Novel synthesis of 19-nor-vitamin D compounds

1,25-Dihydroxy-19-nor-vitamin D₃ was prepared efficiently in a convergent synthesis starting with (−)-quinic acid and a ketone of the Windaus-Grundmann type.     

Transport properties of organic vapors in nanocomposites of isotactic polypropylene

Isotactic polypropylene nanocomposites were obtained by the melt blending of polypropylene‐graft‐maleic anhydride and organophilic layered silicate (OLS) consisting of synthetic fluorohectorite modified by cation exchange with protonated octadecylamine. The composition of the inorganic clay was varied between 2.5 and 10 wt %, and films of the composites were obtained via hot‐press molding. X‐ray analysis showed that nanocomposites in which silicate layers were either delaminated or ordered as in an intercalated structure were obtained. The elastic modulus of the samples was higher than that of the pure polymer over a wide temperature range and increased with increasing inorganic content. The transport properties, sorption and diffusion, were measured for two organic vapors, dichloromethane and n‐pentane. For both vapors, the sorption was not very different from that of the pure polymer, whereas the zero‐concentration diffusion parameter strongly decreased with increasing OLS content. Therefore, the permeability, that is, the product of sorption and diffusion, decreased for both vapors as a result of the decreased value of the diffusion parameter. The decrease was higher for the less interacting n‐pentane. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1798–1805, 2003     

A lower estimate for the modified Steiner functional

We prove inequality (1) for the modified Steiner functionalA(M), which extends the notion of the integral of mean curvature for convex surfaces. For the proof, we also establish an expression forA(M) in terms of an integral over all hyperplanes intersecting the polyhedral surfaceM.     

A stability estimate for the Aleksandrov-Fenchel inequality,with an application to mean curvature

In the quadratic Aleksandrov-Fenchel inequality for mixed volumes, stated as inequality (1) below, whereC ₁, ...,C _n-2 are smooth convex bodies, equality holds only if the convex bodiesK andL are homothetic. Under stronger regularity assumptions onC ₁,...,C _n-2, a stability estimate is proved, expressing thatK andL are close to homothetic if equality is satisfied approximately. This is applied to estimate explicitly the deviation of a closed convex hypersurface with mean curvature close to one from a unit sphere.     

Material Discrimination in Nanoparticle Hetero-Aggregates by Analysis of Scanning Transmission Electron Microscopy Images

Hetero-contacts are interfaces between different materials at the nanoscale leading to novel functional properties. In hetero-aggregates, primary particles of at least two different materials are mixed at primary particle or cluster level. Double flame spray pyrolysis (DFSP) is a versatile technique for the controlled synthesis of such materials. Characterization of hetero-aggregates by scanning transmission electron microscopy (STEM) requires acquisition and evaluation of many aggregate images in order to derive statistically significant results. Usually, STEM energy dispersive X-ray spectroscopy (EDXS) is used to acquire elemental maps providing the material distribution of the primary particles within hetero-aggregates. However, the acquisition of a single EDXS map takes up to several minutes. For this reason, determination of material types of primary particles from the intensity in high-angle annular dark field STEM images alone is desirable. These images can be acquired within a couple of seconds. In the present work, a method is suggested which allows for achieving this objective. It can be applied to distinguish materials with a significant difference in their atomic number and hence sufficient material contrast in the STEM images.