Semigroups satisfying variable identities

The purpose of this note is to generalize a theorem of Tamura’s [3] providing a self-contained and, we think, more elementary proof than Tamura’s in that it avoids using the theory of contents. Tamura’s result states that a semigroup S satisfies an identify xy=f(x,y) with f(x,y) a word of length greater than 2 which starts with y and ends in x if and only if S is an inflation of a semilattice of groups satisfying the same identity. We investigate semigroups as in Tamura’s Theorem, except that we permit f(x,y) to vary with x and y.     

A new bis-andrographolide ether from Andrographis paniculata nees and evaluation of anti-HIV activity

Novel bis-andrographolide ether (1) and six known compounds andrographolide, 14-deoxy-11,12-didehydroandrographolide, andrograpanin, 14-deoxyandrographolide, (+/-)-5-hydroxy-7,8-dimethoxyflavanone, and 5-hydroxy-7,8-dimethoxyflavone have been isolated from the aerial parts of Andrographis paniculata and their structures were established by spectral data. All the isolates were tested for the anti-HIV and cytotoxic activity.     

Estimation of frequency-averaged loss factors by the power injection and the impulse response decay methods

This paper describes a comparison, both analytically and experimentally, between two widely used loss factor estimation techniques frequently used in statistical energy analysis. Analytical models of simple spring/mass/damper systems were created to compare frequency-averaged loss factor values from the single subsystem power injection method and the impulse response decay method. The parameters of the analytical models were varied to study the effects of the total number of modes, amount of damping, location of modes within frequency bands, and the width of the frequency bands on loss factor estimation. The analytical study shows that both methods give accurate loss factor values as long as the damping values remain realistic for linear systems and at least one modal resonance is present in each frequency band. These analytical results were verified experimentally by measuring the loss factors of simple steel plates, with and without damping treatments applied.     

Recovery of spectral features readout with frequency-chirped laser fields

A data-processing technique is proposed for use with conventional frequency-chirped absorption spectroscopy to ensure accurate mapping of spectral features into time-domain signatures with arbitrarily fast readout chirp rates. This technique recovers the spectrum from a signal that is distorted owing to the fast chirp rate and therefore facilitates fast measurement of the spectral features over a broad spectral range with high resolution. Both numerical simulations and experimental results are presented.     

Effects of nonuniform illumination on implosion asymmetry in direct-drive inertial confinement fusion

Target areal density (rhoR) asymmetries in OMEGA direct-drive spherical implosions are studied. The rms variation / for low-mode-number structure is approximately proportional to the rms variation of on-target laser intensity / with an amplification factor of approximately 1/2(C(r)-1), where C(r) is the capsule convergence ratio. This result has critical implications for future work on the National Ignition Facility as well as OMEGA.     

Lewis acid-promoted annulation of O-quinonediimines by allylstannane: a facile synthesis of quinoxaline derivatives

[reaction: see text] Lewis acid-promoted addition of allyltri-n-butylstannane to o-quinonediimines afforded tetrahydroquinoxaline derivatives or allylated amides depending on the nature of the substituent on imine nitrogen.