Non-uniform bounds in local limit theorems in case of fractional moments. I

Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order s ≥ 2, where s may be noninteger.     

SIMS investigations of hydrogen interaction with a zirconium getter alloy surface

The results from secondary ion mass spectrometry (SIMS) investigations of the surface of Zr₅₀V₅₀ intermetallic getter alloy under residual and elevated partial pressures of hydrogen at different temperatures are reported.     

Nonuniform bounds in the Poisson approximation with applications to informational distances. II

Lithuanian Mathematical Journal - We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon...     

Exploring acetylene chemistry in superbasic media: A theoretical study of the effect of water on vinylation and ethynylation reactions with acetylene in KOH/DMSO and NaOH/DMSO systems

A rapidly developing approach adding new dimensions to acetylene chemistry relying on employment of high basicity media such as alkali metal hydroxide suspensions in dimethyl sulfoxide (DMSO) has been, for the first time, investigated theoretically using ab initio models. Extending our recently introduced model of superbase catalysis with a nondissociated KOH (or NaOH) participation, we present here a model for a superbasic reaction center with the first solvation shell explicitly included. The alkali metal hydroxides in a DMSO solution were found to form KOH·5DMSO and NaOH·4DMSO complexes that are stabilized due to the interligand interaction. Our present MP2/6‐311++G**//B3LYP/6‐31+G* computations show that 1 and 2 water molecules can build themselves into the MOH close surrounding without substantially perturbing the DMSO ligands and easily travel between different insertion positions. Our results predict that the activation energies in the series of reactions of nucleophilic addition to a triple bond with water, methanol, methanethiol, sodium hydrosulfide, and acetone in the presence of dihydrated complexes should be larger than those obtained with the participation of monohydrated ones, which is in fair agreement with the experimental findings. The present model also explains an increase in the ethynylation reaction yield in the presence of water by suppression of the competitive enolization reaction.     

M theory solution to the hierarchy problem

An old idea for explaining the hierarchy is strong gauge dynamics. We show that such dynamics also stabilizes the moduli in M theory compactifications on manifolds of G2 holonomy without fluxes. This gives stable vacua with softly broken supersymmetry, grand unification, and a distinctive spectrum of TeV and sub-TeV sparticle masses.     

Correlation of experimental data on the pulsation velocity intensity for turbulent fluid flow in channels of different form

An analysis is made of experimental data on the intensity of the velocity pulsations in turbulent fluid flow in channels of different shape. Correlating relations are constructed for the intensity of the velocity pulsation components as a function of the flow regime and coordinates.Notation x, y, z coordinates in the flow direction, along the normal and parallel to the channel wall, respectively - a normal distance from the channel center to the wall - b distance from the channel corner to the point of intersection with the wall of the normal from the channel center - ₁ dimensionless distance along the normal from the channel wall - ₂ dimensionless distance in the direction parallel to the channel wall - U local fluid velocity - U_m maximal fluid velocity - U average fluid velocity across the section - _i intensity (mean square value) of the i-th component of the velocity pulsations (u, v, w are the indices in the directions x, y, z, respectively) - _i0 value of the intensity of the velocity pulsation components at the center of the channel - U_L velocity difference within the limits of the hydrcdynamic macroscale - q² total turbulence energy at a fixed point of the flow     

Motion of inhomogeneities of a developed fluidized bed at small reynolds numbers

The instability of a fluidized system in which the particles are uniformly distributed in space [1–3] leads to the development of local inhomogeneities in the internal structure, these taking the form of more or less stable formations of packets of particles [4]. In accordance with the existing ideas based on experimental data [5–8, 13], the particle concentration within a packet may vary in a wide range from very small values (10^–2–10^–3 [8]) for bubbles to the concentration of the unfluidized bed for bunches of particles in a nearly closely packed state. The paper considers the steady disturbed motion of the fluid and solid phases near an ascending or descending packet of particles in a developed fluidized bed. It is assumed that the motion of the solid phase corresponds to a creeping flow of viscous fluid, and the viscosity of the fluidizing agent is taken into account only in the terms that describe the interphase interaction. The velocity fields and pressure distributions of the phases inside and outside a packet are determined. If the particle concentration within a packet tends to zero, the solution describes the slow motion of a bubble in a fluidized bed. The results of the paper are compared with results obtained earlier for the model of ideal fluids [9] and Batchelor's model [10], in which the fluidized bed is treated in a simplified form as a viscous quasihomogeneous continuum.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 57–65, July–August, 1984.     

Computer-aided modeling of the chemical process of drying of a moving dense multilayer mass of phosphorite pellets

Mathematical and computer models were developed for the chemical process of drying of a moving dense multilayer mass of phosphorite pellets in a travelling grate machine. These models take into account the intensity of the internal moisture transfer in a pellet and the overmoisturization of individual horizons in the heated bed of pellets, which enables one to determine the technological parameters of the drying mode. The adequacy of the developed mathematical model was tested by comparing the calculated values of the moisture content and temperature of pellets, the characteristics of the heat-transfer gas, and the intensity of the moisture transfer in pellets while drying in a moving dense bed with the results of industrial tests. Numerous computational experiments were performed to determine the relative degree of drying, the moisture content, the pellet drying intensity, and the moisture content of the heat-transfer gas at various characteristics of moist pellets and the operating technological parameters of the travelling grate machine.     

Oligonucleotides Containing Disaccharide Nucleosides

Disaccharide nucleosides with 2′‐O‐(D ‐arabinofuranosyl), 2′‐O‐(L ‐arabinofuranosyl), 2′‐O‐(D ‐ribopyranosyl), 2′‐O‐(D ‐erythrofuranosyl), and 2′‐O‐(5‐azido‐5‐deoxy‐D ‐ribofuranosyl) substituents were synthesized. These modified nucleosides were incorporated into oligonucleotides (see Table). Single substitution resulted in a ΔT_m of +0.5 to −1.4° for DNA/RNA and a ΔT_m of −0.8 to −4.7° for DNA/DNA duplexes. These disaccharide nucleosides can be well accommodated in RNA/DNA duplexes, and the presence of a NH₂−C(5″) group has a beneficial effect on duplex stability.