918 research outputs found
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 version of
the 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 , we prove a Nash type inequality for the fractional
powers of . Under some assumptions, we give ultracontractivity
bounds for the semigroup generated by .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 of a symmetric contracting semigroup then it
implies a corresponding super-Poincar\'e inequality for with any
Bernstein function . We also study the converse statement. We deduce similar
results for the Nash-type inequality. Our results applied to fractional powers
of and to 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
Gauthier, C., Desbiens, J.-F., MaIo, A., Martineau, S. et Simard, D. (dir.). Pour une théorie de la pédagogie : recherches contemporaines sur le savoir des enseignants. Paris / Bruxelles : De Boeck Université.
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 , with $
La médiation des savoirs auprÚs des enseignants inuit en formation
Cet article concerne la formation des enseignants inuit dans le cadre dâun projet de partenariat entre une universitĂ© et deux communautĂ©s du Nunavik. Nous prĂ©sentons dâabord le contexte historique et social de la scolarisation chez les Inuit. Nous mettrons ensuite en Ă©vidence la rĂ©alitĂ© interculturelle et trilingue de la formation et du travail de lâenseignant inuit. Enfin, Ă lâaide des concepts de «cognition situĂ©e» et «rapport au savoir», nous discuterons de notre pratique de formation dans la perspective de la rĂ©ussite 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 âsituated cognitionâ and ârelation to knowledge,â 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 âwabi-sabi mathematicsâ 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
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