Existence of generic homoclinic tangencies for henon mappings

It is an open question whether there is a strange attractor for the Henon mapping. We show that for certain maps close to the Henon map there are strange attractors.     

Dirichlet polyhedra for dihedral groups acting on complex hyperbolic space

We consider groups Γ generated by inversions in a pair of asymptotic complex hyperplanes in complex hyperbolic spaceH _? ⁿ . We show that there exists a Γ-invariant real hypersurfaceF ?H _? ⁿ such that the Dirichlet fundamental polyhedron for Γ centered at z₀ has two sides (resp. infinitely many sides) if and only ifz ₀ ∈F (resp.z ₀ ?F). The Dirichlet regions are determined explicitly in terms of coordinates on Γ-invariant horospheres and the geometry ofH _? ⁿ is developed in terms of these horospherical coordinates.     

Quantum hair and quantum gravity

A black hole may carry quantum numbers that arenot associated with massless gauge fields, contrary to the spirit of the no-hair theorems. The quantum hair is invisible in the classical limit, but measurable via quantum interference experiments. Quantum hair alters the temperature of the radiation emitted by a black hole. It also induces non-zero expectation values for fields outside the event horizon; these expectation values are non-perturbative in , and decay exponentially far from the hole. The existence of quantum hair demonstrates that a black hole can have an intricate quantum-mechanical structure that is completely missed by standard semiclassical theory.Based on an essay which received second award from the Gravity Research Foundation, 1991     

Orientation reversing involutions and the first betti number for finite coverings of 3-manifolds

LetMS ³,P ³ be a closed, orientable irreducible 3-manifold which admits an orientation reversing involution :MM. If dim(Fix )=0, suppose ₁ (M) has a subgroup of even index. We show thatM has finite coverMMM} with ₁(M<0). As an application we show that the hyperbolic dodecahedral space has a finite cover with positive 1st betti number.     

On a class of atmospheres occurring in stellar hydrodynamic theory

Summary A derivation is given of the basic equation governing the behaviour of small disturbances in a stratified compressible atmosphere (with a locally unstable region bounded by semi-infinite stable regions) in which the time of radiative relaxation is constant.By means of a new independent variable that is a function of the equilibrium entropy stratification, various properties of such media can be established in a straightforward manner. A general expression for the wave energy flux is derived, and integral properties arising from this quantity are used to obtain in particular, results pertaining to the eigenfunctions and eigenvalues for strongly radiating systems. In addition, a model of an atmosphere with a strongly-radiating region embedded in a convective zone, and bounded by semi-infinite radiation-free layers is discussed in some detail. The paper is an approach towards providing some preliminary but unified results in the theory of stellar hydrodynamics.

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Résumé Nous donnons une dérivation de l'équation de base qui détermine la propagation des petites perturbations dans une atmosphère compressible stratifiée (présentant une zone d'instabilité locale entre des zones de stabilité semi-infinies) dont le temps de relaxation radiative est constant.Au moyen d'une nouvelle variable indépendante, fonction de la stratification de l'entropie en équilibre, diverses propriétés de tels milieux sont déterminées simplement. On donne une formulation du flux de l'énergie ondulative et on emploie les propriétés intégrales qui en résultent pour obtenir en particulier des résultats concernant les eigenfonctions et les eigenvalues pour des systèmes à forte radiation énergétique. En outre, on étudie en détail le modèle d'une amtosphère caractérisée par une zone à forte radiation insérée dans une zone convective entre des couches semi-infinies sans radiation.Ce travail présente quelques conclusions préliminaires mais cohérentes dans le domaine de la théorie de l'hydrodynamique stellaire.

     

Non-uniqueness of solutions of Percival's Euler-Lagrange equation

Percival [5,6] introduced a Langrangian and an Euler-Lagrange equation for finding quasi-periodic orbits. In [3], we studied area preserving twist homeomorphisms of the annulus, using Percival's formalism. We showed that Percival's Lagrangian has a maximum on a suitable function space, and that a point where it takes its maximum is a solution of Percival's Euler-Lagrange equation. Moreover, in the rigorous interpretation of Percival's formalism which we gave in [3], the solutions of Percival's Euler-Lagrange equation correspond bijectively to a certain class of minimal sets. (We will prove this in Sect. 2.) In [4], we showed that Percival's Lagrangian takes its maximum at only one point. In this paper, we show that there existC area preserving twist diffeomorphisms of the annulus, for which there exists at least one solution of Percival's Euler-Lagrange equation where Percival's Lagrangian does not take its maximum. In other words, solutions of Percival's Euler-Lagrange equation need not be unique.Supported by NSF Grant No. MCS 79-02017     

Spectrophotometric determination of thallium as thallium tetriodide

Iodide ions react with thallic ions at pH 2–8 to form a complex iodide, which is suitable for the spectrophotometric determination of thallium. The reaction has a sensitivity of 0.05 μg Tl per cm² for log $\text{I}{}_0\text{I}$ = 0.001 and obeys Beer's law up to 40 p.p.m. Optimum conditions for the reaction have been established. The standard deviation is 0.6%. The effects of temperature and pH, the ratio of thallium to reagent, stability of the complex, its conformity to Beer's law, and the rate of color formation were studied. The effect of many diverse ions was examined.     

Incoherent inelastic neutron scattering studies of potassium bicarbonate and caesium hydrogen dinitrate

Inelastic neutron scattering spectra of KHCO₃ and CsH(NO₃)₂ have been obtained in the region 400 → 2400 and 400 → 2800 cm^?1 respectively. The in- and out-of-phase bending vibrations of the hydrogen bonds have been observed and assigned. For CsH(NO₃)₂ the two bending modes are closer in frequency than in KHCO₃ and they are not resolved from the antisymmetric stretch.     

Plasma desorption mass spectrometry of transition metal complexes of thio- and selenosemicarbazones of 2-acetylpyridines

Summary Californium-252 plasma desorption mass spectra were recorded for complexes of the anions of various thio-and seleno-semicarbazones of 3-acetylpyridines(1–4) with the transition metal ions iron(III) and cobalt(II). Positive ion spectra gave clear evidence of the cation present and fragmentation with loss of ligands or parts of ligands was straightforward. Negative ion spectra likewise provided evidence of the intact anion except with tetracoordinate metal halide systems [MX₄]^– which lost one or more halide atoms. Evidence of fragmentation of the ligand and recombination of the fragments with the metal ion was also observed in the negative ion mode. Spectra were used to revise the structure of a complex previously reported as [FeLCl₂]⁽¹⁾ to [FeL₂]⁺[FeCl₄]^–.     

Nitration studies of naphtho[2,3-c][1,2,5]thiadiazole

Nitration of naphtho[2,3-c][1,2,5]thiadiazole gives the 5-nitro derivative in 61–66% yield. Chlorination of this product apparently gives an unstable addition product which loses hydrogen chloride on recrystallization to give 4-chloro-8-nitronaphtho[2,3-c][1,2,5]thiadiazole. Thus, naphtho[2,3-c][1,2,5]thiadiazole under nitrating conditions behaves as a 2-substituted naphthalene rather than as an anthracene analog.