Combinatorial preconditioners for scalar elliptic finite-element problems

We present a new preconditioner for linear systems arising from finite-elements discretizations of scalar elliptic partial differential equations. The solver is based on building a symmetric diagonally dominant (SDD) approximation of the stiffness matrix K. The approximation is built by approximating each element inside the collection {K_e } of element matrices by an SDD matrix L_e. The SDD approximation L is built by assembling the collection {L_e }. We then sparsify L using a graph algorithm, and use the sparsified matrix as a preconditioner. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Chiral amide from (1S,2R)-(+)-norephedrine alkaloid in the enantioselective addition of diethylzinc to aryl and heteroaryl aldehydes

Chiral amide synthesized from (1S,2R)-(+)-norephedrine and furoic acid was found to catalyze the enantioselective ethylation of aromatic and heteroaromatic aldehydes to secondary alcohols with 99.8% enantioselectivity at 0 °C without the addition of a promoter such as titanium tetraisopropoxide.     

The different effect of electron-electron interaction on the spectrum of atoms and quantum dots

Though atoms and quantum dots typically contain a comparable number of electrons, the number of discrete levels resolved in spectroscopy experiments is very different for the two systems. In atoms, hundreds of levels are observed while in quantum dots that number is usually smaller than 10. In the present work, this difference is traced to the different confining potentials in these systems. In atoms, the soft confining potential leads to large spatial extent of the excited electron's wave function and hence to weak Coulomb interaction with the rest of the atomic electrons. The resulting level broadening is smaller than the single particle level spacing and decreases as the excitation energy is increased. In quantum dots, on the other hand, the sharp confining potential results in electron-electron scattering rates that grow rapidly with energy and fairly quickly exceed the approximately constant single particle level spacing. The number of discrete levels in quantum dots is hence limited by electron-electron interaction, whose effect is negligible in atoms. Received 3 April 2000 and Received in final form 7 August 2000     

Microscopics of complexation between long DNA molecules and positively charged colloids

Extensive atomic force and electron microscopy reveal a new, generic DNA-colloid complex with a fixed number of DNA bases per colloid. The fiber shaped complex is stable in the presence of excess colloids in the solution. As more DNA is added to the solution and the ratio between colloids and DNA approaches the fiber's stoichiometry, the system undergoes a sharp coagulation transition. The system is restabilized at even higher DNA concentrations through localization of small colloid clusters on extensive DNA networks.     

A quantitative approach to soliton instability

We present an approach for instabilities of solitons that is based on the spectrum of a fourth-order linearized operator. Unlike the standard approach which is based on the slope (Vakhitov-Kolokolov) condition, this approach provides the quantitative value of the instability rate and the qualitative nature of the instability dynamics.     

Carbon nanotubes as nanocarriers in medicine

Carbon nanotubes (CNTs) possess outstanding properties and a unique physicochemical architecture, which may serve as an alternative platform for the delivery of various therapeutic molecules. This review focuses on recent progress in the field of CNTs for biomedical applications. After a short, general physico-chemical introduction to CNTs, we introduce different methods for CNT surface modification, facilitating their dispersions in physiological solutions, on the one hand, and binding a wide range of molecules or drug-loaded liposomes, on the other. We summarize imaging evidences on the structure of CNT-drug conjugates and their relevant uptake mechanisms by the cell. Lastly, we review current repots on CNT toxicity and new developments in CNT-based medical applications: photo-thermal therapy, drug delivery and gene therapy.     

Engineering Metal–Organic Framework Catalysts for C−C and C−X Coupling Reactions: Advances in Reticular Approaches from 2014–2018

Metal–organic frameworks (MOFs) are a class of crystalline porous materials that have been actively used for several industrial and synthetic applications. MOFs are spatially and geometrically extrapolated coordination polymers with intriguing properties such as tunable porosity and dimensionality. In terms of their catalytic efficiency, MOFs combine the easy recoverability of heterogeneous catalysts with the increased selectivity of biological catalysts. It is therefore not surprising that a lot of work on optimizing MOF catalysts for organic transformations has been carried out over the past decade. In this review, recent developments in MOF catalysis are summarized, with special attention being paid to C−C, C−N, and C−O coupling reactions. The influence of pore size, pore environment, and load on catalytic activity is described. Post-synthetic stabilization techniques and host–guest interactions in caged MOF scaffolds are detailed. Mechanistic aspects pertaining to the use of MOFs in asymmetric heterogeneous catalysis are highlighted and categorized.