Adaptive wavelet frame domain decomposition methods for nonlinear elliptic equations

In this article, we are concerned with the numerical treatment of nonlinear elliptic boundary value problems. Our method of choice is a domain decomposition strategy. Partially following the lines from (Cohen, Dahmen and deVore, SIAM J Numer Anal 41 (2003), 1785–1823; Kappei, Appl Anal J Sci 90 (2011), 1323–1353; Lui, SIAM J Sci Comput 21 (2000), 1506–1523; Stevenson and Werner, Math Comp 78 (2009), 619–644), we develop an adaptive additive Schwarz method using wavelet frames. We show that the method converges with an asymptotically optimal rate and support our theoretical results with numerical tests in one and two space dimensions. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013     

Selective Cycloaddition of Tetracyanoethene (TCNE) and 7,7,8,8‐Tetracyano‐p‐quinodimethane (TCNQ) to Afford meso‐Substituted Phenylethynyl Porphyrins

π‐Extended TCBD‐porphyrins that contained a 1,1,4,4‐tetracyanobuta‐1,3‐diene unit were prepared by a highly efficient [2+2] cycloaddition of tetracyanoethene (TCNE) or 7,7,8,8‐tetracyano‐p‐quinodimethane (TCNQ) with meso‐substituted trans‐A₂B₂‐porphyrins that contained two phenylethynyl groups, followed by a retro‐electrocyclization reaction. Depending on the electronic properties of the arylethynyl groups, the cycloaddition reaction took place exclusively on either one or two ethynyl moieties with high yield. The addition of TCNQ proceeded with complete regioselectivity. The resulting π‐expanded TCBD‐porphyrins had a hypsochromically shifted Soret band and showed unique, broad absorption in the visible region.     

Improved chemoenzymatic asymmetric synthesis of (S)-Rivastigmine

(S)-Rivastigmine [(S)-1] was obtained via a four-step synthesis using an asymmetric enzymatic transamination protocol as the key step. An early introduction of the carbamate pharmacophore side chain avoided the use of protective group strategies and hence led to a considerable shortcut. This strategy required a novel ω-transaminase from Paracoccus denitrificans, which could transform the highly polar key substrate 3-acetylphenyl ethyl(methyl)carbamate (4) to the corresponding amine (S)-5 in 99% ee and >80% conversion.     

Asymmetric synthesis of beta-nitro ketones via Michael addition of lithiated alpha-amino nitriles to nitroalkenes

Alpha-amino nitriles, easily prepared from aldehydes, KCN, and an enantiopure secondary amine auxiliary, are metalated and used as nucleophiles in asymmetric Michael additions to nitroalkenes to afford the Michael adducts in good yields and good to excellent diastereoselectivities. After chromatographic purification, the diastereomerically pure 1,4-adducts are cleaved under acidic conditions to give the beta-nitro ketones in good yields and with two exceptions in good to excellent enantiomeric excesses (ee = 86-99%). The absolute configuration was determined by X-ray structure analysis.     

Electronic Structure Calculations for Hole‐Transporting Triphenylamine Derivatives in Polymer Light‐Emitting Diodes

Hole‐transporting polymers based on polyethene‐triphenylamine derivatives are investigated with respect to their UV/Vis spectra. Two substituents, N‐phenyl‐1‐naphthylamine and carbazole, are examined as their respective polymer light‐emitting diodes (PLEDs) show very different luminous efficiencies. In order to identify the origin of these phenomena electronic structure calculations based on TD‐DFT were performed using monomer models of the hole‐transporting polymers. In experiment these hole‐transporting polymers show very specific differences in their absorption and emission (fluorescence and phosphorescence) spectra. The analysis of the simulated absorption and emission spectra, the MOs as well as the ground and excited state geometries give explanations for the different optical performances of the corresponding PLEDs.

