Regularity of certain sets in ℂⁿ

Nguyen Quang Dieu

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Displaying similar documents to “Regularity of certain sets in ℂⁿ”

Inequalities for a regular polygon in $L^{p}$ spaces

M. Pavlović (1992)

Matematički Vesnik

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Remarks on absolutely regular and regular $K^{'} M_{p}$ -distributions

S. Pilipović (1991)

Annales Polonici Mathematici

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nbspAbstract. We give the definition of $K^{'} M_{P}$ regular distributions and some characterizations of absolutely regular and regular $K^{'} M_{p}$ -distributions.

Nonnormality points of βX∖X

William Fleissner, Lynne Yengulalp (2011)

Fundamenta Mathematicae

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Let X be a crowded metric space of weight κ that is either $κ^{ω}$ -like or locally compact. Let y ∈ βX∖X and assume GCH. Then a space of nonuniform ultrafilters embeds as a closed subspace of (βX∖X)∖y with y as the unique limit point. If, in addition, y is a regular z-ultrafilter, then the space of nonuniform ultrafilters is not normal, and hence (βX∖X)∖y is not normal.

Universal completely regular dendrites

K. Omiljanowski, S. Zafiridou (2005)

Colloquium Mathematicae

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We define a dendrite $E_{n}$ which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite $E_{ω}$ is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite $D_{n}$ of order n described by J. J. Charatonik.

On regular $K^{'} M_{P}$ -distributions

Stevan Pilipović (1988)

Annales Polonici Mathematici

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On the density and net weight of regular spaces

Armando Romero Morales (2007)

Colloquium Mathematicae

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We use the cardinal functions ac and lc, due to Fedeli, to establish bounds on the density and net weight of regular spaces which improve some well known bounds. In particular, we use the language of elementary submodels to establish that $d (X) \leq π χ {(X)}^{a c (X)}$ for every regular space X. This generalizes the following result due to Shapirovskiĭ: $d (X) \leq π χ {(X)}^{c (X)}$ for every regular space X.

The genera, reflexibility and simplicity of regular maps

Marston Conder, Jozef Širáň, Thomas Tucker (2010)

Journal of the European Mathematical Society

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This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to $g - 1$ , where $g$ is the genus, all orientably-regular maps of genus $p + 1$ for $p$ prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and...

On $C_{0 \cdot}$ multi-contractions having a regular dilation

Dan Popovici (2005)

Studia Mathematica

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Commuting multi-contractions of class $C_{0 \cdot}$ and having a regular isometric dilation are studied. We prove that a polydisc contraction of class $C_{0 \cdot}$ 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. ...

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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All completely regular elements in $H y p_{G} (n)$

Ampika Boonmee, Sorasak Leeratanavalee (2013)

Discussiones Mathematicae - General Algebra and Applications

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In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties. Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms...

Strongly regular family of boundary-fitted tetrahedral meshes of bounded $C^{2}$ domains

Radim Hošek (2016)

Applications of Mathematics

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We give a constructive proof that for any bounded domain of the class $C^{2}$ there exists a strongly regular family of boundary-fitted tetrahedral meshes. We adopt a refinement technique introduced by Křížek and modify it so that a refined mesh is again boundary-fitted. An alternative regularity criterion based on similarity with the Sommerville tetrahedron is used and shown to be equivalent to other standard criteria. The sequence of regularities during the refinement process is estimated...

Supremum properties of Galois-type connections

Árpád Száz (2006)

Commentationes Mathematicae Universitatis Carolinae

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In a former paper, motivated by a recent theory of relators (families of relations), we have investigated increasingly regular and normal functions of one preordered set into another instead of Galois connections and residuated mappings of partially ordered sets. A function $f$ of one preordered set $X$ into another $Y$ has been called (1) increasingly $g$ -normal, for some function $g$ of $Y$ into $X$ , if for any $x \in X$ and $y \in Y$ we have $f (x) \leq y$ if and only if $x \leq g (y)$ ; (2) increasingly $ϕ$ -regular, for some function $ϕ$ ...

On the asymptotics of counting functions for Ahlfors regular sets

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 $s$ -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 ${lim}_{ε \to 0 +} ε^{s} N (ε, K)$ exist, where $K$ is an $s$ -regular set and $N (ε, K)$ is for instance the $ε$ -packing number of $K$ ?

Wiener's type regularity criteria on the complex plane

Józef Siciak (1997)

Annales Polonici Mathematici

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We present a number of Wiener’s type necessary and sufficient conditions (in terms of divergence of integrals or series involving a condenser capacity) for a compact set E ⊂ ℂ to be regular with respect to the Dirichlet problem. The same capacity is used to give a simple proof of the following known theorem [2, 6]: If E is a compact subset of ℂ such that $d (t^{- 1} E \cap | z - a | \leq 1) \geq c o n s t > 0$ for 0 < t ≤ 1 and a ∈ E, where d(F) is the logarithmic capacity of F, then the Green function of ℂ E with pole at infinity is...

Internally club and approachable for larger structures

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 $P_{κ} (X)$ , where κ ⊆ X. Suppose μ < κ, $μ^{< μ} = μ$ , 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 ${[H (λ)]}^{μ ⁺}$ which are internally club but not internally approachable.

A general upper bound in extremal theory of sequences

Martin Klazar (1992)

Commentationes Mathematicae Universitatis Carolinae

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We investigate the extremal function $f (u, n)$ which, for a given finite sequence $u$ over $k$ symbols, is defined as the maximum length $m$ of a sequence $v = a_{1} a_{2} . . . a_{m}$ of integers such that 1) $1 \leq a_{i} \leq n$ , 2) $a_{i} = a_{j}, i \neq j$ implies $| i - j | \geq k$ and 3) $v$ contains no subsequence of the type $u$ . We prove that $f (u, n)$ is very near to be linear in $n$ for any fixed $u$ of length greater than 4, namely that $f (u, n) = O (n 2^{O (α {(n)}^{| u | - 4})}) .$ Here $| u |$ is the length of $u$ and $α (n)$ is the inverse to the Ackermann function and goes to infinity very slowly. This result extends the estimates in [S] and...