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We give a complete description of quadratic twisted potential algebras on three generators as well as cubic twisted potential algebras on two generators up to graded algebra isomorphisms under the assumption that the ground field is algebraically closed and has characteristic other than 2 or 3.

It is shown that the lattice of invariant subspaces of the operator of multiplication by a cyclic element of a Banach algebra consists of the closed ideals of this algebra. As an application, with the help of some elements of the Gelfand Theory of Banach algebras, the lattice of invariant subspaces of composition operators acting on the Hardy space, whose inducing symbol is a parabolic non-automorphism, is found. In particular, each invariant subspace always consists of the closed span of a set of eigenfunctions. As a consequence, such composition operators have no non-trivial reducing subspaces.

A descriptive characterization of point, continuous, and residual spectra of operators acting on a separable Hilbert space is obtained. The possible point spectra of bounded linear operators acting on lp, 1 < p < ∞ are characterized.

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems., SCOPUS: ar.j, info:eu-repo/semantics/published

A study was performed on resonances and time operator for the cusp map. A theorem on spectra of the operator in different function spaces was presented. It was found that the Forbenius-Perron operator has no analytic eigenfunctions corresponding to the eigenvalues different from 0 and 1 while the natural time operator one has infinite-dimensional space of analytic eigenfunctions corresponding to any of its eigenvalues., SCOPUS: cp.j, info:eu-repo/semantics/published

We prove that the Frobenius-Perron operator U of the cusp map F:[-1,1] →[-1,1], F(x)= 1 -2 √, SCOPUS: ar.j, info:eu-repo/semantics/published

We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion., SCOPUS: ar.j, info:eu-repo/semantics/published

Although the role of the reactions of the decomposition of perchloric acid with the decomposition and burning of ammonium perchlorate (PCA) and in the catalysis of these processes was already repeatedly stressed, quantitatively the connection between them was not checked mainly due to the absence of reliable kinetic data. Given in this work are results of kinetic studies of the decomposition (including catalytic) of the PCA and mixture HClO4+NH3, which are used for finding the quantitative connection between these processes and for the construction of models of burning of the PCA and catalysis of burning., Edited machine trans. of mono. Gorenie i Vzryv, Moscow, 1972 p752-755, by Robert D. Hill.

This paper reports on the temperature conditions during the construction of the Krasnoyarskaya GES under winter conditions. A series of conclusions are presented at the end of the report. (Author), Draft trans. of Energeticheskoe Stroitelstvo (USSR) n5 p31-35 1968.