New crystal structures of fluorinated α-aminophosphonic acid analogues of phenylglycine

The four novel phosphonic acid analogues of phenylglycine with various substituents in phenyl ring (mostly fluorine atoms) have been synthesized by using procedure of amidoalkylation of phosphorus trichloride with aromatic aldehydes and acetamide. The NMR, ESI-MS spectroscopy, and single-crystal X-Ray diffraction methods were used to characterize unusual structures: the amino-(4-trifluoromethylbenzyl)-(1), amino-(3,4-difluorobenzyl)-(2), amino-(2,4,6-trifluorobenzyl)-(3), and amino-(2-fluoro-4-hydroxybenzyl)-(4) phosphonic acids. Since the α-aminophosphonates have a potential for biological activity and could be used as building blocks in medicinal chemistry, it is important to know their detail crystal structures and properties which, in turn, may extend the knowledge on their interaction with physiologic receptors.

     

Convergence of a finite element method for non-parametric mean curvature flow

Summary. Convergence for the spatial discretization by linear finite elements of the non-parametric mean curvature flow is proved under natural regularity assumptions on the continuous solution. Asymptotic convergence is also obtained for the time derivative which is proportional to mean curvature. An existence result for the continuous problem in adequate spaces is included. Received September 30, 1993     

Das Verhalten von Lösungen semilinearer elliptischer Systeme an Ecken eines Gebietes

Ohne Zusammenfassung     

Finite element approximations to surfaces of prescribed variable mean curvature

We give an algorithm for finding finite element approximations to surfaces of prescribed variable mean curvature, which span a given boundary curve. We work in the parametric setting and prove optimal estimates in the H¹ norm. The estimates are verified computationally.     

Correction to: New crystal structures of fluorinated α-aminophosphonic acid analogues of phenylglycine

Structural Chemistry - Corrections are needed to the original version of this article.     

The discrete plateau problem: Convergence results

We solve the problem of finding and justifying an optimal fully discrete finite element procedure for approximating minimal, including unstable, surfaces. In a previous paper we introduced the general framework and some preliminary estimates, developed the algorithm and give the numerical results. In this paper we prove the convergence estimate.

     

An algorithm for evolutionary surfaces

Summary An Algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of Poisson problems on a series of surfaces. This gives a new method to solve Plateau's problem forH-surfaces.     

A fully discrete numerical scheme for weighted mean curvature flow

Summary. We analyze a fully discrete numerical scheme approximating the evolution of n–dimensional graphs under anisotropic mean curvature. The highly nonlinear problem is discretized by piecewise linear finite elements in space and semi–implicitly in time. The scheme is unconditionally stable und we obtain optimal error estimates in natural norms. We also present numerical examples which confirm our theoretical results. Received October 2, 2000 / Published online July 25, 2001