Series representations for densities functions of a family of distributions—Application to sums of independent random variables

Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations.     

Imidazo [4,5-c] - and [4,5-6] pyridines

The synthesis of novel imidazo[4,5-c]pyridines 11-13 and imidazo[4,5-b]pyridines 18-20 is described using 2 as the starting material. The synthesis is generally applicable for the introduction of a wide variety of substituents.     

Fluorimetric assay of redox activity in cells

A simple, sensitive procedure is described for measurement of the redox activity of single cells based on cyanotolyltetrazolium chloride which is reduced to a fluorescent monoformazan. Its efficiency is studied by incubating vital ascites tumor cells or cells treated with different fixatives, under different oxygen concentrations. Redox activity (fluorescence of the formazan) and DNA content (fluorescence of Hoechst dye 333378) of ascites tumor cells are measured simultaneously for the first time, by flow cytometry.     

Precision heterodyne measurements of ozone spectral lines near 9.5 μm

Precision measurements of 26 individual spectral lines of ozone near 9.5 μm were made using the GSFC infrared heterodyne spectrometer. The line profiles of 26 lines in near coincidence with the emission lines from a ¹²C¹⁶O₂ laser local oscillator were measured at resolving powers of 6 × 10⁶. The retrieved absolute line center frequencies, accurate to ±3 MHz, and the relative line intensities were compared to previous experimental results and theoretical calculations.