Displaying similar documents to “Tight bounds for the dihedral angle sums of a pyramid”

Copies of l p n ’s uniformly in the spaces Π 2 ( C [ 0 , 1 ] , X ) and Π 1 ( C [ 0 , 1 ] , X )

Dumitru Popa (2017)

Czechoslovak Mathematical Journal

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We study the presence of copies of l p n ’s uniformly in the spaces Π 2 ( C [ 0 , 1 ] , X ) and Π 1 ( C [ 0 , 1 ] , X ) . By using Dvoretzky’s theorem we deduce that if X is an infinite-dimensional Banach space, then Π 2 ( C [ 0 , 1 ] , X ) contains λ 2 -uniformly copies of l n ’s and Π 1 ( C [ 0 , 1 ] , X ) contains λ -uniformly copies of l 2 n ’s for all λ > 1 . As an application, we show that if X is an infinite-dimensional Banach space then the spaces Π 2 ( C [ 0 , 1 ] , X ) and Π 1 ( C [ 0 , 1 ] , X ) are distinct, extending the well-known result that the spaces Π 2 ( C [ 0 , 1 ] , X ) and 𝒩 ( C [ 0 , 1 ] , X ) are distinct.

A generalization of the Keller-Segel system to higher dimensions from a structural viewpoint

Fujie, Kentarou, Senba, Takasi

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We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than ( 8 π ) 2 , whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known 8 π problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel...

When Min ( G ) - 1 has a clopen π -base

Ramiro Lafuente-Rodriguez, Warren Wm. McGovern (2021)

Mathematica Bohemica

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It is our aim to contribute to the flourishing collection of knowledge centered on the space of minimal prime subgroups of a given lattice-ordered group. Specifically, we are interested in the inverse topology. In general, this space is compact and T 1 , but need not be Hausdorff. In 2006, W. Wm. McGovern showed that this space is a boolean space (i.e. a compact zero-dimensional and Hausdorff space) if and only if the l -group in question is weakly complemented. A slightly weaker topological...

H 2 convergence of solutions of a biharmonic problem on a truncated convex sector near the angle π

Abdelkader Tami, Mounir Tlemcani (2021)

Applications of Mathematics

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We consider a biharmonic problem Δ 2 u ω = f ω with Navier type boundary conditions u ω = Δ u ω = 0 , on a family of truncated sectors Ω ω in 2 of radius r , 0 < r < 1 and opening angle ω , ω ( 2 π / 3 , π ] when ω is close to π . The family of right-hand sides ( f ω ) ω ( 2 π / 3 , π ] is assumed to depend smoothly on ω in L 2 ( Ω ω ) . The main result is that u ω converges to u π when ω π with respect to the H 2 -norm. We can also show that the H 2 -topology is optimal for such a convergence result.

A note on the Π -property of some subgroups of finite groups

Zhengtian Qiu, Guiyun Chen, Jianjun Liu (2024)

Czechoslovak Mathematical Journal

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Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K L / K ) | is a π ( H K / K L / K ) -number. We obtain some criteria for the p -supersolubility or p -nilpotency of a finite group and extend some known results by concerning some subgroups that satisfy the Π -property.

On Π -property of some maximal subgroups of Sylow subgroups of finite groups

Zhengtian Qiu, Jianjun Liu, Guiyun Chen (2023)

Czechoslovak Mathematical Journal

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Let H be a subgroup of a finite group G . We say that H satisfies the Π -property in G if for any chief factor L / K of G , | G / K : N G / K ( H K / K L / K ) | is a π ( H K / K L / K ) -number. We study the influence of some p -subgroups of G satisfying the Π -property on the structure of G , and generalize some known results.

On a question of T. Sheil-Small regarding valency of harmonic maps

Daoud Bshouty, Abdallah Lyzzaik (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The aim of this work is to answer positively a more general question than the following which is due to T. Sheil-Small: Does the harmonic extension in the open unit disc of a mapping f from the unit circle into itself of the form f ( e i t ) = e i φ ( t ) , 0 t 2 π where φ is a continuously non-decreasing function that satisfies φ ( 2 π ) - φ ( 0 ) = 2 N π , assume every value finitely many times in the disc?

On continuous self-maps and homeomorphisms of the Golomb space

Taras O. Banakh, Jerzy Mioduszewski, Sławomir Turek (2018)

Commentationes Mathematicae Universitatis Carolinae

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The Golomb space τ is the set of positive integers endowed with the topology τ generated by the base consisting of arithmetic progressions { a + b n : n 0 } with coprime a , b . We prove that the Golomb space τ has continuum many continuous self-maps, contains a countable disjoint family of infinite closed connected subsets, the set Π of prime numbers is a dense metrizable subspace of τ , and each homeomorphism h of τ has the following properties: h ( 1 ) = 1 , h ( Π ) = Π , Π h ( x ) = h ( Π x ) , and h ( x ) = h ( x ) for all x . Here x : = { x n : n } and Π x denotes the set of...

Simplices rarely contain their circumcenter in high dimensions

Jon Eivind Vatne (2017)

Applications of Mathematics

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Acute triangles are defined by having all angles less than π / 2 , and are characterized as the triangles containing their circumcenter in the interior. For simplices of dimension n 3 , acuteness is defined by demanding that all dihedral angles between ( n - 1 ) -dimensional faces are smaller than π / 2 . However, there are, in a practical sense, too few acute simplices in general. This is unfortunate, since the acuteness property provides good qualitative features for finite element methods. The property...

Higgs bundles and representation spaces associated to morphisms

Indranil Biswas, Carlos Florentino (2015)

Archivum Mathematicum

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Let G be a connected reductive affine algebraic group defined over the complex numbers, and K G be a maximal compact subgroup. Let X , Y be irreducible smooth complex projective varieties and f : X Y an algebraic morphism, such that π 1 ( Y ) is virtually nilpotent and the homomorphism f * : π 1 ( X ) π 1 ( Y ) is surjective. Define f ( π 1 ( X ) , G ) = { ρ Hom ( π 1 ( X ) , G ) A ρ factors through f * } , f ( π 1 ( X ) , K ) = { ρ Hom ( π 1 ( X ) , K ) A ρ factors through f * } , where A : G GL ( Lie ( G ) ) is the adjoint action. We prove that the geometric invariant theoretic quotient f ( π 1 ( X , x 0 ) , G ) / / G admits a deformation retraction to f ( π 1 ( X , x 0 ) , K ) / K . We also show that the space of conjugacy classes of n almost commuting...

Poincaré inequalities and rigidity for actions on Banach spaces

Piotr Nowak (2015)

Journal of the European Mathematical Society

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The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present a condition implying that every affine isometric action of a given group G on a reflexive Banach space X has a fixed point. This last property is a strong version of Kazhdan’s property (T) and is equivalent to the fact that H 1 ( G , π ) = 0 for every isometric representation π of G on X . The condition is expressed in terms of p -Poincaré constants and we...

On the number of isomorphism classes of derived subgroups

Leyli Jafari Taghvasani, Soran Marzang, Mohammad Zarrin (2019)

Czechoslovak Mathematical Journal

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We show that a finite nonabelian characteristically simple group G satisfies n = | π ( G ) | + 2 if and only if G A 5 , where n is the number of isomorphism classes of derived subgroups of G and π ( G ) is the set of prime divisors of the group G . Also, we give a negative answer to a question raised in M. Zarrin (2014).