Equivalent two-level atom method for calculating the kinetics of cosmological hydrogen recombination

The effective coefficient of recombination to the second level, which enters the equations describing the recombination kinetics in the cosmological HII region, is calculated. The calculation method is based on the quasi-steady-state approximation and makes it possible to adequately consider cascade transitions and induced processes without the necessity to numerically solve a complete set of corresponding kinetic equations.     

Cancellation law and attainable classes of linear ω-algebras

With the aid of mixed linear Ω-algebras we prove a theorem to the effect that the cancellation law is satisfied in a groupoid of subvarieties of a variety of Ω-algebras linear over a field and given by identities of zero order. We show that in some varieties of Ω-algebras linear over an infinite ring of principal ideals there are no nontrivial finitely attainable subvarieties. As examples of such varieties we cite the varieties of all Ω-rings, of all rings, of commutative or anticommutative rings (Ω-rings), of Lie rings, et al. In the case of anticommutative rings (Ω-rings) this property holds for Ω-algebras, linear over an arbitrary integral domain without stable ideals.     

The Gamma Distribution and Inventory Control

The paper aims to justify the applicability of the gamma distribution to inventory control and to collect under one heading the properties of the distribution and associated formulae arising from inventory control theory. Algorithms for computer calculation are given.     

Control of selectivity in the generation and reactions of oxonium ylides

Dirhodium catalyzed reactions of aryl-substituted tetrahydropyranone diazoacetoacetates produce ylide intermediates that unexpectedly yield two oxabicyclo[4.2.1]-nonane diastereoisomers, but a single diastereoisomer is formed by increasing the steric bulk of the aryl substituent.     

Approximations by linear operators in spaces of fuzzy continuous functions

In this work, we further develop the Korovkin-type approximation theory by utilizing a fuzzy logic approach and principles of neoclassical analysis, which is a new branch of fuzzy mathematics and extends possibilities provided by the classical analysis. In the conventional setting, the Korovkin-type approximation theory is developed for continuous functions. Here we extend it to the space of fuzzy continuous functions, which contains a great diversity of functions that are not continuous. Furthermore, we give several applications, demonstrating that our new approximation results are stronger than the classical ones.     

A theoretical analysis of the excited states in 2-benzoylthiophene

The lower excited states of 2-benzoylthiophene have been studied using ab initio quantum chemical methods based on multiconfigurational wave functions. Six singlet and six triplet excited states have been characterized. The geometry has been optimized for the two lowest triplet states, which are responsible for the photoreactivity of the chromophore in the photosensitizing drug tiaprofenic acid. The T¹(π → π?) and T₂(n → π?) states have been found to be close in energy with the π → π? state slightly lower. The excited states have been characterized using density difference and spin density plots. The different photochemical behaviour of the two triplet states can be rationalized from the theoretical data.     

II: PROPERTIES OF DIATOMIC AND TRIATOMIC MOLECULES

Results are presented from a theoretical study of the × ⁶Σ⁺, A ⁶Σ⁺ and ⁶Δ electronic states of CrH using multiconfiguration second-order perturbation theory in the multi-state formalism (MS-CASPT2). It is shown that the results for the spectroscopic constants and radiative lifetimes for the A state are in agreement with experiment and an earlier multireference configuration interaction study only if the two close lying × and A states are allowed to interact at a level of approximation that includes dynamic correlation.     

Competitive [2,3]- and [1,2]-oxonium ylide rearrangements. Concerted or stepwise?

The axial-equatorial conformational isomer distribution of the reactant diazoacetoacetate or its metal carbene intermediate is reflected in Rh(II) catalyzed oxonium ylide forming reactions of 3-(trans-2-arylvinyl)tetrahydropyranone-5-diazoacetoacetates that afford diastereoisomeric products for both the symmetry-allowed [2,3]- and the formally symmetry-forbidden [1,2]-oxonium ylide rearrangements.     

Rate constants and kinetic isotope effects for unimolecular 1,2-HX or DX (X = F or Cl) elimination from chemically activated CF3CFClCH3-d0, -d1, -d2, and -d3

Chemically activated CF(3)CFClCH(3), CF(3)CFClCD(3), CF(3)CFClCH(2)D, and CF(3)CFClCHD(2) molecules with 94 kcal mol(-1) of internal energy were formed by the combination of CF(3)CFCl radicals with CH(3), CD(3), CH(2)D, and CHD(2) radicals, which were generated from UV photolysis of CF(3)CFClI and CH(3)I, CD(3)I, CH(2)DI, or CHD(2)I. The total (HF + HCl) elimination rate constants for CF(3)CFClCH(3) and CF(3)CFClCD(3) were 5.3 x 10(6) and 1.7 x 10(6) s(-1) with product branching ratios of 8.7 +/- 0.6 in favor of HCl (or DCl). The intermolecular kinetic isotope effects were 3.22 and 3.18 for the HCl and HF channels, respectively. The product branching ratios were 10.3 +/- 1.9 and 11.8 +/- 1.8 (10.8 +/- 3.8 and 11.6 +/- 1.7) for HCl/HF and DCl/DF, respectively, from CF(3)CFClCH(2)D (CF(3)CFClCHD(2)). The intramolecular kinetic-isotope effects (without correction for reaction path degeneracy) for HCl/DCl and HF/DF elimination from CF(3)CFClCH(2)D (CF(3)CFClCHD(2)) were 2.78 +/- 0.16 and 2.98 +/- 0.12 (0.82 +/- 0.04 and 0.91 +/- 0.03), respectively. Density function theory at the B3PW91/6-311+G(2d,p) and B3PW91/6-31G(d',p') levels was investigated, and the latter was chosen to calculate frequencies and moments of inertia for the molecules and transition states. Rate constants, branching ratios and kinetic-isotope effects then were calculated using RRKM theory with torsional motions treated as hindered internal rotations. Threshold energies for HF and HCl elimination from CF(3)CFClCH(3) were assigned as 61.3 +/- 1.5 and 58.5 +/- 1.5 kcal mol(-1), respectively. The threshold energy for Cl-F interchange was estimated as 67 kcal mol(-1). The difference between the transition states for HCl and HF elimination is discussed.