176 research outputs found
New formulas for decreasing rearrangements and a class of Orlicz-Lorentz spaces
Using a nonlinear version of the well known Hardy-Littlewood inequalities, we
derive new formulas for decreasing rearrangements of functions and sequences in
the context of convex functions. We use these formulas for deducing several
properties of the modular functionals defining the function and sequence spaces
and respectively, introduced earlier in
\cite{HKM} for describing the K\"othe dual of ordinary Orlicz-Lorentz spaces in
a large variety of cases ( is an Orlicz function and a {\it
decreasing} weight). We study these classes in the most general
setting, where they may even not be linear, and identify their K\"othe duals
with ordinary (Banach) Orlicz-Lorentz spaces. We introduce a new class of
rearrangement invariant Banach spaces which proves to
be the K\"othe biduals of the classes. In the case when the
class is a separable quasi-Banach space,
is its Banach envelope.Comment: 25 page
Asymptotically Hilbertian Modular Banach Spaces: Examples of Uncountable Categoricity
We give a criterion ensuring that the elementary class of a modular Banach
space E (that is, the class of Banach spaces, some ultrapower of which is
linearly isometric to an ultrapower of E) consists of all direct sums E\oplus_m
H, where H is an arbitrary Hilbert space and \oplus_m denotes the modular
direct sum. Also, we give several families of examples in the class of Nakano
direct sums of finite dimensional normed spaces that satisfy this criterion.
This yields many new examples of uncountably categorical Banach spaces, in the
model theory of Banach space structures.Comment: 20 page
Ultrapowers of Köthe function spaces
The ultrapowers, relative to a fixed ultrafilter, of all the Köthe function spaces with non trivial concavity over the same measure space can be represented as Köthe function spaces over the same (enlarged) measure space. The existence of a uniform homeomorphism between the unit spheres of two such Köthe function spaces is reproved
Une démarche pour l'enseignement des réseaux et de la communication
Cet article se propose de faire le point sur l'enseignement de l'informatique dans le domaine des réseaux. Il s'appuie sur nos expériences pédagogiques post-baccalauréat dans les filières informatiques ( BTS, IUT, MIAG, MAITRISE, DEA, DESS... ).Nous décrivons dans une première partie le « concept réseau » et son rôle prépondérant dans l'informatique d'aujourd'hui. Face aux problèmes posés par ce domaine complexe, nous énonçons quelques « règles d'or » pour une approche progressive et applicative conduisant à expérimenter des systèmes de communications locaux.Nous exposons notre démarche didactique pour l'une des règles énoncées : « Apprendre la communication ». Nous l'illustrons à travers l'utilisation d'un logiciel d'enseignement assisté par ordinateur. Ce produit réalisé par notre équipe concerne le R.N.I.S. (Réseau Numérique à Intégration de Service). Il permet à un étudiant de se familiariser avec les concepts, les services, l'architecture et la mise en oeuvre d'un réseau R.N.I.S
On complemented subspaces of rearrangement invariant function spaces
A necessary and sufficient condition is given for a r.i. function space to contain a complemented isomorphic copy of
2-positive contractive projections on noncommutative -spaces
We prove the first theorem on projections on general noncommutative
-spaces associated with non-type I von Neumann algebras where . This is the first progress on this topic since the seminal
work of Arazy and Friedman [Memoirs AMS 1992] where the problem of the
description of contractively complemented subspaces of noncommutative
-spaces is explicitly raised. We show that the range of a
2-positive contractive projection on an arbitrary noncommutative
-space is completely order and completely isometrically
isomorphic to some noncommutative -space. This result is sharp
and is even new for Schatten spaces . Our approach relies on non tracial
Haagerup's noncommutative -spaces in an essential way, even in
the case of a projection acting on a Schatten space and is unrelated to the
methods of Arazy and Friedman.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1909.00391,
arXiv:1910.1389
Modeling the effect of soil meso- and macropores topology on the biodegradation of a soluble carbon substrate
Soil structure and interactions between biotic and abiotic processes are increasingly recognized as important for explaining the large uncertainties in the outputs of macroscopic SOM decomposition models. We present a numerical analysis to assess the role of meso- and macropore topology on the biodegradation of a soluble carbon substrate in variably water saturated and pure diffusion conditions . Our analysis was built as a complete factorial design and used a new 3D pore-scale model, LBioS, that couples a diffusion Lattice-Boltzmann model and a compartmental biodegradation model. The scenarios combined contrasted modalities of four factors: meso- and macropore space geometry, water saturation, bacterial distribution and physiology. A global sensitivity analysis of these factors highlighted the role of physical factors in the biodegradation kinetics of our scenarios. Bacteria location explained 28% of the total variance in substrate concentration in all scenarios, while the interactions among location, saturation and geometry explained up to 51% of it
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