On asymptotics of the uniform norm of polynomials with zeros at the roots of unity

The work is related to the problem by P. Erds about the estimation of the numbers

Perron Conditions for Pointwise and Global Exponential Dichotomy of Linear Skew-Product Flows

The aim of this paper is to give necessary and sufficient conditions for pointwise and uniform exponential dichotomy of linear skew-product flows. We shall obtain that the pointwise exponential dichotomy of a linear skew-product flow is equivalent to the pointwise admissibility of the pair As a consequence, we prove that a linear skew-product flow on is uniformly exponentially dichotomic if and only if the pair is uniformly admissible for .     

Distance sets corresponding to convex bodies

Suppose that is a 0-symmetric convex body which denes the usual norm

Exponential Expansiveness and Complete Admissibility For Evolution Families

Connections between uniform exponential expansiveness and complete admissibility of the pair are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.     

Ray escape from a range-dependent underwater sound channel

The problem of sound propagation in a spatially inhomogeneous underwater sound channel is considered. The effect of ray escape, i.e., the ray incidence on the absorbing bottom due to the chaotic swing of rays, is studied. With the use of the Poincaré map and maps of escape, the relation of ray escape to the properties of the phase space of the set of ray equations is demonstrated. It is found that the maximum escape occurs under the vertical resonance conditions, i.e., at the resonance of the ray oscillations in the waveguide with the vertical oscillations of the sound velocity perturbation. A qualitative theory of the vertical resonance is developed. It is shown that the ray escape considerably shortens the time spreading of the signal.     

Growth of Pt thin films on WSe2

The morphology and structure of Pt deposited on a WSe₂(0 0 0 1) van der Waals surface have been investigated by reflection high energy electron diffraction and scanning tunneling microscopy. At room temperature, the initial growth is characterized by the formation of three-dimensional fcc Pt islands with (1 1 1) orientation. In contrast, at higher temperatures of about 450 °C the formation of a novel chemically ordered Pt-Se alloy is observed. Based on the diffraction patterns, a tetragonal DO₂₂-type structure of a Pt₃Se compound is suggested. With increasing Pt thickness, this chemically ordered alloy disappears and an additional superstructure occurs, which is accompanied by the coalescence of the islands. The observed superstructure is attributed to a strong Se diffusion towards the growth surface, forming most likely a PtSe₂ alloy with the CdI₂-type layered structure on the top surface. Due to the lateral lattice mismatch between the Pt(1 1 1) layers and the PtSe₂(1 1 1) top layer, a Moiré pattern with a period of 1.1 nm is created, which might be used as a long-range atomic pattern for further nanostructure growth.     

Reliable cross sections of partial photoneutron reactions on 188,189Os isotopes free of neutron multiplicity sorting problems

Experimental data on the cross sections of partial photoneutron reactions, obtained for ^188,189Os isotopes using quasimonoenergetic annihilation photon beams and neutron multiplicity sorting method, are analyzed. Using special criteria (transition multiplicity functions F _i = σ(γ, in)/σ(γ, xn), the ratios of the cross section of the corresponding partial reaction to the total neutron yield reaction’s cross section σ(γ, xn) = σ(γ, 1n)+ 2σ(γ, 2n) + 3σ(γ, 3n) free of the problems associated with experimental neutron multiplicity sorting), it is demonstrated that the data contain significant systematic errors. New data are evaluated for cross sections of partial photoneutron reactions (γ, 1n), (γ, 2n), (γ, 3n) and total photoneutron reaction (γ, sn) for ^188,189Os isotopes within an experimental-theoretical approach proposed earlier. It is shown that the significant systematic errors in the experimental cross sections of partial reactions can be attributed to the ambiguity of the relation between the photoneutrons’ multiplicity and their kinetic energy.     

FD-Method: the Exponential Rate of Convergence

In this article, we describe a functional–discrete method (FD>-method) for solving operator equations and abstract eigenvalue problems. The algorithm of the method includes a recurrent solution of a sequence of problems with a fixed operator, which is simpler than the initial one, and a changing right-hand side. We prove that, with fairly general assumptions, the FD-method converges with the rate of a geometric progression, i.e., has exponential convergence rate.     

Synthesis and fungicidal activity of S-amino derivatives of O-alkyldithiocarbonic acids

S-Amino derivatives of O-alkyldithiocarbonic acid were prepared by oxidative condensation of certain alkaloids with sodium xanthates. Some of the compounds synthesized exhibit fungicidal activity.