Microcontact printed poly(amidoamine) dendrimer monolayers on silicon oxide surface

Patterning of silicon substrates with poly(amidoamine) generation 5 (PAMAM-G5) dendrimers using soft lithographic microcontact printing (μCP) is presented. μCP is shown to yield monolayers of dendrimers patterned with high level of definition over μm² to mm² areas. The patterns are stable over a period of weeks, which is attributed to the suppressed diffusion of partially charged G5 PAMAM on oxidized silicon. However, the dendrimers studied were shown to be relatively weakly bound to the substrate when subjected to lateral stresses. In aqueous conditions most of the dendrimers desorbed from the substrate.     

On the support of midconvex operators

Summary LetX be a real vector space,D a convex subset ofX and (Y, K) an order complete ordered vector space. The following sandwich theorem holds: Iff: D Y is midconvex,g: D Y {– } is midconcave andg f onD, then there exists a Jensen mappingh: D Y {– } such thatg h f onD. Using this theorem we show that a mappingf: D Y is midconvex if and only if it has Jensen support at every point ofD. Moreover, ifX is a Baire topological vector space and (Y, K) is an ordered topological vector space satisfying some additional conditions, then a mappingf: D Y is continuous whenever it has continuous Jensen support at every point ofD. As an application of these results we obtain the equality of some set-classes connected with additive and midconvex operators.Dedicated to the memory of Alexander M. Ostrowski on the occasion of the 100th anniversary of his birth     

An approach for disaccharide chiron synthesis using a Ferrier-type rearrangement

We report a new approach for the synthesis of new chiral synthons in which two unsaturated sugars are linked via a glycosidic bond. The di-unsaturated disaccharide can be further functionalized using effective, highly selective methods and used in convergent syntheses of relatively complex glycoconjugates. Our approach utilizes in situ generation of active glycosyl donors via Ferrier-type rearrangement under phase-transfer conditions and subsequent reaction with a nucleophile.     

Relaxation to Intermediate Attractors in Nonlinear Wave Equations

We study the dynamics of nonlinear wave equations near the threshold of singularity formation, motivated by some unexpected features observed in the critical gravitational collapse. One of the features, the existence of a universal intermediate attractor in the dynamics at the threshold of singularity formation, is studied in more detail. The result is a scheme of the evolution: for all initial data sufficiently near the threshold, the solutions reach one universal static solution, which plays the role of an intermediate attractor. The solutions remain near the attractor for some time, which scales in a simple way with a parameter of the initial data, and then departs in one of two opposite directions, eventually forming a singularity or dispersing. The relaxation as well as the departure from the attractor is governed in the linear approximation by quasi-normal modes (QNMs) and one growing mode. Moreover, the profiles of the perturbation modes with their oscillation frequencies and damping or amplifying factors, calculated as eigenvalue problems (linear ODEs) have been observed in numerical evolution (nonlinear PDEs). In particular, the exponent of the growing mode determines the lifetime of the intermediate dynamics (near the attractor), and a few least damped QNMs have been observed as ringing in the relaxation process.     

Ideal version of Egorov's theorem for analytic P-ideals

We introduce the notion of equi-ideal convergence and use it to prove an ideal variant of Egorov's theorem. We also show that this variant usually cannot be strengthen to a direct analogue of Egorov's theorem.     

K-subadditive and K-superadditive set-valued functions bounded on “large” sets

Aequationes mathematicae - We prove that every K–subadditive set–valued map weakly K–upper bounded on a “large” set (e.g. not null–finite, not...