On asymptotic approximation of a solution of a boundary-value problem for a nonlinear nonautonomous equation

On the basis of periodic Ateb functions, in the resonance and nonresonance cases, we construct the asymptotic approximation of one-frequency solutions of a boundary-value problem for a nonlinear nonautonomous equation.     

On outer automorphism groups of coxeter groups

Summary It is shown that the outer automorphism group of a Coxeter groupW of finite rank is finite if the Coxeter graph contains no infinite bonds. A key step in the proof is to show that if the group is irreducible andΠ ₁ andΠ ₂ any two bases of the root system ofW, thenΠ ₂ = ±ωΠ ₁ for some ω εW. The proof of this latter fact employs some properties of the dominance order on the root system introduced by Brink and Howlett. This article was processed by the author using the Springer-Verlag TEX PJour1g macro package 1991.     

The Characterisation of the Products of Reduction of Chinkombe Ilmenite

The characterisation of iron-containing species in Chinkombe ilmenite and its reduction products was undertaken using Mössbauer Spectroscopic techniques. The ore was reduced by graphite in an inert atmosphere. The effects of such variables as quantity of reductant, temperature and preoxidation were investigated. The ore was completely reduced to alpha-iron and titanium dioxide with 20% carbon for a period of one hour at 1373 K. Chemical mechanisms are proposed for the reduction and oxidation of Chinkombe ilmenite. In the processing of ilmenite to obtain synthetic rutile, the ultimate desire is to separate the Fe phase from the TiO₂. Mössbauer Spectroscopy has unambiguously confirmed the desired transformation of the iron phase according to thermodynamic predictions. The information gained would be used to choose the conditions of the reduction process. The alpha-iron could be separated physically or chemically from the completely reduced product mass to obtain synthetic titanium dioxide suitable for the paint industry.     

Twistor Geometry for Hyperkähler Metrics on Complex Adjoint Orbits

We study the hyperkähler geometry of complex adjoint orbits from the point of view of twistor theory. We introduce, for complex semisimple adjoint orbits, the associated spectral curve and construct the twistor space as a union of certain regular adjoint orbits; we also exhibit the family of twistor lines. Furthermore, we show how our methods may be applied for describing hyperkähler metrics associated to more general spectral curves. In particular, we give an algebraic characterisation of the twistor lines.     

Field optimized initial state based control of photodissociation

A new scheme for controlling photodissociation through preparation of a variationally optimized linear superposition of field free vibrational eigenstates is applied for selective control of IBr and HI dissociation. The dependence of photodissociation on various field parameters and initial conditions is examined to investigate the mechanistic basis of selective control. The parametric equations of motion approach for determining vibrational dynamics as a function of field parameters without having to solve the time dependent Schrödinger equation explicitly for each field parameter separately is outlined and its use to identify field characteristics which will provide the requisite population mix represented by the optimal linear superposition of vibrational states is advocated.     

Variational and Hamiltonian models in the dynamics of magnetizable conducting fluid

The variational model and the Hamiltonian canonical equation of motion are updated using the Lagrangian invariant for three-dimensional unsteady adiabatic flows of magnetizable, ideally conducting, compressible inviscid fluid. The results are applied to derive Hamiltonian noncanonical equations of motion in physically defined variables. Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie — Sbornik Trudov, No. 2, pp. 44–46, 1994.     

On the conjugate boundary value problem

We study the conjugate boundary-value problem with boundary conditions whose orders can be as large as the order of the differential equation or larger. We construct the Green's function of the problem over the entire space when the separating surface is a hyperplane, and we describe its properties. Bibliography: 6 titles.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 30, 1989, pp. 20–24.     

Unreasonable effectiveness of symmetry in physics

We prove that in some reasonable sense, every possible physical law can be reformulated in terms of symmetries. This result explains the well-known success of the group-theoretic approach in physics.     

Observation of ionic thermocurrents in zirconia-based solid electrolytes

In ionic conductors, long range-migrating charges are a main cause of polarization processes. This has complicated, up to date, the study of ionic thermocurrents (ITC) in solid electrolytes. However, the method is appealing, as it probes directly charge-formation phenomena that are important both from a scientific point of view and for applications. This work reports on the observation of ITC in solid electrolytes. Under appropriate experimental conditions, the ITC response of a zirconia sample electroded with platinum is a reproducible one, thus opening the way to a new characterization method that may complement other well established methods, such as Impedance Spectroscopy and a number of electrochemical techniques. The general trends of the response, which is composed of two well resolved ITC peaks, is discussed. One of them, taking place at higher temperatures, conforms to the standard shape of a first order kinetics depolarization process. Paper presented at the 2nd Euroconference on Solid State Ionics, Funchal, Madeira, Portugal, Sept. 10–16, 1995