Correction to: Involutions of Type G2 over a Field of Characteristic Two

Algebras and Representation Theory - We would like to correct two errors in our paper Involutions of type G2 over a field of characteristic 2 [2].     

Sur Les Groupes D’Homotopie Des Espaces Dont La Cohomologie Modulo 2 Est Nilpotente

The main object of this note is to prove the following generalisation of a theorem of Serre. A simply connected space of finite type whose mod. 2 cohomology is nilpotent (and non-trivial) has infinitely many homotopy groups which are not of odd torsion. Incidentally we show that for every fibrationF( _→ ^ί )E ( _→ ^p )B, satisfying certain mild conditions, the following holds. If a classx in the mod. 2 cohomology ofE belongs to the kernel ofi*, then some power ofx belongs to the ideal generated by the image underp* of the mod. 2 reduced cohomology ofB.      

The Interaction of Shocks with Dispersive Waves II. Incompressible-Integrable Limit

This is the second in a two-part series of articles in which we analyze a system similar in structure to the well-known Zakharov equations from weak plasma turbulence theory, but with a nonlinear conservation equation allowing finite time shock formation. In this article we analyze the incompressible limit in which the shock speed is large compared to the underlying group velocity of the dispersive wave (a situation typically encountered in applications). After presenting some exact solutions of the full system, a multiscale perturbation method is used to resolve several basic wave interactions. The analysis breaks down into two categories: the nonlinear limit and the linear limit, corresponding to the form of the equations when the group velocity to shock speed ratio, denoted by ε, is zero. The former case is an integrable limit in which the model reduces to the cubic nonlinear Schrödinger equation governing the dispersive wave envelope. We focus on the interaction of a “fast” shock wave and a single hump soliton. In the latter case, the ε=0 problem reduces to the linear Schrödinger equation, and the focus is on a fast shock interacting with a dispersive wave whose amplitude is cusped and exponentially decaying. To motivate the time scales and structure of the shock-dispersive wave interactions at lowest orders, we first analyze a simpler system of ordinary differential equations structurally similar to the original system. Then we return to the fully coupled partial differential equations and develop a multiscale asymptotic method to derive the effective leading-order shock equations and the leading-order modulation equations governing the phase and amplitude of the dispersive wave envelope. The leading-order interaction equations admit a fairly complete analysis based on characteristic methods. Conditions are derived in which: (a) the shock passes through the soliton, (b) the shock is completely blocked by the soliton, or (c) the shock reverses direction. In the linear limit, a phenomenon is described in which the dispersive wave induces the formation of a second, transient shock front in the rapidly moving hyperbolic wave. In all cases, we can characterize the long-time dynamics of the shock. The influence of the shock on the dispersive wave is manifested, to leading order, in the generalized frequency of the dispersive wave: the fast-time part of the frequency is the shock wave itself. Hence, the frequency undergoes a sudden jump across the shock layer.In the last section, a sequence of numerical experiments depicting some of the interesting interactions predicted by the analysis is performed on the leading-order shock equations.     

Nitrogen bridgehead compounds. Part 70. Studies on quinolizine derivatives. Part 4. Ultraviolet-visible spectra and chemical properties of some quinolizine derivatives and their monocyclic tautomers

Ultraviolet-visible spectra of 4-oxo 1 and 4-imino 2 quinolizines or their monocyclic tautomers 3, 4 have been studied in neutral, acidic and basic ethanolic solution as well as in dimethyl sulfoxide and chloroform. Ring B of 4-oxo and 6-unsubstituted 4-imino compounds can be cleaved by sodium ethanolate more or less easily. Ring B of 6-methyl-4-iminoquinolizines is very unstable and they are present mainly in the monocyclic form which are partly dissociated in ethanol and dimethyl sulfoxide especially in higher dilution or in the presence of sodium ethanolate. In dilute acidic ethanol or chloroform, the dissociation is suppressed and in the latter solvent and in some cases, absorption bands can be observed due to a small amount of the 4-imino-6-methylquinolizines. In acidic solution of compounds 3B=C, 3D, 4E, 4F=G having simultaneously cyano and ethoxycarbonyl groups in 1 and 3 position, not simple reprotonation occurs but irreversible changes can be observed.     

Die Bestimmung von Methylpropan

Ohne Zusammenfassung     

Comparison between biokinetics of inhaled plutonium nitrate and gadolinium oxide in humans and animals

Due to the paucity of human data after inhalation of different chemical forms of radionuclides, the implications for human exposure are often based on animal studies. This paper describes biokinetic studies of plutonium nitrate and gadolinium oxide in human volunteers and rats. The results, together with information from other studies with radionuclides, suggests that animal studies can be used with advantage for assessing the biokinetic behavior in humans, and for providing guidance on the assessment of intake and optimal monitoring regimens.     

A simple derivation of Vonnegut's equation for the determination of interfacial tension by the spinning drop technique

A simple derivation of Vonnegut's equation for use in the determination of interfacial tension by the spinning drop technique is described. The derivation involves a cylindrical approximation and calculates the kinetic energy of rotation of the system from a consideration of its moment of inertia.     

A propos de conjectures de Serre et Sullivan

Summary We first give a new proof of a conjecture of J.-P. Serre on the homotopy of finite complexes, which was recently proved by C. McGibbon and J. Neisendorfer. The emphasis is on a property of the mod. 2 homology of certain spaces: their quasi-boundedness as right modules over the Steenrod algebra. This property is preserved when one goes from a simply connected space to its loop space and also when one takes a covering of anH-space. Then we show that this notion of quasi-boundedness simplifies H. Miller's proof of D. Sullivan's conjecture on the contractibility of the space of pointed maps from the classifying space of the groupe /2 into a finite complex.