Synthesis of 12-Membered and 13-Membered Sulfur-Containing Lactones by Homolytic Macrocyclization of Mercaptoacetic Esters with Alkynes

Starting from mercaptoacetic acid esters of 1,2- or 1,3-diols and substituted acetylenes 12- and 13-membered sulfur-containing lactones as 1:1 adducts were synthesized in yields up to 48%. The mechanism of this homolytic reaction, which is initiated by the tripropylborane/oxygen system, includes generation of thiyl radicals and their addition to the triple bond of alkynes

A Family of Nonlinear Fourth Order Equations of Gradient Flow Type

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on $R^d$ are studied. These equations constitute gradient flows for the perturbed information functionals $F[u] = 1/(2\alpha) \int | D (u^\alpha) |^2 dx + \lambda/2 \int |x|^2 u dx$ with respect to the $L^2$-Wasserstein metric. The value of $\alpha$ ranges from $\alpha=1/2$, corresponding to a simplified quantum drift diffusion model, to $\alpha=1$, corresponding to a thin film type equation.Comment: 33 pages, no figure

A posteriori error estimates for the virtual element method

An a posteriori error analysis for the virtual element method (VEM) applied to general elliptic problems is presented. The resulting error estimator is of residual-type and applies on very general polygonal/polyhedral meshes. The estimator is fully computable as it relies only on quantities available from the VEM solution, namely its degrees of freedom and element-wise polynomial projection. Upper and lower bounds of the error estimator with respect to the VEM approximation error are proven. The error estimator is used to drive adaptive mesh refinement in a number of test problems. Mesh adaptation is particularly simple to implement since elements with consecutive co-planar edges/faces are allowed and, therefore, locally adapted meshes do not require any local mesh post-processing

An Approach to 8-Membered, 16-Membered and 24-Membered Sulfur- Containing Heterocycles Via Homolytic Cycloaddition of Alkynes with Butane-1,4-Dithiol

Homolytic cycloaddition of butane-1,4-dithiol with alkynes offers a facile one-pot route to 8-membered 1,4-dithiocanes and 16-and 24-membered crown thioethers, 1,4,9,12-tetrathiacyclohexadecanes and 1,4,9,12,17,20-hexathiacyclotetracosanes

Numerical Mathematics and Advanced Applications 2011Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 /

XVI, 859 p. 258 illus.online resource

Synthesis of 12- and 13-Membered Sulfur-Containing Lactones by Homolytic Macrocyclization of Mercaptoacetic Esters with Alkynes

Starting from mercaptoacetic acid esters of 1,2- or 1,3-diols and substituted acetylenes 12- and 13-membered sulfur-containing lactones as 1:1 adducts were synthesized in yields up to 48%. The mechanism of this homolytic reaction, which is initiated by the tripropylborane/oxygen system, includes generation of thiyl radicals and their addition to the triple bond of alkynes