Structure and stability of isoxazoline compounds

Structure of isoxazoline compounds formed via the reaction of alkyl-substituted benzonitrile oxides with ethylene was determined by X-ray diffraction method. Isoxazoline ring is flattened, the bond lengths in it depend slightly on the nature of substituents (CH₃, C₂H₅) and their position in the benzene ring and the angle of rotation relative to the isoxazoline ring. The connection N-O has a length 1.422 Å. Thermal decomposition of isoxazolines in a liquid phase (160–280°C) is accompanied by the release of acetaldehyde and aromatic nitrile. Both the structure of the cycle and its stability is practically independent of the structure of an aromatic substituent. The rate constant of the initial stage is characterized by the low significance of kinetic parameters, E = 104°8 kJ mol^?1 and log a(A/c) = 7.2±0.8. The results obtained are rationalized in terms of biradical mechanism of isoxazoline ring-opening that includes an efficient recombination of the biradical and its disappearance as a result of synchronous multi-center rearrangement with the release of acetaldehyde.     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >...     

The B-factor index for the binding site (BFIbs) to prioritize crystal protein structures for docking

Structural Chemistry - In cheminformatics, protein-ligand docking is a powerful tool applied for virtual screening, pose prediction, and binding affinity estimation. However, docking results depend...     

Cluster structure of stable dissolved gas nanobubbles in highly purified water

Experiments using phase-modulation interference microscopy and Mueller-matrix polarimetry show that double-distilled water free of foreign solid matter contains macroscopic light scatterers. Numerical calculations suggest that these scatterers can be represented as micrometer-size clusters of polydisperse air bubbles with effective radii between 70 and 90 nm. The fractal dimension of the clusters varies from 2.4 to 2.8, and their concentration is on the order of 10⁶ cm^?3.     

Alkaline Earth–Olefin Complexes with Secondary Interactions

Strontium and calcium (alkaline earth: Ae) olefin complexes stabilised by secondary Ae???F?C and β‐agostic Ae???H?Si interactions are presented. Olefin coordination onto the alkaline earths is plain in the solid state, and it is thermodynamically favoured over the coordination of THF. The existence of the Ae???olefin interactions is corroborated by solution NMR data and DFT computations. The coordination mode of the olefin varies with steric effects and, if enforced, olefin dissociation can be compensated by the other non‐covalent interactions, as supported by DFT computations.     

A dynamic model of spherical perturbations in the Friedmann universe. I

A self-consistent set of equations describing the evolution of linear spherically symmetrical perturbations in the Friedmann world is derived for an arbitrary equation of state. A singular part of perturbations corresponding to a massive particle-like source is separated, an evolution equation for calculating the source mass is obtained and solved exactly. An exact solution to evolution equations for perturbations at an arbitrary equation of state is constructed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 66–76, January, 2008.     

Study of nanostructure of highly purified water by measuring scattering matrix elements of laser radiation

Experiments on modulation interference microscopy and measurement of light scattering matrix elements showed that double distilled water purified from solid impurities contains macroscopic scatterers of optical radiation. It follows from numerical calculation that these scatterers can be micrometer-scale clusters formed by polydisperse air bubbles with effective radii of 70 to 90 nm. The fractal dimension of such clusters is within 2.4–2.8 and their concentration is ∼ 10⁶ cm⁻³.     

Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1])

In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω2-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].     

Hydrodynamics of binary fluid phase segregation

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.