Stereochemistry of cercosporin

The absolute configuration of the asymmetric carbons and the axial chirality of the natural mold metabolite cercosporin (from $\text{Cercospora sp}$.) have been established on the basis of X-ray analysis and chemical reactions. The results confirm the inherent dissymmetry of the perylenequinone ring, the twisting of which gives rise to the diastereoisomer isocercosporin. The energy barrier for the conversion of cercosporin into isocercosporin has been evaluated.     

Infinitesimal 2-braidings and differential crossed modules

We categorify the notion of an infinitesimal braiding in a linear strict symmetric monoidal category, leading to the notion of a (strict) infinitesimal 2-braiding in a linear symmetric strict monoidal 2-category. We describe the associated categorification of the 4-term relations, leading to six categorified relations. We prove that any infinitesimal 2-braiding gives rise to a flat and fake flat 2-connection in the configuration space of n particles in the complex plane, hence to a categorification of the Knizhnik–Zamolodchikov connection. We discuss infinitesimal 2-braidings in a certain monoidal 2-category naturally assigned to every differential crossed module, leading to the notion of a symmetric quasi-invariant tensor in a differential crossed module. Finally, we prove that symmetric quasi-invariant tensors exist in the differential crossed module associated to Wagemann's version of the String Lie-2-algebra. As a corollary, we obtain a more conceptual proof of the flatness of a previously constructed categorified Knizhnik–Zamolodchikov connection with values in the String Lie-2-algebra.     

A mean value theorem for metric spaces

We present a form of the Mean Value Theorem (MVT) for a continuous function f between metric spaces, connecting it with the possibility to choose the relation of f in a homeomorphic way. We also compare our formulation of the MVT with the classic one when the metric spaces are open subsets of Banach spaces. As a consequence, we derive a version of the Mean Value Propriety for measure spaces that also possesses a compatible metric structure.     

Product Markovian Quantization of a Diffusion Process with Applications to Finance

Methodology and Computing in Applied Probability - We introduce a new methodology for the quantization of the Euler scheme for a d-dimensional diffusion process. This method is based on a Markovian...     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

W01,1 solutions in some borderline cases of Calderon–Zygmund theory

In this paper we study the existence of $W_0^{1,1}(\Omega )$ distributional solutions of Dirichlet problems whose simplest example is$\{\begin{array}{cc}?\mathrm{div}\left({|\mathrm{?}u|}^{p?2}\mathrm{?}u\right)=f(x),\hfill & \text{in}\Omega ;\hfill \\ u=0,\hfill & \text{on}?\Omega .\hfill \end{array}$     

Two-dimensional incompressible viscous flow around a small obstacle

In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity ω₀ and the circulation γ of the initial flow around the obstacle. We prove that, if γ is sufficiently small, the limit flow satisfies the full-plane Navier–Stokes system, with initial vorticity ω₀ + γδ, where δ is the standard Dirac measure. The result should be contrasted with the corresponding inviscid result obtained by the authors in Iftimie et al. (Comm. Part. Differ. Eqn. 28, 349–379 (2003)), where the effect of the small obstacle appears in the coefficients of the PDE and not only in the initial data. The main ingredients of the proof are L ^p − L ^q estimates for the Stokes operator in an exterior domain, a priori estimates inspired on Kato’s fixed point method, energy estimates, renormalization and interpolation.     

Existence of a Weak Solution in L p to the Vortex-Wave System

The vortex-wave system is a coupling of the two-dimensional vorticity equation with the point-vortex system. It is a model for the motion of a finite number of concentrated vortices moving in a distributed vorticity background. In this article, we prove existence of a weak solution to this system with an initial background vorticity in L ^p , p>2, up to the time of first collision of point vortices.