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Displaying similar documents to “Orbit projections as fibrations”

On the generalized Massey–Rolfsen invariant for link maps

A. Skopenkov (2000)

Fundamenta Mathematicae

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For K = K 1 . . . K s and a link map f : K m let K = i < j K i × K j , define a map f : K S m - 1 by f ( x , y ) = ( f x - f y ) / | f x - f y | and a (generalized) Massey-Rolfsen invariant α ( f ) π m - 1 ( K ) to be the homotopy class of f . We prove that for a polyhedron K of dimension ≤ m - 2 under certain (weakened metastable) dimension restrictions, α is an onto or a 1 - 1 map from the set of link maps f : K m up to link concordance to π m - 1 ( K ) . If K 1 , . . . , K s are closed highly homologically connected manifolds of dimension p 1 , . . . , p s (in particular, homology spheres), then π m - 1 ( K ) i < j π p i + p j - m + 1 S .

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

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Let D be a nonempty compact subset of a Banach space X and denote by S ( X ) the family of all nonempty bounded closed convex subsets of X . We endow S ( X ) with the Hausdorff metric and show that there exists a set S ( X ) such that its complement S ( X ) is σ -porous and such that for each A and each x ˜ D , the set of solutions of the best approximation problem x ˜ - z min , z A , is nonempty and compact, and each minimizing sequence has a convergent subsequence.

On the eigenvalues of a Robin problem with a large parameter

Alexey Filinovskiy (2014)

Mathematica Bohemica

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We consider the Robin eigenvalue problem Δ u + λ u = 0 in Ω , u / ν + α u = 0 on Ω where Ω n , n 2 is a bounded domain and α is a real parameter. We investigate the behavior of the eigenvalues λ k ( α ) of this problem as functions of the parameter α . We analyze the monotonicity and convexity properties of the eigenvalues and give a variational proof of the formula for the derivative λ 1 ' ( α ) . Assuming that the boundary Ω is of class C 2 we obtain estimates to the difference λ k D - λ k ( α ) between the k -th eigenvalue of the Laplace operator with...