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.     

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...     

Cosmology with torsion: An alternative to cosmic inflation

We propose a simple scenario which explains why our Universe appears spatially flat, homogeneous and isotropic. We use the Einstein–Cartan–Kibble–Sciama (ECKS) theory of gravity which naturally extends general relativity to include the spin of matter. The torsion of spacetime generates gravitational repulsion in the early Universe filled with quarks and leptons, preventing the cosmological singularity: the Universe expands from a state of minimum but finite radius. We show that the dynamics of the closed Universe immediately after this state naturally solves the flatness and horizon problems in cosmology because of an extremely small and negative torsion density parameter, ΩS≈−¹⁰⁻⁶⁹${\Omega }_S\approx -{10}^{-69}$. Thus the ECKS gravity provides a compelling alternative to speculative mechanisms of standard cosmic inflation. This scenario also suggests that the contraction of our Universe preceding the bounce at the minimum radius may correspond to the dynamics of matter inside a collapsing black hole existing in another universe, which could explain the origin of the Big Bang.