The Gibbs phenomenon and Lebesgue constants for regular means
V. Swaminathan (1977)
Matematički Vesnik
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V. Swaminathan (1977)
Matematički Vesnik
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Dušan Pokorný, Marc Rauch (2022)
Commentationes Mathematicae Universitatis Carolinae
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We deal with the so-called Ahlfors regular sets (also known as -regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit exist, where is an -regular set and is for instance the -packing number of ?
John Krueger (2008)
Fundamenta Mathematicae
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We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of , where κ ⊆ X. Suppose μ < κ, , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in which are internally club but not internally approachable.
Carlos Rito (2007)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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This paper classifies surfaces of general type with having an involution such that has non-negative Kodaira dimension and that the bicanonical map of factors through the double cover induced by It is shown that is regular and either: a) the Albanese fibration of is of genus 2 or b) has no genus 2 fibration and is birational to a surface. For case a) a list of possibilities and examples are given. An example for case b) with is also constructed.
S. Moll (2008)
Banach Center Publications
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Let X be a completely regular Hausdorff topological space and the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of .
Yoshishige Haraoka (2012)
Banach Center Publications
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For a Fuchsian system , (F) being distinct points in ℂ and , the number α of accessory parameters is determined by the spectral types , where . We call the set of α parameters a regular coordinate if all entries of the are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues...
K. Omiljanowski, S. Zafiridou (2005)
Colloquium Mathematicae
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We define a dendrite which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite of order n described by J. J. Charatonik.
Krishnan Selvakumar, Manoharan Subajini (2016)
Czechoslovak Mathematical Journal
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Let be a commutative ring with nonzero identity and the Jacobson radical of . The Jacobson graph of , denoted by , is defined as the graph with vertex set such that two distinct vertices and are adjacent if and only if is not a unit of . The genus of a simple graph is the smallest nonnegative integer such that can be embedded into an orientable surface . In this paper, we investigate the genus number of the compact Riemann surface in which can be embedded and...
Mehdi Badie (2016)
Commentationes Mathematicae Universitatis Carolinae
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In this article we study the comaximal graph of the ring . We have tried to associate the graph properties of , the ring properties of and the topological properties of . Radius, girth, dominating number and clique number of the are investigated. We have shown that and if then . We give some topological properties of equivalent to graph properties of . Finally we have proved that is an almost -space which does not have isolated points if and only if is an almost...
Pietro Donatini, Patrizio Frosini (2007)
Journal of the European Mathematical Society
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Let us consider two closed surfaces , of class and two functions , of class , called measuring functions. The natural pseudodistance between the pairs , is defined as the infimum of as varies in the set of all homeomorphisms from onto . In this paper we prove that the natural pseudodistance equals either , , or , where and are two suitable critical values of the measuring functions. This shows that a previous relation between the natural pseudodistance and...
Xiaodan Chen, Yaoping Hou (2015)
Czechoslovak Mathematical Journal
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Let be the algebraic connectivity, and let be the Laplacian spectral radius of a -connected graph with vertices and edges. In this paper, we prove that with equality if and only if is the complete graph or . Moreover, if is non-regular, then where stands for the maximum degree of . Remark that in some cases, these two inequalities improve some previously known results.
R. Frankiewicz (1978)
Colloquium Mathematicae
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Tien-Cuong Dinh, Nessim Sibony (2008)
Annales scientifiques de l'École Normale Supérieure
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Let be a non-invertible holomorphic endomorphism of a projective space and its iterate of order . We prove that the pull-back by of a generic (in the Zariski sense) hypersurface, properly normalized, converges to the Green current associated to when tends to infinity. We also give an analogous result for the pull-back of positive closed -currents and a similar result for regular polynomial automorphisms of .
Graziano Gentili, Simon Salamon, Caterina Stoppato (2014)
Journal of the European Mathematical Society
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The theory of slice-regular functions of a quaternion variable is applied to the study of orthogonal complex structures on domains of . When is a symmetric slice domain, the twistor transform of such a function is a holomorphic curve in the Klein quadric. The case in which is the complement of a parabola is studied in detail and described by a rational quartic surface in the twistor space .
