Essential hyperbolic Coxeter polytopes

We introduce a notion of an essential hyperbolic Coxeter polytope as a polytope which fits some minimality conditions. The problem of classification of hyperbolic reflection groups can be easily reduced to classification of essential Coxeter polytopes. We determine a potentially large combinatorial class of polytopes containing, in particular, all the compact hyperbolic Coxeter polytopes of dimension at least 6 which are known to be essential, and prove that this class contains finitely many polytopes only. We also construct an effective algorithm of classifying polytopes from this class, realize it in the four-dimensional case, and formulate a conjecture on finiteness of the number of essential polytopes.     

Reflection subgroups of reflection groups

Let G be a discrete group generated by reflections in hyperbolic or Euclidean space, and let H G be a finite index reflection subgroup. Suppose that the fundamental chamber of G is a finite volume polytope with k facets. We prove that the fundamental chamber of H has at least k facets.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 90–92, 2004Original Russian Text Copyright © by A. A. Felikson and P. V. Tumarkin     

Growth of YBa2Cu3O7−x thin films on sapphire with a cerium-oxide sublayer

The possibility is demonstrated of preparing high-quality films of the high-temperature superconductor YBa₂Cu₃C_7-δ with thicknesses up to 2.6 μm by dc magnetron sputtering. It is found that inclusions consisting of CuO and YBa₂Cu₃O₈ coexist with the growing film and are “sinks” for defects, nonstoichiometric atoms, and mechanical stresses. Using x-ray diffraction and Rutherford backscattering, we find that the structural perfection of the films is improved by increasing the thickness when using the proposed fabrication technique. Zh. Tekh. Fiz. 69, 94–98 (January 1999)     

Initial Stages of Growth of Barium Zirconate Titanate and Barium Stannate Titanate Films on Single-Crystal Sapphire and Silicon Carbide

Physics of the Solid State - The initial stages of growth of barium zirconate titanate and barium stannate titanate ferroelectric films on single-crystal sapphire and silicon carbide are studied...     

Development and applications of a microfluidic reactor with multiple analytical probes

We report the development of a versatile microfluidic (MF) reactor with multiple analytical probes, which can be used for (i) quantitative characterisation of molecular vibrational signatures of reactants or products, (ii) the localised real-time monitoring of temperature and (iii) site-specific measurements of pH of the reaction system. The analytical probes utilised for in situ reaction analysis include an ATR-FTIR probe, a temperature probe, and a pH probe. We demonstrate the applications of the MF reactor with integrated probes for the parallel monitoring of multiple variables in acid/base neutralisation reaction, of changes in buffer pH, temperature, and vibrational absorption bands, and for monitoring the kinetics of the reaction between CO(2) and a buffer system with therapeutic applications.     

Groups of Signature (0; <Emphasis Type="Italic">n</Emphasis>; 0)

Let M be an ideal polygon with 2n − 2 vertices. Consider a pairing of the symmetrical (with respect to some fixed diagonal) sides of M by mappings S _i , 1 ⩽ i ⩽ n − 1, and denote by Γ the group generated by these mappings. Each S _i depends on one parameter. We prove a necessary and sufficient condition for the possibility of choosing these parameters so that our polygon M would be a fundamental domain for the action of Γ.__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 259–262, 2003.     

Glycine–Nitrate Synthesis of Solid Solutions of Barium–Strontium Metatitanate

Physics of the Solid State - The influence of composition of glycine–nitrate systems on the completeness of the formation of solid solutions of barium–strontium metatitanate was...     

Microfluidic production of biopolymer microcapsules with controlled morphology

We report a microfluidic approach to generating capsules of biopolymer hydrogels. Droplets of an aqueous solution of a biopolymer were emulsified in an organic phase comprising a cross-linking agent. Polymer gelation was achieved in situ (on a microfluidic chip) by diffusion-controlled ionic cross-linking of the biopolymer, following the transfer of the cross-linking agent from the continuous phase to the droplets. Gelation was quenched by collecting particles in a large pool of cross-linking agent-free liquid. The structure of microgels (from capsules to gradient microgels to particles with a uniform structure) was controlled by varying the time of residence of droplets on the microfluidic chip and the concentration of the cross-linking agent in the continuous phase. We demonstrated the encapsulation of a controlled number of polystyrene beads in the microgel capsules. The described approach was applied to the preparation of capsules of several polysaccharides such as alginate, kappa-carrageenan, and carboxymethylcellulose.