Noncoercive convection–diffusion elliptic problems with Neumann boundary conditions

We study the existence and uniqueness of solutions of the convective–diffusive elliptic equation

Molecular dynamics simulation in aqueous solution of N-methylazetidinone as a model of β-lactam antibiotics

In this article, we analyze the results of a molecular dynamics simulation in aqueous solution of the N-methylazetidinone molecule, often used to model β-lactam antibiotics. The radial distribution functions (RDFs) corresponding to the most interesting atoms, in terms of reactivity, are presented. We focus our study on the effect of a polar environment on the molecule. The solvent structure around the system is compared to the structure of β-lactam-water complexes, as obtained in a previous study of reaction mechanisms for the neutral and alkaline hydrolyses of N-methylazetidinone. Two types of complexes have been considered which are related to different hydrolysis mechanisms having similar energy barriers at the rate-limiting step of the reaction path. In the first type, the β-lactam-water interaction takes place through the oxygen carbonyl atom and there is agreement between the maxima of the RDFs obtained here and the ab initio structure of the complexes previously reported. In the second type, the interaction takes place through the nitrogen atom and we do not predict a coordination layer around the β-lactam nitrogen atom. The results suggest that in aqueous solution hydrolysis of the carbonyl group is the most probable starting point for the overall hydrolysis reaction. Some discussion on the use of cluster models to represent the solvent effect is included. Received: 29 July 1998 / Accepted: 13 October 1998 / Published online: 1 February 1999     

Modeling β-lactam interactions in aqueous solution through combined quantum mechanics–molecular mechanics methods

In this article, we have carried out a series of theoretical computations intended to analyze the interactions of β-lactam compounds in aqueous solution. The final aim is to rationalize the influence of the medium on β-lactam antibiotics reactivity. In particular, the hydrolysis reaction has been studied because of the considerable interest due to its relationship with resistance mechanisms developed by bacteria. The study is extended to the simplest β-lactam molecule, propiolactam or 2-azetidinone, and to the corresponding hydroxylated complex (resulting from the addition of a hydroxyl anion to the carbonyl group) that plays a crucial role in hydrolysis processes. Molecular Dynamics simulations have been carried out using a hybrid quantum mechanics–molecular mechanics potential: the solute is described using the density functional theory, whereas water solvent molecules are treated classically. This represents a sophisticated computational level which, compared to usual force-field simulations, has the advantage of allowing a detailed analysis of solute's electronic properties. The discussion of results is focused on the role played by solute–solvent hydrogen bonds and solvent fluctuations on solute's structure. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1401–1411, 1999     

Removable singularities of some strongly nonlinear elliptic equations

Let Ω be some open subset of ?^N containing 0 and Ω′=Ω?{0}. If g is a continuous function from ? × ? into ? satisfying some power like growth assumption, then any u∈L _loc ^∞ (Ω′) satisfying $$\begin{array}{*{20}c} { - div (Du \left| {Du} \right|^{p - 2} ) + g(.,u) = 0} & {in \mathcal{D}'(\Omega ')} \\ \end{array} $$ , remains bounded in Ω and satisfies the equation in D'(Ω). We give extensions when the singular set is some compact submanifold of Ω. When g is bounded below on ?⁺ and above on ?^?, then we prove that any subset Σ with 1-capacity zero is a removable singularity for a function u∈L _loc ^∞ (ω?Σ) satisfying $$\begin{array}{*{20}c} { - div \left( {\frac{{Du}}{{\sqrt {1 + \left| {Du} \right|^2 } }}} \right) + g(.,u) = 0} & {in \mathcal{D}'(\Omega - \Sigma )} \\ \end{array} $$ .     

A geometric algorithm for winding number computation with complexity analysis

Many methods to compute the winding number of plane curves have been proposed, often with the aim of counting the number of roots of polynomials (or, more generally, zeros of analytic functions) inside some region by using the principle of argument. In this paper we propose another method, which are not based on numerical integration, but on discrete geometry. We give conditions that ensure its correct behavior, and a complexity bound based on the distance of the curve to singular cases. Besides, we provide a modification of the algorithm that detects the proximity to a singular case of the curve. If this proximity is such that the number of operations required grows over certain threshold, set by the user, the modified algorithm returns without winding number computation, but with information about the distance to singular case. When the method is applied to polynomials, this information refers to the localization of the roots placed near the curve.     

Reversibility and diffusion in mandelythiamin decarboxylation. Searching dynamical effects in decarboxylation reactions

Decarboxylation of mandelylthiamin in aqueous solution is analyzed by means of quantum mechanics/molecular mechanics simulations including solvent effects. The free energy profile for the decarboxylation reaction was traced, assuming equilibrium solvation, while reaction trajectories allowed us to incorporate nonequilibrium effects due to the solvent degrees of freedom as well as to evaluate the rate of the diffusion process in competition with the backward reaction. Our calculations that reproduce the experimental rate constant show that decarboxylation takes place with a non-negligible free energy barrier for the backward reaction and that diffusion of carbon dioxide is very fast compared to the chemical step. According to these findings catalysts would not act by preventing the backward reaction.     

Weak and smooth solutions for a fractional Yamabe flow: The case of general compact and locally conformally flat manifolds

As a counterpart of the classical Yamabe problem, a fractional Yamabe flow has been introduced by Jin and Xiong (2014) on the sphere. Here we pursue its study in the context of general compact smooth manifolds with positive fractional curvature. First, we prove that the flow is locally well posed in the weak sense on any compact manifold. If the manifold is locally conformally flat with positive Yamabe invariant, we also prove that the flow is smooth and converges to a constant fractional curvature metric. We provide different proofs using extension properties introduced by Chang and González (2011) for the conformally covariant fractional order operators.