Paragrassmann differential calculus

This paper significantly extends and generalizes the paragrassmann calculus of our previous paper [1]. Here we discuss explicit general constructions for paragrassmann calculus with one and many variables. For one variable, nondegenerate differentiation algebras are identified and shown to be equivalent to the algebra of (p+1)×(p+1) complex matrices. If (p+1) is a prime integer, the algebra is nondegenerate and so unique. We then give a general construction of many-variable diffeentiation algebras. Some particular examples are related to multi-parametric quantum deformations of the harmonic oscillators.Dedication This paper is in memory of Mikhail Constantinovich Polivanov. One of the authors (A.T.F.) had a privilege to be a friend of him for many and many years. He was not only a distinguished scientist but a true Russian intellectual having deep roots in Russian culture. It is a deep sorrow that we can no more have a talk with him on science, poetry, religion ...Laboratory of Theoretical Physics, JINR, Dubna. SU-101 000 Moscow, Russia. Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 2, pp. 213–231, February, 1993.     

Phase transition and superconductivity high-T<Subscript>c</Subscript> oxides

On the basis of new experimental studies of specific heat, magnetic properties and thermal expansion, it was shown that dielectric-metal phase transitions were the consequence of delocalization of the heavy holes located on metalapical oxygen bonds in the high-T_c oxide systems. The ordered arrays of such holes (CDW) results in the dielectric gaps in electron spectrum and anomalous negative thermal expansion. The free carriers introduced by doping can couple through excitations of these localized holes, (local bosons). The high-T_c superconductivity will possess anomalous H_c2(T) dependence and γ-type specific heat jump at T_c. This local bosons model is the basis for explanation of the obtained experimental data.     

On the congruence lattice of a Scott-domain

We prove that the congruence lattice of a Scott-domain can be characterized as a complete lattice.Presented by V. Trnkova.The research of the first author was supported by the NSERC of Canada.The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903.     

Micron-image transfer system with brightness amplifier in gold-vapor laser

A gas-discharge gold-vapor laser on self-terminating transitions with operating wavelength λ=312.2 nm has been used to develop a highly efficient system for image transfer. An optical scheme and all its parameters have been chosen optimal for image quality. It has been found both theoretically and experimentally that the best results on micron-structure image transfer are obtained with 2–5-times image reduction. Various types of masks have been used. A 1-µm structure has been resolved due to the choice of optimal exposure time of 10 ms under a period of pulse repetition (0.6 – 0.8) ms; in this case, the minimal fringe dimension was ≈2 µm with an image dimension of 2 mm for a laser tube 1.8 cm in diameter.     

Exciton dynamics within growth islands of GaAs/Al x Ga1−x As single quantum wells

Il Nuovo Cimento D - The localization dynamics of excitons within growth islands of GaAs/Al x Ga1−x As single quantum wells (SQW) have been investigated by time-resolved photoluminescence...     

The Gauss-Bonnet theorem for the torsion-free hyperbolic connection space τ 3 0

We consider the torsion-free hyperbolic connection space ₃ ⁰ . In this space we introduce the concept of Lobachevskií parallelism. Using Lobachevskií parallelism we define the geodesic curvature of a curve, find a formula for computing it, and prove a Gauss-Bonnet theorem for the space in question.Translated from Ukrainskií Geometricheskií Sbornik, Issue 29, 1986, pp. 96–102.     

Inequivalent quantizations for non-linear σ model

We compute the homotopy groups ₀ and ₁ of the classical configuration space of anO(3) invariant field theory on ×, where is a compact two dimensional manifold for arbitrary genusg and- denotes the time coordinate. We also present the finite dimensional, unitary, irreducible, inequivalent representations of the appropriate fundamental groups and comment on some of their implications.