Why is space three-dimensional and how may groups be seen?

First we propose a model of visual perception essentially based on the Keldysh-Chernavsky-Sossinsky three-channel theorem, from which three-dimensionality of space follows. Second, we associate with a system of subgroups H ₁, ..., H_s of a given group G a geometric object, called a group crystal, in order to visualize G. How this notion works is illustrated via the Burnside problem.     

New Synthetic Approaches to Functionally Substituted 4,5-Dihydro-1,2,3-oxadiazole 2-Oxides

A practical procedure has been proposed for the synthesis of functionally substituted 4,5-dihydro-1,2,3-oxadiazole 2-oxides on the basis ofsulfamic acid derivatives.__________Translated from Zhurnal Organicheskoi Khimii, Vol. 41, No. 1, 2005, pp. 121–123.Original Russian Text Copyright © 2005 by Tartakovskii, Ermakov, Strelenko, Vinogradov, Petrov.     

Nitropyrazoles

A method for the synthesis of bi-, ter-, and quaterpyrazoles by cyclization ofC-(diformylmethyl)nitropyrazoles with hydrazine has been elaborated. Some of theirC- andN-derivatives have been obtained. The compounds prepared have been characterized by¹H,¹³C,¹⁴N, and¹⁵N NMR spectra.For communication 6, see Ref. 1.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1941–1945, November, 1993.     

On the nature of paramagnetism in macromolecules with conjugated cc bonds

The paramagnetic properties of one-dimensional macromolecules with conjugated C?C bonds are discussed on the basis of low-lying quasi-homeopolar triplet excitations. A good agreement with the experimental results is shown.     

Boron trifluoride-methanol complex—mild and powerful reagent for deprotection of labile acetylated amines

A set of amino-group possessing cyanine dyes is obtained from their N-acetyl derivatives via deprotection with boron trifluoride-methanol complex in good yields.     

Decomposition of weakly aging distributions

A class of weakly aging distribution functions is introduced and a number of properties of this class are derived. It is proved in particular that a random variable , having a weakly aging distribution function, can be written as a sum of two independent random variables, one of which has exponential distribution with a parameter equal to the modulus of the singular point of Me^–s nearest the coordinate origin.Translated from Matematicheskie Zametki, Vol. 22, No. 4, pp. 571–574, October, 1977.     

Lifetimes and the dynamics of hydrogen bonds in liquid water

Based on Raman spectra of light, heavy, and half-heavy water in the region of O-H and O-D stretching vibrations and on the independent-oscillator model, it is shown that a peculiarity of the liquid state of water is the nonequivalence of O-H groups of water molecules in hydrogen bonding. The structure of liquid water and the mechanism of its molecular mobility are considered in this context.