Antoine Delcroix (2010)
Banach Center Publications
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In analogy to the classical isomorphism between ((ℝⁿ), and (resp. and ), we show that a large class of moderate linear mappings acting between the space of compactly supported generalized functions and (ℝⁿ) of generalized functions (resp. the space of Colombeau rapidly decreasing generalized functions and the space of temperate ones) admits generalized integral representations, with kernels belonging to specific regular subspaces of (resp. ). The main novelty is to use...
Jay Jorgenson, Jürg Kramer (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
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In his seminal paper on arithmetic surfaces Faltings introduced a new invariant associated to compact Riemann surfaces , nowadays called Faltings’s delta function and here denoted by . For a given compact Riemann surface of genus , the invariant is roughly given as minus the logarithm of the distance with respect to the Weil-Petersson metric of the point in the moduli space of genus curves determined by to its boundary . In this paper we begin by revisiting a formula derived...
Takashi Noiri (1981)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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Se ed sono spazi topologici, una funzione è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di in un insieme chiuso di . Si dimostra che una funzione regolarmente chiusa risulta chiusa se è normale.
Rafael von Känel (2014)
Journal de Théorie des Nombres de Bordeaux
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Let be a hyperelliptic curve of genus over a number field with good reduction outside a finite set of places of . We prove that has a Weierstrass model over the ring of integers of with height effectively bounded only in terms of , and . In particular, we obtain that for any given number field , finite set of places of and integer one can in principle determine the set of -isomorphism classes of hyperelliptic curves over of genus with good reduction outside...
Dan Popovici (2005)
Studia Mathematica
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Commuting multi-contractions of class and having a regular isometric dilation are studied. We prove that a polydisc contraction of class is the restriction of a backwards multi-shift to an invariant subspace, extending a particular case of a result by R. E. Curto and F.-H. Vasilescu. A new condition on a commuting multi-operator, which is equivalent to the existence of a regular isometric dilation and improves a recent result of A. Olofsson, is obtained as a consequence. ...
M. Cristina Ronconi (2009)
Bollettino dell'Unione Matematica Italiana
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The range of the bigenus is one of the unsolved problems concerning smooth complex projective regular threefolds of general type with : The examples in the literature have . In the present paper we present a non-singular threefold with ; ; the bicanonical map is stably birational.
Azam Babai, Zeinab Akhlaghi (2017)
Czechoslovak Mathematical Journal
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Let be a group and be the set of element orders of . Let and be the number of elements of order in . Let nse. Assume is a prime number and let be a group such that nse nse, where is the symmetric group of degree . In this paper we prove that , if divides the order of and does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.
Fabrizio Catanese, Fabio Tonoli (2007)
Journal of the European Mathematical Society
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We determine the possible even sets of nodes on sextic surfaces in , showing in particular that their cardinalities are exactly the numbers in the set . We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, and of homological and computer algebra on the other. We give a detailed geometric construction for the new case of an even set of 56 nodes, but the ultimate verification...
Jean Saint Raymond (2007)
Fundamenta Mathematicae
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Let X be a Polish space, and let C₀ and C₁ be disjoint coanalytic subsets of X. The pair (C₀,C₁) is said to be complete if for every pair (D₀,D₁) of disjoint coanalytic subsets of there exists a continuous function such that and . We give several explicit examples of complete pairs of coanalytic sets.
Mbekezeli Nxumalo (2024)
Archivum Mathematicum
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Given a topological space , let and denote, respectively, the Salbany compactification of and the compactification map called the Salbany map of . For every continuous function , there is a continuous function , called the Salbany lift of , satisfying . If a continuous function has a stably compact codomain , then there is a Salbany extension of , not necessarily unique, such that . In this paper, we give a condition on a space such that its Salbany map is open. In...