A5034803508- Nonlinear Waves and Solitons
- Advanced Topics in Algebra
- Algebraic structures and combinatorial models
- Homotopy and Cohomology in Algebraic Topology
- Geometric Analysis and Curvature Flows
- Multi-Criteria Decision Making
- Advanced Operator Algebra Research
- Advanced Algebra and Geometry
- Advanced Numerical Analysis Techniques
- Geometric and Algebraic Topology
- Data Management and Algorithms
- Geometry and complex manifolds
- Rough Sets and Fuzzy Logic
- Advanced Algebra and Logic
- Stability and Controllability of Differential Equations
- Advanced Differential Geometry Research
- Algebraic Geometry and Number Theory
- Mathematical and Theoretical Analysis
- Nonlinear Photonic Systems
- Mathematical Analysis and Transform Methods
- advanced mathematical theories
- Advanced Topology and Set Theory
- Mathematical Dynamics and Fractals
- Quantum chaos and dynamical systems
- Optimization and Variational Analysis
Université d'Angers
2015-2024
Laboratoire Angevin de Recherche en Mathématiques
2013-2024
Hôpital Jeanne d'Arc
2013-2024
Centre National de la Recherche Scientifique
2018-2024
Institut für Angewandte Statistik
2002-2007
Université Clermont Auvergne
2002-2006
Laboratoire de Mathématiques
2000-2002
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We consider two principal bundles of embeddings with total space E m b ( M , N ) structure groups D i f and + where is the orientation preserving diffeomorphisms. The aim this paper to describe group tangent bundle base manifolds: B = / from various properties described, an adequate seems be a Fourier integral operators, which carefully studied. It main goal analyze group, central extension diffeomorphisms by pseudo-differential operators slightly different one developped in mathematical...
In this paper, we start from an extension of the notion holonomy on diffeological bundles, reformulate regular Lie group or Frölicher groups, state Ambrose–Singer theorem that enlarges one stated in [J.-P. Magnot, Structure groups and infinite dimensions, Bull. Sci. Math.128 (2004) 513–529], conclude with a differential geometric treatment KP hierarchy. The examples are studied principally those obtained by enlarging some graded (Lie) algebras such as formal q-series quantum algebra...
Using weighted traces which are linear functionals of the type [Formula: see text] defined on whole algebra (classical) pseudo-differential operators (P.D.Os) and where Q is some admissible invertible elliptic operator, we investigate geometry loop groups in light cohomology operators. We set up a geometric framework to study class infinite dimensional manifolds recover results groups, using again traces. Along way, properties extensions Radul Schwinger cocycles with help
Abstract We describe a framework for random pairwise comparisons matrices, inspired by selected constructions related to the so called inconsistency reduction of (PC) matrices. In order build up structures on set (deterministic) PC matrices non-reciprocal is completed. Basic concepts such as indices and geometric mean method are extended completed new notions which seem useful us. Two procedures (random) sketched, based well-known existing objects, fiber bundle-like decomposition proposed.
We establish a rigorous link between infinite-dimensional regular Frölicher Lie groups built out of non-formal pseudodifferential operators and the Kadomtsev-Petviashvili hierarchy.We introduce (parameter-depending) version hierarchy on group series odd-class operators.We solve its corresponding Cauchy problem, we dressing operator our action diffeomorphisms Sato-like jet spaces.In appendix, describe Fourier integral in which this correspondence seems to take place.Also, motivated by...
We show that a group of diffeomorphisms $\D$ on the open unit interval $I,$ equipped with topology uniform convergence any compact set derivatives at order, is non regular: exponential map not defined for some path Lie algebra. this result extends to finite dimensional, manifold $M.$
Mulase solved the Cauchy problem of Kadomtsev-Petviashvili (KP) hierarchy in an algebraic category "Solvability super KP equation and a generalization Birkhoff decomposition" (Inventiones Mathematicae, 1988), making use delicate factorization infinite-dimensional group formal pseudodifferential operators infinite order.We prove Mulase's theorem smooth setting pseudo-differential with coefficients (non-commutative) algebra equipped valuation.As application, we solve initial value for using...
The aim of this paper is to examine how people perceive correspondence between the 5-item Likert scale and percentage (the LS-PS thereinafter). Are all five items equidistant? Do use same when evaluating different objects? men women different? from countries / cultures method study was a questionnaire with 661 participating respondents altogether Czech Republic, Ecuador, France. results indicate that neither equidistant, nor symmetrical. Furthermore, there are (highly) statistically...
Abstract We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, are currently used to prove explicitly existence weak solutions functional equations. describe framework, highlight several examples and how two well-known proofs fit with our setting. The first one is a re-interpretation classical proof an implicit functions theorem inverse limit branch setting, for which setting enables us state without additional norm...
We describe a mathematical link between aspects of information theory, called pairwise comparisons, and discretized gauge theories. The is made by the notion holonomy along edges simplex. This correspondence leads to open questions in both fields.
We describe a smooth structure, called Fr\"olicher space, on CW complexes and spaces of triangulations. This structure enables differential methods for e.g. minimization functionnals. As an application, we exhibit how optimized triangulation can be obtained in order to solve standard PDE.