The properties of volume holograms used for correction of laser beams

A theoretical study of hologram correction of laser beams is described. The result of experiments with this correction method are described for media with local response.     

Reactivity of Water and Alcohols toward Carbocations Generated in the Photolysis of 2,2,4,6-Tetramethyl-1,2-dihydroquinoline

The rate constants of the decay of carbocation generated in the photolysis of 2,2,4,6-tetramethyl-1,2-dihydroquinoline and the composition of reaction products were studied as a function of solvent composition in the mixtures H₂O–ROH and MeOH–ROH (R = Et, n-Pr, and i-Pr). The rate constants of carbocation decay in alcohols are more than 20 times higher than the corresponding rate constants in water. As follows from the composition of the products obtained in the photolysis in the alcohol–water mixtures, MeOH is only 1.4 times more reactive than water, and EtOH and n-PrOH are even less active than water. The inconsistency in the product composition in the mixtures and the values of the observed rate constants in these solvents was explained by the two-step mechanism of the reaction: the reversible formation of an adduct of the carbocation with the solvent components and subsequent proton transfer to the solvent to form the final product, with the first step determining the product composition and the second step determining the rate of carbocation decay. The relative rate constants of alcohols and water were determined for the two steps. The preferred solvation of the carbocation with water also contributes significantly to the reaction kinetics and the product composition in the water–alcohol solutions.     

Kinetics and Mechanism of the Photoinduced Addition of Water and Methanol to the Double Bond of 2,2,4-Trimethyl-8-Methoxy-1,2-Dihydroquinoline

The mechanism of the photoinduced Markovnikov addition of water and methanol to the double bond of 2,2,4-trimethyl-8-methoxy-1,2-dihydroquinoline was studied by flash photolysis over a wide range of acid and alkali concentrations. In neutral MeOH solutions, the successive formation of two active intermediates was observed. These intermediates have absorption bands at _max = 420 and 500 nm, respectively, and lifetimes of a few milliseconds. The rate constants of decay for these species (k ₁ and k ₂) were measured over the temperature range from 10 to 45°C, and the activation energies E ₁ (3.7 ± 0.4) and E ₂ (6.9 ± 0.7) kcal/mol were determined in MeOH. The addition of an acid accelerates the conversion of the former intermediate into the latter. The rate constant for the reaction of the former intermediate with the acid is (2.0 ± 0.4) × 10⁸ l mol^–1 s^–1. The latter intermediate was proposed to be a corresponding carbocation. In H₂O at pH < 9, the formation of the carbocation (_max = 500 nm) was observed on a millisecond timescale, with the lifetime being an order of magnitude higher than that in MeOH. In alkaline media, only the former intermediate (_max = 420 nm) was observed with a lifetime of 150 or 400 ms in MeOH or H₂O, respectively, at [NaOH] > 2 × 10^–3 mol/l. The quantum yields of the product and the quantum yields of fluorescence were measured as functions of acidity. Possible mechanisms of the reaction are discussed.     

Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

We study the limit behaviour of solutions of with initial data k δ ₀ when k → ∞, where h is a positive nondecreasing function and p > 1. If h(r) = r ^β , β > N(p − 1) − 2, we prove that the limit function u _∞ is an explicit very singular solution, while such a solution does not exist if β ≤  N(p − 1) − 2. If lim inf _{r→ 0} r ² ln (1/h(r))  >  0, u _∞ has a persistent singularity at (0, t) (t ≥  0). If , u _∞ has a pointwise singularity localized at (0, 0).     

Engineering Margin Factors Used in the Design of the VVER Fuel Cycles

The article describes methods for determination of the engineering margin factors currently used to estimate the uncertainties of the VVER reactor design parameters calculated via the KASKAD software package developed at the National Research Center Kurchatov Institute. These margin factors ensure the meeting of the operating (design) limits and a number of other restrictions under normal operating conditions.     

On the Absence of Global Solutions of a Class of Higher-Order Evolution Inequalities

Mathematical Notes -     

The equilibrium molecular structure of 2-cyanopyridine from combined analysis of gas-phase electron diffraction and microwave data and results of ab initio calculations

Structural Chemistry - The gas-phase electron diffraction study of 2-cyanopyridine was carried out for the first time. Results of ab initio structure calculations performed at the CCSD(T) level of...     

Molecular structure of (cyanomethoxy)(dimethylamino)methane as studied by gas-phase electron diffraction and quantum-chemical calculations

The molecular structure of (cyanomethoxy)(dimethylamino)methane in the gas phase is investigated by means of gas-phase electron diffraction and quantum-chemical studies for the first time. It is shown that in the gaseous state, (cyanomethoxy)(dimethylamino)methane is a mixture of gauche-anti (65%) and anti-gauche (35%) conformers. The slight influence of the anomeric effect on the compound’s structural parameters was noted.     

Semiexperimental equilibrium structure of 1-methylisatin from gas-phase electron diffraction data and structural changes in isatin due to 1-methyl and 5-fluoro substituents as predicted by coupled cluster computations

ABSTRACT

The molecular structure of 1-methylisatin (1) has been studied by gas-phase electron diffraction (GED) and quantum chemical computation up to the coupled cluster (CCSD(T)) level of theory. The semiexperimental equilibrium structure (C_s point group symmetry) has been determined from the GED data taking into account anharmonic vibrational corrections calculated in curvilinear coordinates with the B2PLYP force field. To observe fine structural effects due to the presence of different kinds of substituents, the accurate molecular structures of isatin (2) and 5-fluoroisatin (3) were also computed at the CCSD(T) level. The (O=)C–C(=O) carbon–carbon bonds of the pyrroline moiety in 1–3 are found to be remarkably longer than the typical single C–C bond. The electron donating methyl group causes a decrease of the C?N?C angle and an elongation of the N?C bond lengths in the pyrroline ring by 0.7° and up to 0.008?Å, respectively, whereas the electron withdrawing fluorine atom increases the ipso CCC angle by 2.5° in comparison to that in unsubstituted isatin.     

Mechanism of Photoinduced Addition of Water and Methanol to the Double Bond of 1,2-Dihydroquinolines

The kinetics and mechanism of photoinduced addition of water and methanol to the double bond of 2,2,4-trimethyl-1,2-dihydroquinoline (DHQ) bearing different substituents in the 6- and 8-positions and N-methylated DHQ were studied by flash photolysis. The reaction affords corresponding Markovnikov adducts, 4-hydroxy- and 4-methoxy-1,2,3,4-tetrahydroquinolines. On the basis of time-resolved experiments and the measurement of quantum yields of the reaction in media of different acidities or basicities, a general scheme of the reaction is suggested, which involves the formation of two intermediate species. The principal rate constants, activation parameters, and their dependence on substituents were determined.