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Computational Methods and Function Theory最新文献

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On Bloch’s “Principle of Topological Continuity” 论布洛赫的 "拓扑连续性原理"
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-04-04 DOI: 10.1007/s40315-024-00531-w
Walter Bergweiler, Alexandre Eremenko
{"title":"On Bloch’s “Principle of Topological Continuity”","authors":"Walter Bergweiler, Alexandre Eremenko","doi":"10.1007/s40315-024-00531-w","DOIUrl":"https://doi.org/10.1007/s40315-024-00531-w","url":null,"abstract":"<p>We discuss to what extent certain results about totally ramified values of entire and meromorphic functions remain valid if one relaxes the hypothesis that some value is totally ramified by assuming only that all islands over some Jordan domain are multiple. In particular, we prove a result suggested by Bloch which says that an entire function of order less than 1 has a simple island over at least one of two given Jordan domains with disjoint closures.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570483","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
Normality Criterion Concerning Total Derivatives of Holomorphic Functions in $$ {mathbb {C}}^n $$ 关于 $$ {mathbb {C}}^n $$ 中全态函数总衍生物的正态性标准
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-04-03 DOI: 10.1007/s40315-024-00523-w
Molla Basir Ahamed, Sanju Mandal
{"title":"Normality Criterion Concerning Total Derivatives of Holomorphic Functions in $$ {mathbb {C}}^n $$","authors":"Molla Basir Ahamed, Sanju Mandal","doi":"10.1007/s40315-024-00523-w","DOIUrl":"https://doi.org/10.1007/s40315-024-00523-w","url":null,"abstract":"<p>This paper continues investigation of conditions involving values shared by holomorphic functions and their total derivatives which imply the normality for a family of holomorphic functions concerning the total derivatives in <span>( {mathbb {C}}^n )</span>. Consequently, we obtain normality criterion of a family <span>( {mathcal {F}} )</span> of holomorphic functions <i>f</i>, where each function shares complex values with their linear total differential polynomials <span>( L_D^k(f) )</span> in <span>( {mathbb {C}}^n )</span>.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140603103","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
Critical Points for Least-Squares Estimation of Dipolar Sources in Inverse Problems for Poisson Equation 泊松方程反问题中双极性源最小二乘估计的临界点
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-04-03 DOI: 10.1007/s40315-024-00535-6
Paul Asensio, Juliette Leblond
{"title":"Critical Points for Least-Squares Estimation of Dipolar Sources in Inverse Problems for Poisson Equation","authors":"Paul Asensio, Juliette Leblond","doi":"10.1007/s40315-024-00535-6","DOIUrl":"https://doi.org/10.1007/s40315-024-00535-6","url":null,"abstract":"<p>In this work, we study some aspects of the solvability of the minimization of a non-convex least-squares criterion involved in dipolar source recovery issues, using boundary values of a solution to a Poisson problem in a domain of dimension 3. This Poisson problem arises in particular from the quasi-static approximation of Maxwell equations with localized sources modeled as dipoles. We establish the uniqueness of the minimizer of the criterion for general geometries and the uniqueness of its critical point for the Euclidean geometry, that is when the boundary is a plane. This has consequences on the numerical approach, for the convergence of the computed solution to the global minimizer. Related inverse potential problems have applications in biomedical imaging issues pertaining to neurosciences, and in paleomagnetism issues pertaining to geosciences. There, solutions to such inverse problems are used to recover electric currents in the brain, or rock magnetizations, from measurements of the induced electric potential or magnetic field.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570217","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
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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Maximum and Average Valence of Meromorphic Functions 微函数的最大值和平均值
IF 2.1 4区 数学
Computational Methods and Function Theory Pub Date : 2024-01-24 DOI: 10.1007/s40315-024-00533-8
A. Hinkkanen, Joseph Miles
{"title":"Maximum and Average Valence of Meromorphic Functions","authors":"A. Hinkkanen, Joseph Miles","doi":"10.1007/s40315-024-00533-8","DOIUrl":"https://doi.org/10.1007/s40315-024-00533-8","url":null,"abstract":"","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140497216","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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