytic functions. In this note we introduce the <i>characteristic function</i> of these schemes and explore how it encodes properties of the FDS. Visualizations of the characteristic function and their modifications allow one to read off these properties by visual inspection of phase portraits. The cover of this volume shows a phase portrait of a function which is related to a FDS with nine nodes that approximates the 4th derivative with an error of order <span>(h^8)</span>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"272 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140046717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Uniqueness of L-Functions and Meromorphic Functions Under the Aegis of two Shared Sets 论两个共享集支持下的 L 函数和同调函数的唯一性
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-01-23 DOI: 10.1007/s40315-023-00513-4
Sanjay Mallick, Pratap Basak
{"title":"On the Uniqueness of L-Functions and Meromorphic Functions Under the Aegis of two Shared Sets","authors":"Sanjay Mallick, Pratap Basak","doi":"10.1007/s40315-023-00513-4","DOIUrl":"https://doi.org/10.1007/s40315-023-00513-4","url":null,"abstract":"<p>The paper presents general criteria for the uniqueness of a non-constant meromorphic function having finitely many poles and a non-constant <i>L</i>-function in the Selberg class when they share two sets. Our results provide the best cardinalities ever obtained in the literature improving all the existing results Li et al. (Lith. Math. J. <b>58</b>(2), 249–262 (2018)), Kundu and Banerjee (Rend. Circ. Mat. Palermo (2) <b>70</b>(3), 1227–1244 (2021), Banerjee and Kundu (Lith. Math. J. <b>61</b>(2), 161–179 (2021) with regard to the most general setting. Further, we have exhibited a number of examples throughout the paper showing the far reaching applications of our results.\u0000</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"10 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139552376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the Hyperbolic Metric of Certain Domains 论某些域的双曲公设
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-01-17 DOI: 10.1007/s40315-023-00518-z
Aimo Hinkkanen, Matti Vuorinen
{"title":"On the Hyperbolic Metric of Certain Domains","authors":"Aimo Hinkkanen, Matti Vuorinen","doi":"10.1007/s40315-023-00518-z","DOIUrl":"https://doi.org/10.1007/s40315-023-00518-z","url":null,"abstract":"<p>We prove that if <i>E</i> is a compact subset of the unit disk <span>({{mathbb {D}}})</span> in the complex plane, if <i>E</i> contains a sequence of distinct points <span>(a_nnot = 0)</span> for <span>(nge 1)</span> such that <span>(lim _{nrightarrow infty } a_n=0)</span> and for all <i>n</i> we have <span>( |a_{n+1}| ge |a_n|/2 )</span>, and if <span>(G={{mathbb {D}}} {setminus } E)</span> is connected and <span>(0in partial G)</span>, then there is a constant <span>(c&gt;0)</span> such that for all <span>(zin G)</span> we have <span>( lambda _{G } (z) ge c/|z| )</span> where <span>(lambda _{G } (z))</span> is the density of the hyperbolic metric in <i>G</i>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"108 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139501543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Explicit Meromorphic Solutions of a Second Order Briot–Bouquet Differential Equation 二阶布里奥-布凯特微分方程的显式单态解
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-01-05 DOI: 10.1007/s40315-023-00519-y
{"title":"Explicit Meromorphic Solutions of a Second Order Briot–Bouquet Differential Equation","authors":"","doi":"10.1007/s40315-023-00519-y","DOIUrl":"https://doi.org/10.1007/s40315-023-00519-y","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper, a special second-order Briot–Bouquet differential equation is studied. We construct explicit meromorphic solutions by the Kowalevski–Gambier method and a careful discussion. How we take into account the corresponding series at zeros, as opposed to the Laurent series at poles. This method is also useful for the study of many other non-linear differential equations.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"273 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2024-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139373730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Maximizing the Second Robin Eigenvalue of Simply Connected Curved Membranes 最大化简单连接曲面膜的第二罗宾特征值
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2023-12-26 DOI: 10.1007/s40315-023-00516-1
Jeffrey J. Langford, Richard S. Laugesen
{"title":"Maximizing the Second Robin Eigenvalue of Simply Connected Curved Membranes","authors":"Jeffrey J. Langford, Richard S. Laugesen","doi":"10.1007/s40315-023-00516-1","DOIUrl":"https://doi.org/10.1007/s40315-023-00516-1","url":null,"abstract":"<p>The second eigenvalue of the Robin Laplacian is shown to be maximal for a spherical cap among simply connected Jordan domains on the 2-sphere, for substantial intervals of positive and negative Robin parameters and areas. Geodesic disks in the hyperbolic plane similarly maximize the eigenvalue on a natural interval of negative Robin parameters. These theorems extend work of Freitas and Laugesen from the Euclidean case (zero curvature) and the authors’ hyperbolic and spherical results for Neumann eigenvalues (zero Robin parameter). Complicating the picture is the numerically observed fact that the second Robin eigenfunction on a large spherical cap is purely radial, with no angular dependence, when the Robin parameter lies in a certain negative interval depending on the cap aperture.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"71 1","pages":""},"PeriodicalIF":2.1,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139055175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
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