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Remarks on CR-manifolds of codimension 2 in C 4

Schmalz, Gerd (1999)

Proceedings of the 18th Winter School "Geometry and Physics"

The aim of the article is to give a conceptual understanding of Kontsevich’s construction of the universal element of the cohomology of the coarse moduli space of smooth algebraic curves with given genus and punctures. In a first step the author presents a toy model of tree graphs coloured by an operad 𝒫 for which the graph complex and the universal cycle will be constructed. The universal cycle has coefficients in the operad for Ω ( 𝒫 * ) -algebras with trivial differential over the (dual) cobar construction...

Remarks on effect-tribes

Sylvia Pulmannová, Elena Vinceková (2015)

Kybernetika

We show that an effect tribe of fuzzy sets 𝒯 ⊆ [ 0 , 1 ] X with the property that every f ∈ 𝒯 is ℬ 0 ( 𝒯 ) -measurable, where ℬ 0 ( 𝒯 ) is the family of subsets of X whose characteristic functions are central elements in 𝒯 , is a tribe. Moreover, a monotone σ -complete effect algebra with RDP with a Loomis-Sikorski representation ( X , 𝒯 , h ) , where the tribe 𝒯 has the property that every f ∈ 𝒯 is ℬ 0 ( 𝒯 ) -measurable, is a σ -MV-algebra.

Remarks on q-CCR relations for |q| > 1

Marek Bożejko (2007)

Banach Center Publications

In this paper we give a construction of operators satisfying q-CCR relations for q > 1: A ( f ) A * ( g ) - A * ( g ) A ( f ) = q N ⟨ f , g ⟩ I and also q-CAR relations for q < -1: B ( f ) B * ( g ) + B * ( g ) B ( f ) = | q | N ⟨ f , g ⟩ I , where N is the number operator on a suitable Fock space ℱ q ( ) acting as Nx₁ ⊗ ⋯ ⊗ xₙ = nx₁ ⊗ ⋯ ⊗xₙ. Some applications to combinatorial problems are also given.

Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients

Kenichi Ito, Shu Nakamura (2012)

Annales de l’institut Fourier

We consider Schrödinger operators H on ℝ n with variable coefficients. Let H 0 = - 1 2 ▵ be the free Schrödinger operator and we suppose H is a “short-range” perturbation of H 0 . Then, under the nontrapping condition, we show that the time evolution operator: e - i t H can be written as a product of the free evolution operator e - i t H 0 and a Fourier integral operator W ( t ) which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators. These results...

Renormalization of exponential sums and matrix cocycles

Alexander Fedotov, Frédéric Klopp (2004/2005)

Séminaire Équations aux dérivées partielles

In this paper, we present a new point of view on the renormalization of some exponential sums stemming from number theory. We generalize this renormalization procedure to study some matrix cocycles arising in spectral problems of quantum mechanics

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