Interaction of Alkyl Radicals with Dihydric Phenol Derivatives in Hexane Solutions under γ-Radiolysis

The influence of structurally different dihydric phenols on the radical reactions of hexane in deaerated solutions under -irradiation was studied. It was found that 4-tert-butylpyrocatechol (I), 3,5-diisopropylpyrocatechol (II), 2,5-di-tert-butylhydroquinone (III), and 4,6-di-tert-butylresorcinol (IV) effectively inhibited the formation of hexyl radical combination products. Using the chromatography–mass spectrometry technique, it was shown that the adducts of alkyl radicals with I–III have the structure of a monoalkyl ether. Phenol IV gave a mixture of dimers with O- and C-alkylation products.     

Effects of anisotropic diffraction on quadratic multisoliton excitation in noncritically p hase-matched crystals

The generation of multiple quadratic spatial solitons aligned approximately along a crystal axis in a biaxial noncritically phase-matched crystal is shown theoretically and experimentally to be the consequence of anisotropic diffraction.     

Fluidization of Nano-size Particles

Fluidization and collapsing bed experiments were performed with 'Tullanox', 10nm diameter fumed silica. The minimum fluidization velocity was determined to be 0.0115m/s at the unusually low volume fraction of solids of 0.0077. The solids volume fraction was measured using a -ray densitometer. Fluidization was without large bubbles, with a high bed expansion ratio. The highest granular temperature was of the order of that of Geldart B particles, as measured by Cody et al. (1996). The sedimentation process was simulated using a two-fluid hydrodynamic model. The input into the model was a measured solids stress modulus and an agglomerate size determined from the settling curves. With these two rheological parameters, there was good agreement between the sedimentation theory and the experiment. This study shows that the standard collapse bed experiment used in industry is a good test of rheological properties of particles.     

A Note on Error Bounds for Convex and Nonconvex Programs

Given a single feasible solution and a single infeasible solution of a mathematical program, we provide an upper bound to the optimal dual value. We assume that satisfies a weakened form of the Slater condition. We apply the bound to convex programs and we discuss its relation to Hoffman-like bounds. As a special case, we recover a bound due to Mangasarian [11] on the distance of a point to a convex set specified by inequalities.     

Study of hyperfine interaction and electronic relaxation using coincidence Mössbauer spectroscopy

Coincidence Mössbauer spectroscopy (CMS) in the presence of a hyperfine field and electronic spin relaxation is discussed. The resulting expression for the transmission through a resonant absorber as a function of time is found with the help of the joint solution of the Maxwell equations and the density matrix equations. It is shown that the radiation that reaches the detector behind the absorber is modulated by the hyperfine field. The various polarization schemes for the CMS observation are analyzed. Numerical calculations were made for an⁵⁷ Fe nucleus.     

A problem concering characteristic functions of linear operators

The construction of a bounded operator in terms of its characteristic function is investigated.Translated from Matematicheskie Zametki, Vol. 9, No. 2, pp. 171–180, February, 1971.     

Analysis of the states of stress and strain of circular oriented-plastic plates

Retaining the fundamental assumption _z=0, the author investigates two-dimensional problems of the bending of cylindrically orthotropic circular plates in relation to the anisotropy parameter k=E/E_r and a generalized parameter depending both on the transverse shears and the dimensions of the plates h²/a²×E_r/G_rz. Equations are given for calculating certain quantities from the classical variant of the solutions. There are shown to be important differences in the solutions for boundary conditions of the clamped-edge type (when a horizontal or vertical element of the edge is fixed). The effect of the stress _z is estimated from the standpoint of the Ambartsumyan theory [2]. Two types of loading, a distributed load q=const and a concentrated load P applied at the center of the plate, are considered.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 899–908, September–October, 1969.     

The string coupling accelerates the expansion of the universed

Generic cosmological models in non-critical string theory have a time-dependent dilaton background at a late epoch. The cosmological deceleration parameter q ₀ is given by the square of the string coupling, g _s ², up to a negative sign. Hence the expansion of the Universe must accelerate eventually, and the observed value of q ₀ corresponds to g _s ² ∼ 0.6. In this scenario, the string coupling is asymptotically free at large times, but its present rate of change is imperceptibly small. First Award in the 2005 Essay Competition of the Gravity Research Foundation. - Ed.