Interferometric study of the growth kinetics of K2Co(SO4)2 · 6H2O and K2Ni(SO4)2 · 6H2O crystals

Crystallography Reports - The growth kinetics of the (001) and (110) faces of K2Co(SO4)2 · 6H2O and K2Ni(SO4)2 · 6H2O crystals in the kinetic mode has been in situ investigated for the...     

Online adaptive local multiscale model reduction for heterogeneous problems in perforated domains

In this paper, we develop and analyze an adaptive multiscale approach for heterogeneous problems in perforated domains. We consider commonly used model problems including the Laplace equation, the elasticity equation, and the Stokes system in perforated regions. In many applications, these problems have a multiscale nature arising because of the perforations, their geometries, the sizes of the perforations, and configurations. Typical modeling approaches extract average properties in each coarse region, that encapsulate many perforations, and formulate a coarse-grid problem. In some applications, the coarse-grid problem can have a different form from the fine-scale problem, e.g. the coarse-grid system corresponding to a Stokes system in perforated domains leads to Darcy equations on a coarse grid. In this paper, we present a general offline/online procedure, which can adequately and adaptively represent the local degrees of freedom and derive appropriate coarse-grid equations. Our approaches start with the offline procedure, which constructs multiscale basis functions in each coarse region and formulates coarse-grid equations. We presented the offline simulations without the analysis and adaptive procedures, which are needed for accurate and efficient simulations. The main contributions of this paper are (1) the rigorous analysis of the offline approach, (2) the development of the online procedures and their analysis, and (3) the development of adaptive strategies. We present an online procedure, which allows adaptively incorporating global information and is important for a fast convergence when combined with the adaptivity. We present online adaptive enrichment algorithms for the three model problems mentioned above. Our methodology allows adding and guides constructing new online multiscale basis functions adaptively in appropriate regions. We present the convergence analysis of the online adaptive enrichment algorithm for the Stokes system. In particular, we show that the online procedure has a rapid convergence with a rate related to the number of offline basis functions, and one can obtain fast convergence by a sufficient number of offline basis functions, which are computed in the offline stage. The convergence theory can also be applied to the Laplace equation and the elasticity equation. To illustrate the performance of our method, we present numerical results with both small and large perforations. We see that only a few (1 or 2) online iterations can significantly improve the offline solution.     

A new simple and convenient method for preparation of oligonucleotides containing a pyrene or a cholesterol moiety

Russian Chemical Bulletin - A new simple and convenient approach to the synthesis of oligonucleotides containing pyrene or cholesterol moieties is described. The approach does not require a special...     

Study of the Radial Heterogeneity and Mosaic Microheterogeneity in KCNSH Mixed Crystals

Crystallography Reports - Mixed crystals of potassium?cobalt sulfate hexahydrate/potassium?nickel sulfate hexahydrate (K2Co(SO4)2 · 6H2O/K2Ni(SO4)2 · 6H2O (KCNSH)) have been...     

Dimerization of Phthalate Ion in Non-Aqueous Solvents

Russian Journal of General Chemistry - Solutions of tetraethylammonium phthalate in non-aqueous solvents (ethanol, dimethylsulfoxide, dimethylformamide, and acetonitrile) were studied by electronic...     

Subgroups of the Fan of Sylow Subgroups and the Supersolvability of a Finite Group

Mathematical Notes - The notion of the fan of a subgroup of a group, which was introduced in 1979 by Z. I. Borevich, is used to prove the supersolvability of finite groups. It is proved that a...     

Synthesis of trifluoromethylated α-hydroxy acids and their derivatives based on alkyl trifluoropyruvates

The reactions of trifluoropyruvates with nitromethane and arylmagnesium bromides leading to trifluoromethyl-containing α-hydroxy acid esters were studied and various derivatives of the acids were obtained.     

Synthesis of 2-(12-aryldodecanoyl)cyclohexane-1,3-diones

Synthesis was developed of 2-(10-undecenoyl)cyclohexane-1,3-diones containing in the side chain keto and hydroxy groups and a phenyl substituent. The synthesis is underlain by a nitrile oxide approach. The scheme included isoxazole synthesis for the protection of the β,β′-tricarbonyl fragment, building up of a heterocycle by 1,3-dipolar cycloaddition of nitrile oxide in situ to the terminal double bond, cycle opening (of isoxazole and isoxazoline), and alkaline hydrolysis.