Search results for "PSC"

Cytoprotective effect of NMDA receptor antagonists on prion protein (PrionSc)-induced toxicity in rat cortical cell cultures

1993

Rat cortical cells were incubated with the Scrapie prion protein, PrionSc. At concentrations of 3 ng/ml of PrionSc and higher, the viability of the cells decreased significantly after a 12-h incubation period. Simultaneously, the degree of DNA fragmentation increased. In control experiments with antibodies against PrionSc, PrionSc lost its deleterious effect on neurons. PrionSc did not affect the viability of astrocytes. Drugs known to block NMDA receptor channels, such as memantine (1-amino-3,5-dimethyl-adamantane) (Mem), its analogue 1-N-methylamino-3,5-dimethyl-adamantane as well as (+)-5-methyl-10,11-dihydro-5H-dibenzo[a,d]cyclohepten-5,10-imine maleate (MK-801) prevented the effect of …

Unexpected synthesis by a non-classical Pschorr reaction of 3,5-dimethyl-1-phenyl-1,5-dihydro-4H-pyrazolo[4,3-c]quinolin-4-one, with binding affinity…

2014

The reaction of the diazonium salt 12 derived from N-(2-aminophenyl)-N,3-dimethyl-1-phenyl-1H-pyrazole-5-carboxamide with copper sulfate and sodium chloride in the presence of ascorbic acid afforded the unexpected products 3,5-dimethyl-1-phenyl-1,5-dihydro-4H-pyrazolo[4,3-c]¬quinolin-4-one (17) and N-methyl-2-(3-methyl-1-phenyl-1H-pyrazol-5-yl)aniline (19), accompanied by N-(2-chlorophenyl)-N,3-dimethyl-1-phenyl-1H-pyrazole-5-carboxamide (18). Products 17 and 19 are formed via a non-classical Pschorr reaction. The formation of 17 represents an alternative to the literature synthesis of this biologically active compound. The molecular structure of 18 was confirmed by single-crystal X-ray ana…

Harnack's inequality for p-harmonic functions via stochastic games

2013

We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipsc...

Pełczyński space is isomorphic to the Lipschitz free space over a compact set

2019

International audience

2020

Abstract This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main contribution will be a consequence of the following result: there exists a C ∞ -hypersurface S without characteristic points that has uncountably many pairwise non-isomorphic tangent groups on every positive-measure subset. The example is found in a Carnot group of topological dimension 8, it has Hausdorff dimension 12 and so we use on it the Hausdorff measure H 12 . As a consequence, we show that any Lipschitz map defined on a subset of a Carnot group of Hausdorf…

Principal eigenvalue of a very badly degenerate operator and applications

2007

Abstract In this paper, we define and investigate the properties of the principal eigenvalue of the singular infinity Laplace operator Δ ∞ u = ( D 2 u D u | D u | ) ⋅ D u | D u | . This operator arises from the optimal Lipschitz extension problem and it plays the same fundamental role in the calculus of variations of L ∞ functionals as the usual Laplacian does in the calculus of variations of L 2 functionals. Our approach to the eigenvalue problem is based on the maximum principle and follows the outline of the celebrated work of Berestycki, Nirenberg and Varadhan [H. Berestycki, L. Nirenberg, S.R.S. Varadhan, The principal eigenvalue and maximum principle for second-order elliptic operator…

A min-max principle for non-differentiable functions with a weak compactness condition

2009

A general critical point result established by Ghoussoub is extended to the case of locally Lipschitz continuous functions satisfying a weak Palais-Smale hypothesis, which includes the so-called non-smooth Cerami condition. Some special cases are then pointed out.

Multiple solutions for a Neumann-type differential inclusion problem involving the p(.)-Laplacian

2012

Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian.

Universal differentiability sets and maximal directional derivatives in Carnot groups

2019

We show that every Carnot group G of step 2 admits a Hausdorff dimension one `universal differentiability set' N such that every real-valued Lipschitz map on G is Pansu differentiable at some point of N. This relies on the fact that existence of a maximal directional derivative of f at a point x implies Pansu differentiability at the same point x. We show that such an implication holds in Carnot groups of step 2 but fails in the Engel group which has step 3.

On a class of compactly epi-Lipschitzian sets

2003

The paper is devoted to the study of the so-called compactly epi-Lipschitzian sets. These sets are needed for many aspects of generalized differentiation, particulary for necessary optimality conditions, stability of mathematical programming problems and calculus rules for subdifferentials and normal cones. We present general conditions under which sets defined by general constraints are compactly epi-Lipschitzian. This allows us to show how the compact epi-Lipschitzness properties behave under set intersections.