A transient two-photon–one-photon double resonance on interband transitions in crystals: II. Calculation of absorbed of light energy

The dependences of the energy that is absorbed in a crystal exposed to the action of a femtosecond light pulse on the radiation intensity at a fixed pulse duration and on the pulse duration at a fixed pulse energy have been determined under the conditions of a two-photon–one-photon double resonance on interband transitions in the crystal.     

Model of organization of the epitropic liquid phase

We propose a molecular-statistical model of organization of the epitropic liquid-crystal phase, according to which the presence of fluctuation associates in the bulk of the liquid and active (adsorption) centers on the solid substrate is essential for the formation of this phase. Using this model, it is possible to describe the experimental temperature dependence of the thickness of the epitropic liquid-crystal layer of nitrobenzene on quartz. Quantitative agreement between the theory and experiment is reached in the close proximity (～10 K) of the crystallization temperature. Important thermodynamic parameters of the model can be corrected from comparison with experimental results.     

Analysis of experimental data within the statistical theory of critical phenomena

An approach devised earlier is generalized for a binodal line and used to analyze experiments on a broad set of fluids from He⁴ to organic compounds. Experimental binodal lines and isothermal compressibility are described with precision for the above substances. The error characterizing the theory’s deviation from the experimental data is several times lower than in a similar analysis using the Ising model.     

New oxazoline-containing phosphoramidite ligand for palladium-catalyzed asymmetric allylic sulfonylation

New chiral oxazoline-containing phosphoramidite was synthesized and its complex formation with rhodium(i) and palladium(ii) was examined. The new ligand is a highly efficient chiral inductor (ee up to 92%) in palladium-catalyzed asymmetric sulfonylation of 1,3-diphenylallyl acetate with sodium p-toluenesulfinate.     

Estimation of rated influence in parabolic systems.L 2-approach

By using observations of solutions of the first initial boundary-value problem for a parabolic quasilinear equation with fast random oscillations, we estimate the nonlinear term of the equation. In the metric of the space L₂, we study large deviations of a nonparametric estimate of nonlinear influence.     

On the Existence of a Globally Lyapunov Unstable Differential System All of Whose Solutions Tend to Zero as Time Tends to Infinity

Differential Equations - Using a particular example, we constructively prove that the convergence of all solutions of a nonautonomous two-dimensional differential system to zero at infinity does...     

Palladium-catalyzed asymmetric synthesis of allylic alcohols from unsymmetrical and symmetrical racemic allylic carbonates featuring C-O-bond formation and dynamic kinetic resolution

Described is the asymmetric synthesis of the allylic alcohols 11 (85% ee), 15 (99% ee), 17 (93% ee), 19 (61% ee), and 21 (69% ee) through a Pd-catalyzed reaction of the unsymmetrical carbonates rac-10, rac-12, rac-14, rac-16, rac-18, and rac-20, respectively, with KHCO₃ and H₂O in the presence of bisphosphane 6. Similarly the allylic alcohols 23 (99% ee) and 25 (97% ee) have been obtained from the symmetrical carbonates rac-22 and rac-24, respectively. Reaction of the meso-biscarbonate 26 with H₂O and Pd(0)/6 afforded alcohol 27 (96% ee), which was converted to the PG building block 32. The unsaturated bisphosphane 33 showed in the synthesis of alcohols 36, 37, and 39 a similar high selectivity as 6. The formation of alcohols 11, 15, and 17 involves an efficient dynamic kinetic resolution.     

Reaction of ammonia with β,β′-dithioalkyl-α,α′-divinyl ketones

Conclusions Syntheses are reported for ,-dithioalkyldivinyl ketones, which react with ammonia to give -amino--thioalkyldivinyl ketones.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2414–2415, October, 1988.The authors thank A. M. Kachurin for assistance in taking the spectra.     

On linear and nonlinear aspects of dynamic mode decomposition

The approximation of reduced linear evolution operator (propagator) via dynamic mode decomposition (DMD) is addressed for both linear and nonlinear events. The 2D unsteady supersonic underexpanded jet, impinging the flat plate in nonlinear oscillating mode, is used as the first test problem for both modes. Large memory savings for the propagator approximation are demonstrated. Corresponding prospects for the estimation of receptivity and singular vectors are discussed. The shallow water equations are used as the second large‐scale test problem. Excellent results are obtained for the proposed optimized DMD method of the shallow water equations when compared with recent POD‐based/discrete empirical interpolation‐based model reduction results in the literature. Copyright © 2016 John Wiley & Sons, Ltd.