On the invariance of classes under composition

The necessary and sufficient condition for to be in the class for every of that class whose range is in the domain of is that be in .

     

Effect of pigment packaging on diffuse reflectance spectroscopy of samples containing red blood cells

We present the results of diffuse reflectance measurements made on the surface of a tissue-simulating phantom containing intact human erythrocytes. These measurements indicate that the absorption spectrum of hemoglobin in its natural environment is significantly different from that measured in homogeneous fluid solution, especially in the spectral regions of highest absorption. We show that this difference can be explained by the pigment packaging theory developed by Duysens [Biochim. Biophys. Acta 19, 1 (1956)] and that the adoption of basis spectra that take this effect into account improves the accuracy of fitting diffuse reflectance spectra.     

Highly selective formation of linear esters from terminal and internal alkenes catalysed by palladium complexes of bis-(di-tert-butylphosphinomethyl)benzene

The methoxycarbonylation of terminal or internal alkenes catalysed by palladium complexes of bis-(di-tert-butylphosphinomethyl)benzene under mild conditions leads to linear esters in 99% selectivity via a hydride mechanism.     

Measuring hearing in the harbor seal (Phoca vitulina): comparison of behavioral and auditory brainstem response techniques

Auditory brainstem response (ABR) and standard behavioral methods were compared by measuring in-air audiograms for an adult female harbor seal (Phoca vitulina). Behavioral audiograms were obtained using two techniques: the method of constant stimuli and the staircase method. Sensitivity was tested from 0.250 to 30 kHz. The seal showed good sensitivity from 6 to 12 kHz [best sensitivity 8.1 dB (re 20 microPa2 x s) RMS at 8 kHz]. The staircase method yielded thresholds that were lower by 10 dB on average than the method of constant stimuli. ABRs were recorded at 2, 4, 8, 16, and 22 kHz and showed a similar best range (8-16 kHz). ABR thresholds averaged 5.7 dB higher than behavioral thresholds at 2, 4, and 8 kHz. ABRs were at least 7 dB lower at 16 kHz, and approximately 3 dB higher at 22 kHz. The better sensitivity of ABRs at higher frequencies could have reflected differences in the seal's behavior during ABR testing and/or bandwidth characteristics of test stimuli. These results agree with comparisons of ABR and behavioral methods performed in other recent studies and indicate that ABR methods represent a good alternative for estimating hearing range and sensitivity in pinnipeds, particularly when time is a critical factor and animals are untrained.     

Synthesis of a hexaalkoxybenzo[b]triphenylene mesogen

The synthesis of the first mesogenic hexaalkoxybenzo[b]triphenylene derivative is reported; this compound exhibits a broad columnar liquid crystal phase at temperatures only slightly above room temperature.     

Finding prime pairs with particular gaps

By a prime gap of size , we mean that there are primes and such that the numbers between and are all composite. It is widely believed that infinitely many prime gaps of size exist for all even integers . However, it had not previously been known whether a prime gap of size existed. The objective of this article was to be the first to find a prime gap of size , by using a systematic method that would also apply to finding prime gaps of any size. By this method, we find prime gaps for all even integers from to , and some beyond. What we find are not necessarily the first occurrences of these gaps, but, being examples, they give an upper bound on the first such occurrences. The prime gaps of size listed in this article were first announced on the Number Theory Listing to the World Wide Web on Tuesday, April 8, 1997. Since then, others, including Sol Weintraub and A.O.L. Atkin, have found prime gaps of size with smaller integers, using more ad hoc methods. At the end of the article, related computations to find prime triples of the form , , and their application to divisibility of binomial coefficients by a square will also be discussed.

     

Hankel Operators on Bounded Analytic Functions

For a domain in the complex plane and a bounded measurable function on , the generalized Hankel operator on is the operator of multiplication by followed by projection into . Under certain conditions on we show that either is compact or there is an embedded on which is bicontinuous. We characterize those 's for which is compact in the case that is a Behrens roadrunner domain.