Displaying similar documents to “Числа разложения групп 𝒥 ^ 2 и Aut ( 𝒥 2 )

Characterization of automorphisms of Radford's biproduct of Hopf group-coalgebra

Xing Wang, Daowei Lu, Ding-Guo Wang (2024)

Czechoslovak Mathematical Journal

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We study certain subgroups of the Hopf group-coalgebra automorphism group of Radford’s π -biproduct. Firstly, we discuss the endomorphism monoid End π -Hopf ( A × H , p ) and the automorphism group Aut π -Hopf ( A × H , p ) of Radford’s π -biproduct A × H = { A × H α } α π , and prove that the automorphism has a factorization closely related to the factors A and H = { H α } α π . What’s more interesting is that a pair of maps ( F L , F R ) can be used to describe a family of mappings F = { F α } α π . Secondly, we consider the relationship between the automorphism group Aut π -Hopf ( A × H , p ) and the automorphism group...

On a sequence formed by iterating a divisor operator

Bellaouar Djamel, Boudaoud Abdelmadjid, Özen Özer (2019)

Czechoslovak Mathematical Journal

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Let be the set of positive integers and let s . We denote by d s the arithmetic function given by d s ( n ) = ( d ( n ) ) s , where d ( n ) is the number of positive divisors of n . Moreover, for every , m we denote by δ s , , m ( n ) the sequence d s ( d s ( ... d s ( d s ( n ) + ) + ... ) + ) m -times = d s ( n ) for m = 1 , d s ( d s ( n ) + ) for m = 2 , d s ( d s ( d s ( n ) + ) + ) for m = 3 , We present classical and nonclassical notes on the sequence ( δ s , , m ( n ) ) m 1 , where , n , s are understood as parameters.

On Kneser solutions of the n -th order nonlinear differential inclusions

Martina Pavlačková (2019)

Czechoslovak Mathematical Journal

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The paper deals with the existence of a Kneser solution of the n -th order nonlinear differential inclusion x ( n ) ( t ) - A 1 ( t , x ( t ) , ... , x ( n - 1 ) ( t ) ) x ( n - 1 ) ( t ) - ... - A n ( t , x ( t ) , ... , x ( n - 1 ) ( t ) ) x ( t ) for a.a. t [ a , ) , where a ( 0 , ) , and A i : [ a , ) × n , i = 1 , ... , n , are upper-Carathéodory mappings. The derived result is finally illustrated by the third order Kneser problem.

Persistence of Coron’s solution in nearly critical problems

Monica Musso, Angela Pistoia (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider the problem - Δ u = u N + 2 N - 2 + λ in Ω ε ω , u > 0 in Ω ε ω , u = 0 on Ω ε ω , where Ω and ω are smooth bounded domains in N , N 3 , ε > 0 and λ . We prove that if the size of the hole ε goes to zero and if, simultaneously, the parameter λ goes to zero at the appropriate rate, then the problem has a solution which blows up at the origin.

The group of automorphisms of L is algebraically reflexive

Félix Cabello Sánchez (2004)

Studia Mathematica

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We study the reflexivity of the automorphism (and the isometry) group of the Banach algebras L ( μ ) for various measures μ. We prove that if μ is a non-atomic σ-finite measure, then the automorphism group (or the isometry group) of L ( μ ) is [algebraically] reflexive if and only if L ( μ ) is *-isomorphic to L [ 0 , 1 ] . For purely atomic measures, we show that the group of automorphisms (or isometries) of ( Γ ) is reflexive if and only if Γ has non-measurable cardinal. So, for most “practical” purposes, the automorphism...