相关论文: Euler-Poincar'e functions
We prove a version of Poincar\'e's polyhedron theorem whose requirements are as local as possible. New techniques such as the use of discrete groupoids of isometries are introduced. The theorem may have a wide range of applications and can…
We study Euler-Poincare systems (i.e., the Lagrangian analogue of Lie-Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler-Poincare equations for a parameter dependent Lagrangian…
We review the construction and applications of exactly Poincar\'e invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincar\'e group on few-particle Hilbert…
Entropy-conservative numerical flux functions can be used to construct high-order, entropy-stable discretizations of the Euler and Navier-Stokes equations. The purpose of this short communication is to present a novel family of such…
In this paper we extend and Poincare dualize the concept of Euler structures, introduced by Turaev for manifolds with vanishing Euler-Poincare characteristic, to arbitrary manifolds. We use the Poincare dual concept, co-Euler structures, to…
In this note, we develop a theory of Euler-Poincare reduction for discrete Lagrangian field theories. We introduce the concept of Euler-Poincare equations for discrete field theories, as well as a natural extension of the Moser-Veselov…
In this paper we consider non-linear differential equations which are closely related to the generating functions of Frobenius-Euler polynomials. From our non-linear differential equations, we derive some new identities between the sums of…
In this article we obtain new irrationality measures for values of functions which belong to a certain class of hypergeometric functions including shifted logarithmic functions, binomial functions and shifted exponential functions. We…
We study Poincar\'e Duality in the context of abstract 6-functor formalisms. In particular, we give a small and simple list of assumptions that implies Poincar\'e Duality. As an application, we give new uniform (and essentially formal)…
A review is given of some recently obtained results on analytic contractions of Lie algebras and Lie groups and their applications to special function theory.
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
We establish analogues in the context of group actions or group representations of some classical problems and results in additive combinatorics of groups. We also study the notion of left invariant submodular function defined on power sets…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
The results presented in this paper are refinements of some results presented in a previous paper. Three such refined results are presented. The first one relaxes one of the basic hypotheses assumed in the previous paper, and thus extends…
Let $ P \colon \mathbb{C} \to \mathbb{C} $ be an entire function. A Poincar\'e function $ L \colon \mathbb{C} \to \mathbb{C} $ of $ P $ is the entire extension of a linearising coordinate near a repelling fixed point of $ P $. We propose…
In this paper, a formula for the solution of the Poincar\'{e} functional equation in algebra of formal power series and its application to continuous iteration are presented.
Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations…
We introduce and study functorial and combinatorial constructions concerning equivariant Burnside groups.
A function group is a finitely generated Kleinian group with an invariant connected component of its region of discontinuity. An extended function group is a finitely generated extended Kleinian group that contains orientation reversing…
We generalize the classical construction principles of infinite-dimensional real (and complex) Lie groups to the case of Lie groups over non-discrete topological fields. In particular, we discuss linear Lie groups, mapping groups, test…