On the existence of minimal τ-closed ω-saturated non-$ mathfrak{H} $-formations

We study minimal τ-closed ω-local non- mathfrakH mathfrak{H} -formations in the case where H is a formation of the classic type.     

Amination with Pd-NHC complexes: rate and computational studies on the effects of the oxidative addition partner

Pd-PEPPSI-IPent, a recently-developed N-heterocyclic carbene (NHC) complex, has been evaluated in amination reactions with secondary amines and it has shown superb reactivity under the most mildly basic reaction conditions. Rate and computational studies were conducted to provide insight into the mechanism of the transformation. The IPent catalyst coordinates to the amine much more strongly than the IPr variant, thus favouring deprotonation with comparatively weak bases. Indeed the reaction is first order in base and only slightly more than zeroth order in amine.     

Photoreflection and photoconduction spectra of CdS crystals: Excitons in the electric fields of surface states

The exciton photoreflection spectra of CdS crystals are studied. It is found that the form of the exciton photoreflection spectrum is determined by a Stark shift of the exciton energy in the electric field of surface states. The dependences of the exciton photoreflection spectrum on temperature on the intensity and wavelength of the modulating radiation, and on the processes by which the photoreflection signal relaxes is determined. An energy scheme is proposed for the surface states which explains the observed effects of photoinduced changes in the surface field. A correlation is established between the exciton photoreflection spectrum and the form of the fine structure in the photoconductivity. Fiz. Tverd. Tela (St. Petersburg) 40, 875–876 (May 1998)     

Emulsifier-free emulsion copolymerization of styrene with methacrylic acid as a method of preparing building blocks for photonic crystals

Monodisperse polymer particles with diameters from 230 to 420 nm have been synthesized by the emulsifier-free emulsion copolymerization of styrene with methacrylic acid. It has been shown that an initiator, chain regulators, comonomer ratio, and pH of a medium influence the dispersity of latexes, the distribution of carboxyl groups in polymer particles, as well as their swelling behavior and electrophoretic mobility. These characteristics of polymer particles are substantial for designing perfect lattices of three-dimensional photonic crystals on their basis.     

Normal subgroups of finite groups and formations with normalizer conditions

The structure of a normal subgroupK of a finite groupG is studied under the condition that nontrivial intersections ofK with maximal subgroups ofG belong to an arbitrary formation with normalizer condition. Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 867–870, December, 1999.     

Some Finiteness Results in the Representation Theory of Isometry Groups of Regular Trees

Let G denote the isometry group of a regular tree of degree ≥3. The notion of congruence subgroup is introduced and finite generation of the congruence Hecke algebras is proven. Let U be congruence subgroup and (G; U) be the category of smooth representations of G generated by their U-fixed vectors. We also show that this subcategory is closed under taking subquotients. All these results are analogues of well-known results in the case of p-adic groups. It is also shown that the category of admissible representation of G is Noetherian in the sense that every subrepresentation of a finitely generated admissible representation is again finitely generated. Since we want to emphesize the similarities between these groups and p-adic groups, we give the same proofs which also work in the p-adic case whenever possible.