Search results for "Theorem"
showing 10 items of 1250 documents
Nambu structures and super-theorem of Amitsur-Levitzki
2004
In this thesis, we establish new polynomial identities in a non commutative combinatorial framework. In the first part, we present new Nambu-Lie structures by classifying all (n-1)-structures in \R^n and we give a method for defining all-order brackets in Lie algebras. We are able to quantify one of our structures, thanks to standard polynomials and even Clifford algebras. In the second part of our work, we generalize the notion of standard polynomials to graded algebras, and we prove an Amitsur-Levitzki type theorem for the Lie superalgebras \osp(1,2n) inspired by Kostant's cohomological interpretation of the classical theorem. We give super versions of properties and results needed in Kos…
Geodesic flow of the averaged controlled Kepler equation
2008
A normal form of the Riemannian metric arising when averaging the coplanar controlled Kepler equation is given. This metric is parameterized by two scalar invariants which encode its main properties. The restriction of the metric to $\SS^2$ is shown to be conformal to the flat metric on an oblate ellipsoid of revolution, and the associated conjugate locus is observed to be a deformation of the standard astroid. Though not complete because of a singularity in the space of ellipses, the metric has convexity properties that are expressed in terms of the aforementioned invariants, and related to surjectivity of the exponential mapping. Optimality properties of geodesics of the averaged controll…
A new invariant-based method for building biomechanical behavior laws - Application to an anisotropic hyperelastic material with two fiber families
2013
Abstract In this article, we present a general constructive and original approach that allows us to calculate the invariants associated with an anisotropic hyperelastic material made of two families of collagen fibers. This approach is based on mathematical techniques from the theory of invariants: • Definition of the material symmetry group. • Analytical calculation of a set of generators using the Noether’s theorem. • Analytical calculation of an integrity basis. • Comparison between the proposed invariants and the classical ones.
On Gelfand-Mazur Theorem
2015
From a suitable extension of the notion of spectrum drew from normed algebra theory, it will be possible, among other things, to provide some generalizations of the well-known Gelfand-Mazur theorem. In this brief research report, we wish to pursue one of these, as achieved in I,4.
Quantifier elimination in the quasi-analytic framework
2012
We associate to every compact polydisk B [belonging to ] Rn an algebra CB of real functions defined in a neighborhood of B. The collection of these algebras is supposed to be closed under several operations, such as composition and partial derivatives. Moreover, if the center of B is the origin, we assume that the algebra of germs at the origin of elements of CB is quasianalytic (it does not contain any flat germ). We define with these functions the collection of C-semianalytic and C-subanalytic sets according to the classical process in real analytic geometry. Our main result is an analogue of Tarski-Seidenberg's usual result for these sets. It says that the sub-C-subanalytic sets may be d…
Synchronization and fluctuations for interacting stochastic systems with individual and collective reinforcement
2020
The Pólya urn is the paradigmatic example of a reinforced stochastic process. It leads to a random (non degenerated) time-limit. The Friedman urn is a natural generalization whose a.s. time-limit is not random anymore. In this work, in the stream of previous recent works, we introduce a new family of (finite) systems of reinforced stochastic processes, interacting through an additional collective reinforcement of mean field type. The two reinforcement rules strengths (one componentwise, one collective) are tuned through (possibly) different rates n −γ. In the case the reinforcement rates are like n −1 , these reinforcements are of Pólya or Friedman type as in urn contexts and may thus lead …
Statistics of transitions for Markov chains with periodic forcing
2013
The influence of a time-periodic forcing on stochastic processes can essentially be emphasized in the large time behaviour of their paths. The statistics of transition in a simple Markov chain model permits to quantify this influence. In particular the first Floquet multiplier of the associated generating function can be explicitly computed and related to the equilibrium probability measure of an associated process in higher dimension. An application to the stochastic resonance is presented.
Statistical consequences of the Devroye inequality for processes. Applications to a class of non-uniformly hyperbolic dynamical systems
2005
In this paper, we apply Devroye inequality to study various statistical estimators and fluctuations of observables for processes. Most of these observables are suggested by dynamical systems. These applications concern the co-variance function, the integrated periodogram, the correlation dimension, the kernel density estimator, the speed of convergence of empirical measure, the shadowing property and the almost-sure central limit theorem. We proved in \cite{CCS} that Devroye inequality holds for a class of non-uniformly hyperbolic dynamical systems introduced in \cite{young}. In the second appendix we prove that, if the decay of correlations holds with a common rate for all pairs of functio…
A Bayesian Reconstruction of a Historical Population in Finland, 1647–1850
2020
This article provides a novel method for estimating historical population development. We review the previous literature on historical population time-series estimates and propose a general outline to address the well-known methodological problems. We use a Bayesian hierarchical time-series model that allows us to integrate the parish-level data set and prior population information in a coherent manner. The procedure provides us with model-based posterior intervals for the final population estimates. We demonstrate its applicability by estimating the long-term development of Finlands population from 1647 onward and simultaneously place the country among the very few to have an annual popula…
Fixed point theorems for twisted (α,β)-ψ-contractive type mappings and applications
2013
The purpose of this paper is to discuss the existence and uniqueness of fixed points for new classes of mappings defined on a complete metric space. The obtained results generalize some recent theorems in the literature. Several applications and interesting consequences of our theorems are also given.