Chaotic Kabanov formula for the Azéma martingales

We derive the chaotic expansion of the product of nth- and first-order multiple stochastic integrals with respect to certain normal martingales. This is done by application of the classical and quantum product formulae for multiple stochastic integrals. Our approach extends existing results on chaotic calculus for normal martingales and exhibits properties, relative to multiple stochastic integrals, polynomials and Wick products, that characterize the Wiener and Poisson processes.

Des biens communaux et de la police rurale et forestière. [Avec une notice historique sur la vie et les ouvrages de l'auteur (3e édition corrigée et augmentée) / par le président Henrion de Pansey ; par M. L. Rozet]

Comprend : Notice historique sur la vie et les ouvrages de M. Henrion de Pansey

De la compétence des juges de paix (10e édition) / par M. Henrion de Pansey,...

Comprend : Notice historique sur la vie et les ouvrages de M. Henrion de Pansey

[Pise. Chiesa di San Nicola]

Référence bibliographique : Weigert, 352

Notch signaling is a direct determinant of keratinocyte growth arrest and entry into differentiation.

The role of Notch signaling in growth/differentiation control of mammalian epithelial cells is still poorly defined. We show that keratinocyte-specific deletion of the Notch1 gene results in marked epidermal hyperplasia and deregulated expression of multiple differentiation markers. In differentiating primary keratinocytes in vitro endogenous Notch1 is required for induction of p21WAF1/Cip1 expression, and activated Notch1 causes growth suppression by inducing p21WAF1/Cip1 expression. Activated Notch1 also induces expression of 'early' differentiation markers, while suppressing the late markers. Induction of p21WAF1/Cip1 expression and early differentiation markers occur through two different mechanisms. The RBP-Jkappa protein binds directly to the endogenous p21 promoter and p21 expression is induced specifically by activated Notch1 through RBP-Jkappa-dependent transcription. Expression of early differentiation markers is RBP-Jkappa-independent and can be induced by both activated Notch1 and Notch2, as well as the highly conserved ankyrin repeat domain of the Notch1 cytoplasmic region. Thus, Notch signaling triggers two distinct pathways leading to keratinocyte growth arrest and differentiation.

Les balades servant à l'histoire. Reveuës & Augmentées.

[Mazarinade. 1652]