An abstract approach to Bohr's phenomenon

In 1914 Bohr discovered that there exists such that if a power series converges in the unit disk and its sum has modulus less than , then for the sum of absolute values of its terms is again less than . Recently analogous results were obtained for functions of several variables. Our aim here is to present an abstract approach to the problem and show that Bohr's phenomenon occurs under very general conditions.

     

Patterned colloidal deposition controlled by electrostatic and capillary forces

We use substrates chemically micropatterned with anionic and cationic regions to govern the deposition of charged colloidal particles. The direct observation of the colloidal assembly suggests that this process includes two steps: an initial patterned attachment of colloids to the substrate and an additional ordering of the structure upon drying. The driving forces of the process, i.e. , screened electrostatic and lateral capillary interactions, are discussed. This approach makes it possible to fabricate complex, high-resolution two-dimensional arrays of colloidal particles.     

On the Bohr Radius for Two Classes of Holomorphic Functions

Using some multidimensional analogs of the inequalities of E. Landau and F. Wiener for the Taylor coefficients of special classes of holomorphic functions on Reinhardt domains we obtain some estimates for the Bohr radius.     

Synthesis and Optical Resolution of the Floral Odorant (±)‐2,3‐Dihydro‐2,5‐dimethyl‐1H‐indene‐2‐methanol,and Preparation of Analogues

The title compound (±)‐ 1 , a recently discovered, valuable, floral‐type odorant, has been synthesized by a straightforward procedure (Scheme 1). To determine the properties of the enantiomers of 1 , their separation by preparative HPLC and the determination of their absolute configuration by X‐ray crystallography were carried out (Figure). Furthermore, the analogues 2 – 6 were synthesized, either from differently methylated 2‐methylindan‐1‐ones (Schemes 2 and 3) or, in the case of the 2,4,6‐trimethylated homologue 6 , by a completely different synthetic approach (Scheme 4). An evaluation of (+)‐(S)‐ 1 , (−)‐(R)‐ 1 , and (±)‐ 1 showed only minor differences in terms of odor (Table).     

Thermochromatographic separation of the products of nuclear reactions in the form of β-diketonates

Volatile hexafluoroacetylacetonates of hafnium, ytterbium, scandium, as well as scandium trifluoroacetylacetonate and acetylacetonate have been obtained by interaction of -diketone vapours with radionuclides formed in a cyclotron in on-line operation. The application of volatile -diketonates for transport and separation of the short-life isotopes of metallic elements has been shown.