New Proofs of Davies-Simon's Theorems about Ultracontractivity and Logarithmic Sobolev Inequalities related to Nash Type Inequalities

We present new proofs of two theorems of E.B. Davies and B. Simon about ultracontractivity property for of semigroups of operators and logarithmic Sobolev inequalities with parameter (LSIWP for short) satisfied by the generator of the semigroup. In our proof, we use neither the $L^p$ version of the $LSIWP$ nor Stein's interpolation. Our tool is Nash type inequality. We also present new results. In particular, we show that Nash type inequality and LSIWP are equivalent.Comment: 31 page

Nash type inequalities for fractional powers of non-negative self-adjoint operators

Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator $A$, we prove a Nash type inequality for the fractional powers $A^{\alpha}$ of $A$. Under some assumptions, we give ultracontractivity bounds for the semigroup $(T_{t,{\alpha}})$ generated by $-A^{\alpha}$.Comment: January,31 (2002). Submitte

Super-Poincar\'e and Nash-type inequalities for Subordinated Semigroups

We prove that if a super-Poincar\'e inequality is satisfied by an infinitesimal generator $-A$ of a symmetric contracting semigroup then it implies a corresponding super-Poincar\'e inequality for $-g(A)$ with any Bernstein function $g$. We also study the converse statement. We deduce similar results for the Nash-type inequality. Our results applied to fractional powers of $A$ and to $\log(I+A)$ and thus generalize some results of Biroli and Maheux, and Wang 2007. We provide several examples.Comment: submitted. 23p. no figure. Title slightly changed. Results and text improve

Alien Registration- Maheux, Florence (Auburn, Androscoggin County)

https://digitalmaine.com/alien_docs/30523/thumbnail.jp

Weighted Nash Inequalities

Nash or Sobolev inequalities are known to be equivalent to ultracontractive properties of Markov semigroups, hence to uniform bounds on their kernel densities. In this work we present a simple and extremely general method, based on weighted Nash inequalities, to obtain non-uniform bounds on the kernel densities. Such bounds imply a control on the trace or the Hilbert-Schmidt norm of the heat kernels. We illustrate the method on the heat kernel on \dR naturally associated with the measure with density $C_a\exp(-|x|^a)$, with $

La médiation des savoirs auprès des enseignants inuit en formation

Cet article concerne la formation des enseignants inuit dans le cadre d’un projet de partenariat entre une université et deux communautés du Nunavik. Nous présentons d’abord le contexte historique et social de la scolarisation chez les Inuit. Nous mettrons ensuite en évidence la réalité interculturelle et trilingue de la formation et du travail de l’enseignant inuit. Enfin, à l’aide des concepts de «cognition située» et «rapport au savoir», nous discuterons de notre pratique de formation dans la perspective de la réussite scolaire des Inuit.This article is about the training of Inuit teachers in a partnership project between a university and two Nunavik communities. We first identify the historical and social context of schooling among the Inuit. Then we present the intercultural and trilingual reality of Inuit teacher training and work. Finally, using the concepts of “situated cognition” and “relation to knowledge,” we discuss our training experience from the perspective of Inuit academic achievement

Wabi-Sabi Mathematics

Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabi-sabi mathematics” by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematic

Alien Registration- Pareau, Anntoinette (Auburn, Androscoggin County)

https://digitalmaine.com/alien_docs/30522/thumbnail.jp