Functorial methods in the theory of group representations I

We introduce a candidate for the group algebra of a Hausdorff group which plays the same role as the group algebra of a finite group. It allows to define a natural bijection betweenk-continuous representations of the group in a Hilbert space and continuous representations of the group algebra. Such bijections are known, but to our knowledge only for locally compact groups. We can establish such a bijection for more general groups, namely Hausdorff groups, because we replace integration techniques by functorial methods, i.e., by using a duality functor which lives in certain categories of topological Banach balls (resp., unit balls of Saks spaces).This paper was written while the authors were supported by the Swiss National Science Foundation under grant 21-33644.92.     

Spectrum and polarization of electrons in neutron beta-decay in an electromagnetic wave field

A study is made on a polarized neutron undergoing -decay induced by an intense electromagnetic wave. The angular distribution of electrons in the decay is obtained and their polarization is studied. A comparison is made with the decay of a moving neutron.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 33–37, March, 1987.The authors are grateful to L. I. Lapidus, B. K. Kerimov, and G. A. Chizhov for their interest in this work and for their constructive criticism.     

Synthesis and properties of polyenic oligosulfides derived from acetylene and elemental sulfur

Oligosulfides derived from ethyne-1,2-dithiol were synthesized in up to 96% yield via insertion of elemental sulfur into the Na-C_sp bond of sodium acetylides (HC≡CNa, NaC≡CSNa) in liquid ammonia, followed by hydrolysis and spontaneous oligomerization of ethynethiols, ethynedithiols, and mono-and bis-(polysulfanyl)ethynes (HC≡CSH, HSC≡CSH, HC≡CS_xH, HS_xC≡CS_yH). The resulting polyenic oligosulfides were isolated as brown powders melting in the temperature range from 122 to 203°C and containing up to 77% of sulfur; they are sparingly soluble in organic solvents and are high-resistance semiconductors (10^?13–10^?14 S cm^?1) possessing paramagnetic (10¹⁷–10¹⁸ spin g^?1) and redox properties. According to the data of IR and ESR spectroscopy and cyclic voltammetry, the oligomers obtained consist mainly of different oligosulfide units, including oligothienothiophene structures. They also ensure a high discharge capacity (345–720 mA h g^?1) of lithium sulfur rechargeable batteries.     

Synthesis and characteristics of the mass spectra of 2,5-dimercapto-2,5-dimethyltetrahydrothiophene

2,5-Dimercapto-2,5-dimethyltetrahyrothiophene was synthesized by the reaction of 1-iodopropan-2-one with hydrogen sulfide in an ether solution of hydrogen chloride at-70°C. Its structure was established by mass spectrometry, ¹H and ¹³C NMR spectroscopy. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, 216–219, February, 2007.     

Detection of the Electric Potential Surface Distribution with a Local Probe Based on a Field Effect Transistor with a Nanowire Channel

Technical Physics - A non-destructive method of scanning probe microscopy for simultaneous measurements of the surface topography and electric field (charge, potential) distribution is...