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Phosphatidylinositol bisphosphate (PIP2) directly regulates functions as diverse as the organization of the cytoskeleton, vesicular transport and ion channel activity. It is not known, however, whether dynamic changes in PIP2 levels have a regulatory role of physiological importance in such functions. Here, we show in both native cardiac cells and… (More)
We study existence and uniqueness of traveling fronts, and asymptotic speed of propagation for a non local reaction diffusion equation with spatial and genetic trait structure.
One of the objectives in the development of effective cancer therapy is induction of tumor-selective cell death. Toward this end, we have identified a small peptide that, when introduced into cells via a TAT cell-delivery system, shows a remarkably potent cytoxicity in a variety of cancer cell lines and inhibits tumor growth in vivo, whereas sparing normal… (More)
This paper is a continuation of our earlier work " [T. fractional Nirenberg problem, part I: blow up analysis and compactness of solutions, to appear in J. Eur. Math. Soc.] " , where compactness results were given on a fractional Nirenberg problem. We prove two existence results stated there. We also obtain a fractional Aubin inequality.
Making use of integral representations, we develop a unified approach to establish blow up profiles, compactness and existence of positive solutions of the conformally invariant equations P σ (v) = Kv n+2σ n−2σ on the standard unit sphere S n for all σ ∈ (0, n/2), where P σ is the intertwining operator of order 2σ. Finding positive solutions of these… (More)
We study a family of 3D models for the incompressible axisymmetric Euler and Navier–Stokes equations. The models are derived by changing the strength of the convection terms in the equations written using a set of transformed variables. The models share several regularity results with the Euler and Navier–Stokes equations, including an energy identity, the… (More)
In this paper, we study existence, regularity, classification, and asymptotical behaviors of solutions of some Monge-Ampère equations with isolated and line singularities. We classify all solutions of det ∇ 2 u = 1 in R n with one puncture point. This can be applied to characterize ellipsoids, in the same spirit of Serrin's overdetermined problem for the… (More)