     

Mathematical programs with vanishing constraints: critical point theory

We study mathematical programs with vanishing constraints (MPVCs) from a topological point of view. We introduce the new concept of a T-stationary point for MPVC. Under the Linear Independence Constraint Qualification we derive an equivariant Morse Lemma at nondegenerate T-stationary points. Then, two basic theorems from Morse Theory (deformation theorem and cell-attachment theorem) are proved. Outside the T-stationary point set, continuous deformation of lower level sets can be performed. As a consequence, the topological data (such as the number of connected components) then remain invariant. However, when passing a T-stationary level, the topology of the lower level set changes via the attachment of a q-dimensional cell. The dimension q equals the stationary T-index of the (nondegenerate) T-stationary point. The stationary T-index depends on both the restricted Hessian of the Lagrangian and the number of bi-active vanishing constraints. Further, we prove that all T-stationary points are generically nondegenerate. The latter property is shown to be stable under C ²-perturbations of the defining functions. Finally, some relations with other stationarity concepts, such as strong, weak, and M-stationarity, are discussed.     

Optimal error estimates for finite element discretization of elliptic optimal control problems with finitely many pointwise state constraints

In this paper we consider a model elliptic optimal control problem with finitely many state constraints in two and three dimensions. Such problems are challenging due to low regularity of the adjoint variable. For the discretization of the problem we consider continuous linear elements on quasi-uniform and graded meshes separately. Our main result establishes optimal a priori error estimates for the state, adjoint, and the Lagrange multiplier on the two types of meshes. In particular, in three dimensions the optimal second order convergence rate for all three variables is possible only on properly refined meshes. Numerical examples at the end of the paper support our theoretical results.     

Improved native UV laser induced fluorescence detection for single cell analysis in poly(dimethylsiloxane) microfluidic devices

Single cell analytics is a key method in the framework of proteom research allowing analyses, which are not subjected to ensemble-averaging, cell-cycle or heterogeneous cell-population effects. Our previous studies on single cell analysis in poly(dimethylsiloxane) microfluidic devices with native label-free laser induced fluorescence detection [W. Hellmich, C. Pelargus, K. Leffhalm, A. Ros, D. Anselmetti, Electrophoresis 26 (2005) 3689] were extended in order to improve separation efficiency and detection sensitivity. Here, we particularly focus on the influence of poly(oxyethylene) based coatings on the separation performance. In addition, the influence on background fluorescence is studied by the variation of the incident laser power as well as the adaptation of the confocal volume to the microfluidic channel dimensions. Last but not least, the use of carbon black particles further enhanced the detection limit to 25 nM, thereby reaching the relevant concentration ranges necessary for the label-free detection of low abundant proteins in single cells. On the basis of these results, we demonstrate the first electropherogram from an individual Spodoptera frugiperda (Sf9) cell with native label-free UV-LIF detection in a microfluidic chip.     

Tuning the Halogen Bonding Strength of Cyclic Diaryliodonium Salts

Diaryliodonium(III) salts have recently received increasing interest as a new class of strong halogen bonding noncovalent organocatalysts. Even though this utilization of their Lewis acidity has only been investigated in few studies, their high potential in comparison to classical monovalent iodine based XB donors has become very apparent. So far, only acyclic and cyclic five-membered core structures have been used, and titration studies have shown the latter to be superior in terms of binding constants towards Lewis bases. Herein, we now compare the Lewis acidity and activity of these five-membered iodolium salts with those of six-membered iodininium derivatives. X-Ray structural analyses, ITC measurements and the reaction kinetics of a Ritter-type solvolysis reaction in wet acetonitrile (a typical halogen bond donor benchmark reaction) all demonstrate that iodolium salts are stronger halogen bond donors and catalysts than iodininium salts. Subsequently, we were able to improve the activity of both core structures significantly by introducing electron-withdrawing substituents.     

Guanine‐Stabilized Formamidinium Lead Iodide Perovskites

Formamidinium (FA) lead iodide perovskite materials feature promising photovoltaic performances and superior thermal stabilities. However, conversion of the perovskite α‐FAPbI₃ phase to the thermodynamically stable yet photovoltaically inactive δ‐FAPbI₃ phase compromises the photovoltaic performance. A strategy is presented to address this challenge by using low‐dimensional hybrid perovskite materials comprising guaninium (G) organic spacer layers that act as stabilizers of the three‐dimensional α‐FAPbI₃ phase. The underlying mode of interaction at the atomic level is unraveled by means of solid‐state nuclear magnetic resonance spectroscopy, X‐ray crystallography, transmission electron microscopy, molecular dynamics simulations, and DFT calculations. Low‐dimensional‐phase‐containing hybrid FAPbI₃ perovskite solar cells are obtained with improved performance and enhanced long‐term stability.