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Displaying similar documents to “Why quintic polynomial equations are not solvable in radicals”

Random Galois extensions of Hilbertian fields

Lior Bary-Soroker, Arno Fehm (2013)

Journal de Théorie des Nombres de Bordeaux

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Let L be a Galois extension of a countable Hilbertian field K . Although L need not be Hilbertian, we prove that an abundance of large Galois subextensions of L / K are.

Some non-multiplicative properties are l -invariant

Vladimir Vladimirovich Tkachuk (1997)

Commentationes Mathematicae Universitatis Carolinae

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A cardinal function ϕ (or a property 𝒫 ) is called l -invariant if for any Tychonoff spaces X and Y with C p ( X ) and C p ( Y ) linearly homeomorphic we have ϕ ( X ) = ϕ ( Y ) (or the space X has 𝒫 ( X 𝒫 ) iff Y 𝒫 ). We prove that the hereditary Lindelöf number is l -invariant as well as that there are models of Z F C in which hereditary separability is l -invariant.

Sharp estimates for bubbling solutions of a fourth order mean field equation

Chang-Shou Lin, Juncheng Wei (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider a sequence of multi-bubble solutions u k of the following fourth order equation Δ 2 u k = ρ k h ( x ) e u k Ω h e u k in Ω , u k = Δ u k = 0 on Ω , ( * ) where h is a C 2 , β positive function, Ω is a bounded and smooth domain in 4 , and ρ k is a constant such that ρ k C . We show that (after extracting a subsequence), lim k + ρ k = 32 σ 3 m for some positive integer m 1 , where σ 3 is the area of the unit sphere in 4 . Furthermore, we obtain the following sharp estimates for  ρ k : ρ k - 32 σ 3 m = c 0 j = 1 m ϵ k , j 2 l j Δ G 4 ( p j , p l ) + Δ R 4 ( p j , p j ) + 1 32 σ 3 Δ log h ( p j ) + o j = 1 m ϵ k , j 2 where c 0 > 0 , log 64 ϵ k , j 4 = max x B δ ( p j ) u k ( x ) - log ( Ω h e u k ) and u k 32 σ 3 j = 1 m G 4 ( · , p j ) in C loc 4 ( Ω { p 1 , ... , p m } ) . This yields a bound of solutions as...

F σ -absorbing sequences in hyperspaces of subcontinua

Helma Gladdines (1993)

Commentationes Mathematicae Universitatis Carolinae

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Let 𝒟 denote a true dimension function, i.e., a dimension function such that 𝒟 ( n ) = n for all n . For a space X , we denote the hyperspace consisting of all compact connected, non-empty subsets by C ( X ) . If X is a countable infinite product of non-degenerate Peano continua, then the sequence ( 𝒟 n ( C ( X ) ) ) n = 2 is F σ -absorbing in C ( X ) . As a consequence, there is a homeomorphism h : C ( X ) Q such that for all n , h [ { A C ( X ) : 𝒟 ( A ) n + 1 } ] = B n × Q × Q × , where B denotes the pseudo boundary of the Hilbert cube Q . It follows that if X is a countable infinite product of non-degenerate...

Counting discriminants of number fields

Henri Cohen, Francisco Diaz y Diaz, Michel Olivier (2006)

Journal de Théorie des Nombres de Bordeaux

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For each transitive permutation group G on n letters with n 4 , we give without proof results, conjectures, and numerical computations on discriminants of number fields L of degree n over such that the Galois group of the Galois closure of L is isomorphic to G .