Displaying similar documents to “Topological structure of the space of lower semi-continuous functions”

On the vanishing of Iwasawa invariants of absolutely abelian p-extensions

Gen Yamamoto (2000)

Acta Arithmetica

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1. Introduction. Let p be a prime number and ℤ p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k ∞ a ℤ p -extension of k, k n the nth layer of k ∞ / k , and A n the p-Sylow subgroup of the ideal class group of k n . Iwasawa proved the following well-known theorem about the order A n of A n : Theorem A (Iwasawa). Let k ∞ / k be a ℤ p -extension and A n the p-Sylow subgroup of the ideal class group of k n , where k n is the n th layer of k ∞ / k . Then there exist integers λ = λ ( k ∞ / k ) ≥ 0 , μ = μ ( k ∞ / k ) ≥ 0 , ν = ν ( k ∞ / k ) , and n₀ ≥ 0...

Guidance properties of a cylindrical defocusing waveguide

Oldřich John, Charles A. Stuart (1994)

Commentationes Mathematicae Universitatis Carolinae

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We discuss the propagation of electromagnetic waves of a special form through an inhomogeneous isotropic medium which has a cylindrical symmetry and a nonlinear dielectric response. For the case where this response is of self-focusing type the problem is treated in [1]. Here we continue this study by dealing with a defocusing dielectric response. This tends to inhibit the guidance properties of the medium and so guidance can only be expected provided that the cylindrical stratification...

Baireness of C k ( X ) for ordered X

Michael Granado, Gary Gruenhage (2006)

Commentationes Mathematicae Universitatis Carolinae

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We show that if X is a subspace of a linearly ordered space, then C k ( X ) is a Baire space if and only if C k ( X ) is Choquet iff X has the Moving Off Property.

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 ⊂ ℝ 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...

A note on evaluations of some exponential sums

Marko J. Moisio (2000)

Acta Arithmetica

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1. Introduction. The recent article [1] gives explicit evaluations for exponential sums of the form S ( a , p α + 1 ) : = ∑ x ∈ q χ ( a x p α + 1 ) where χ is a non-trivial additive character of the finite field q , q = p e odd, and a ∈ * q . In my dissertation [5], in particular in [4], I considered more generally the sums S(a,N) for all factors N of p α + 1 . The aim of the present note is to evaluate S(a,N) in a short way, following [4]. We note that our result is also valid for even q, and the technique used in our proof can also be used to evaluate...

For a dense set of equivalent norms, a non-reflexive Banach space contains a triangle with no Chebyshev center

Libor Veselý (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let X be a non-reflexive real Banach space. Then for each norm | · | from a dense set of equivalent norms on X (in the metric of uniform convergence on the unit ball of X ), there exists a three-point set that has no Chebyshev center in ( X , | · | ) . This result strengthens theorems by Davis and Johnson, van Dulst and Singer, and Konyagin.