Prime divisors of sparse integers

We obtain a lower bound on the number of prime divisors of integers whose g-ary expansion contains a fixed number of nonzero digits. This revised version was published online in August 2006 with corrections to the Cover Date.     

The evolution of a truncated gaussian probability density through time—modelling animal liveweights after selection

The form of the probability density derived from the evolution in time of a previously truncated frequency distribution of animal Liveweights is of interest in animal husbandry. Truncated frequency distributions arise when the heavier animals are sold for slaughter and the lighter animals retained. The demands of modern quality assurance schemes require that, given information on animal growth, the farmer is able to estimate the number of animals that would meet the specifications at some time in the future after truncation. Assuming that animal growth can be described by a linear stochastic differential equation, we derive an explicit expression for the probability density of animal Liveweights at any time after the truncation of an initial Gaussian density. It is shown that this probability density converges rapidly to a Gaussian density, so that after about 20 days of typical growth rates for lambs, the resulting density is practically indistinguishable from Gaussian.     

Three-dimensional structure of Saccharomyces cerevisiae inorganic pyrophosphatase complexed with cobalt and phosphate ions

Crystals of Saccharomyces cerevisiae inorganic pyrophosphatase suitable for X-ray diffraction study were grown by cocrystallization of the enzyme with cobalt chloride and imidodiphosphate. Saccharomyces cerevisiae is a metal-dependent enzyme which catalyzes hydrolysis of inorganic pyrophosphate to orthophosphate. The three-dimensional structure of this enzyme was solved by the molecular-replacement method and refined at 1.8 Å resolution to an R factor of 19.5%. Cobalt and phosphate ions were revealed in the active centers of both identical subunits (A and B) of the pyrophosphatase molecule. In subunit B, a water molecule was found between two cobalt ions. It is believed that this water molecule acts as an attacking nucleophile in the enzymatic cleavage of the pyrophosphate bond. It was demonstrated that cobalt ions and a phosphate group occupy only part of the potential binding sites (two chemically identical and crystallographically independent subunits have different binding sites). The arrangement of ligands and the structure of the nucleophile-binding site are discussed in relation to the mechanism of action of the enzyme and the nature of the metal activator.     

Electronic molecule-like spectrum of quantum wells in crossed fields

We show that an electron confined to a single finite parabolic quantum well in crossed electric and magnetic fields can behave as a double quantum well system. The magnetic field is parallel to the heterostructure layers and the electric field is perpendicular to those. For a suitable choice of both fields and quantum well width, the electron can be confined to a double quantum well effective potential that is very similar to the electronic potential model for diatomic molecules. The double quantum well spectrum is calculated using a numerical algorithm based on semiclassical methods. A physical interpretation of this quantum system is given based on the analogy to the electrons bound to diatomic molecules.     

On nonspecular “total internal reflection” of powerful electromagnetic waves

It is shown that the nonstable character of nonlinear interaction of a system of waves similar to that resulting from double stimulated Brillouin scattering is retained upon the oblique incidence of a powerful electromagnetic wave on a layer of supercritical plasma. In this case we have nonlinear back reflection from a layer of supercritical plasma. The threshold intensity of the pump wave is greater than that in the case of subcritical plasma for TE polarization waves but can markedly decrease for waves polarized in the incidence plane. Instability is possible only for a layer of finite thickness.Radiophysical Research Institute, Nizhny Novgorod. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, Nos. 3–4, pp. 298–303, March–April, 1995.     

Optical detection of NO3 and NO2 in “pure” HNO3 vapor,the liquid-phase decomposition of HNO3

Flowing and static gas-phase samples of HNO₃ in O₂ and N₂ were analyzed by long-path ultraviolet/visible (UV/VIS) spectroscopy to reveal the presence of both NO₂ and NO₃, the concentrations of which were calculated using differential absorption cross sections. NO₂ is produced predominantly by the heterogeneous decomposition of HNO₃, whereas NO₃ is generated in the gas phase by the thermal decomposition of N₂O₅, a product of the self-disproportionation of liquid HNO₃. © 1993 John Wiley & Sons, Inc.     

Selective quenching of tryptophanyl fluorescence in bovine serum albumin by the iodide ion

Modified Stern-Volmer equation is obeyed by bovine serum albumin (BSA)-iodide system showing selective quenching of tryptophanyl fluorescence of BSA. The fraction of accessible protein fluorescence is 0.56 and the effective Stern-Volmer constant is 290 M^-1 at pH 7.4 in 0.005 M phosphate buffer at 25°C. Collisional quenching is operative both in the BSA -I⁻¹ system and the model system, tryptophan-I⁻¹. It is supported by the observed relationship between the ratio of quenching rate constants (k _q ) and diffusion coefficients and alsok _q with bulk viscosity.