Displaying similar documents to “A system of simultaneous congruences arising from trinomial exponential sums”

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

Gen Yamamoto (2000)

Acta Arithmetica

Similarity:

1. Introduction. Let p be a prime number and p the ring of p-adic integers. Let k be a finite extension of the rational number field ℚ, k a 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 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...

Topological structure of the space of lower semi-continuous functions

Katsuro Sakai, Shigenori Uehara (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let L ( X ) be the space of all lower semi-continuous extended real-valued functions on a Hausdorff space X , where, by identifying each f with the epi-graph epi ( f ) , L ( X ) is regarded the subspace of the space Cld F * ( X × ) of all closed sets in X × with the Fell topology. Let LSC ( X ) = { f L ( X ) f ( X ) , f ( X ) ( - , ] } and LSC B ( X ) = { f L ( X ) f ( X ) is a bounded subset of } . We show that L ( X ) is homeomorphic to the Hilbert cube Q = [ - 1 , 1 ] if and only if X is second countable, locally compact and infinite. In this case, it is proved that ( L ( X ) , LSC ( X ) , LSC B ( X ) ) is homeomorphic to ( Cone Q , Q × ( 0 , 1 ) , Σ × ( 0 , 1 ) ) (resp. ( Q , s , Σ ) ) if X is compact (resp. X is non-compact), where Cone Q = ( Q × 𝐈 ) / ( Q × { 1 } ) is...

Some results on the product of distributions and the change of variable

Emin Özçag, Brian Fisher (1991)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let F and G be distributions in 𝒟 ' and let f be an infinitely differentiable function with f ' ( x ) > 0 , (or < 0 ). It is proved that if the neutrix product F G exists and equals H , then the neutrix product F ( f ) G ( f ) exists and equals H ( f ) .

Best approximations and porous sets

Simeon Reich, Alexander J. Zaslavski (2003)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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.