Dans cette note, on présente l’énoncé et les principales idées de la démonstration d’un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie. Ce résultat est un analogue quasi-hamiltonien du théorème de O’Shea et Sjamaar dans le cadre hamiltonien usuel. On démontre que l’image par l’application moment du lieu des points fixes d’une involution renversant la 2-f...

Parry showed that every continuous transitive piecewise monotonic map τ of the interval is conjugate (by an order preserving homeomorphism) to a uniformly piecewise linear map T (i.e., one with slopes ±s). In the current article, it is shown that the map T is unique. This is proven by showing that any order-preserving conjugacy between two continuous transitive uniformly piecewise linear maps i...

A beam line map construction method for linear and circular high-energy colliders is described which avoids truncated power-series maps through systematic use of a two-term Baker-Campbell-Hausdorff (BCH) formula in combination with similarity transformations. The beam line map ultimately assumes the form of a product of a linear map and a single-exponential Lie-operator map. The method i) provi...

The concept of a coset-preserving skew-morphism is a generalization of the widely studied t-balanced skew-morphisms of regular Cayley maps which are in turn generalizations of group automorphisms. In case of abelian groups, all skew-morphisms of regular Cayley maps are roots of coset-preserving skew-morphisms, and therefore, classification of cosetpreserving skew-morphisms of finite abelian gro...

We give a description of a weakly continuous rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps. We also show that a rank preserving map can be implemented by only one type if the corresponding lat...

We give a description of a rank preserving map on a reflexive algebra on complex Hilbert space with commutative completely distributive subspace lattice. We show that the implementation of a rank preserving map can be described by the combination of two different types of maps. We also show that a rank preserving map can be implemented by only one type if the corresponding lattice is irreducibl...

An explicit character formula is established for any strongly generic nite-dimensional irreducible g-module, g being an arbitrary nite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible nite-dimensional g-module, i.e. such that its highest weight is far enough from the walls of the Weyl chambers....

Let G be a simple algebraic group in defining characteristic p>0, and let V an irreducible G-module which is the tensor product of exactly two non-trivial modules. We obtain criterion for to have zero weight. In addition, we provide uniform representation Lie algebra over complex numbers multiple prescribed fundamental

in this paper,  we introduce  the notion of $m$-fuzzifying interval spaces, and discuss the relationship between $m$-fuzzifying interval spaces and $m$-fuzzifying convex structures.it is proved that  the category  {bf mycsa2}  can be embedded in  the category  {bf  myis}  as a reflective subcategory, where  {bf mycsa2} and   {bf  myis} denote  the category of $m$-fuzzifying convex structures of...

We introduce implicit zero-knowledge arguments (iZK) and simulation-sound variants thereof (SSiZK); these are lightweight alternatives to zero-knowledge arguments for enforcing semi-honest behavior. Our main technical contribution is a construction of efficient two-flow iZK and SSiZK protocols for a large class of languages under the (plain) DDH assumption in cyclic groups in the common referen...