Microwave-Assisted One-Pot Synthesis of Bioactive UGI-4CR Using Fluorite as Benign and Heterogeneous Catalyst

Fluorite has been used as an activating heterogeneous catalyst for a rapid and facile one-pot synthesis of biologically active Ugi four-component reaction (Ugi-4CR) under microwave irradiation in good to moderate yields with short reaction times. The catalyst is environmentally benign, commercially available, and reusable several times with no reduction in its efficiency. The resulting Ugi derivatives 5(a–h) were characterized on the basis of ¹H and ¹³C NMR, infrared, elemental analysis, and mass spectral data. The synthesized moieties were screened for their potential antibacterial activities in vitro against a few microorganisms: Staphylococcus aureus (Gram positive), Bacillus subtilis (Gram positive), Escherichia coli (Gram negative), and Proteus vulgaris (Gram negative). The screening data show that compounds 5a, 5c, 5e, and 5h are highly active against the strains.

[Supplementary materials are available for this article. Go to the publisher's online edition of Synthetic Communications® for the following free supplemental resource(s): Full experimental and spectral details.]     

An Alternate Approach to Optimal L 2-Error Analysis of Semidiscrete Galerkin Methods for Linear Parabolic Problems with Nonsmooth Initial Data

In this article, we propose and analyze an alternate proof of a priori error estimates for semidiscrete Galerkin approximations to a general second order linear parabolic initial and boundary value problem with rough initial data. Our analysis is based on energy arguments without using parabolic duality. Further, it follows the spirit of the proof technique used for deriving optimal error estimates for finite element approximations to parabolic problems with smooth initial data and hence, it unifies both theories, that is, one for smooth initial data and other for nonsmooth data. Moreover, the proposed technique is also extended to a semidiscrete mixed method for linear parabolic problems. In both cases, optimal L ²-error estimates are derived, when the initial data is in L ². A superconvergence phenomenon is also observed, which is then used to prove L ^∞-estimates for linear parabolic problems defined on two-dimensional spatial domain again with rough initial data.     

Semidiscrete Galerkin method for equations of motion arising in Kelvin‐Voigt model of viscoelastic fluid flow

Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L^∞( L ²) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L^∞( L ²) as well as in L^∞( H )‐norms and the pressure in L^∞(L²)‐norm are derived which again preserves the exponential decay property. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

N-Substituted benzoxazolyl ureas and thioureas in Biginelli reaction promoted by trifluoromethane sulfonic acid:An efficient and convenient synthesis of substituted benzoxazolyl 3,4-dihydropyrimidine(1H)-(thio)-ones

An efficient synthesis of 3,4-dihydropyrimidine 2(1H)-ones and thiones(3,4-DHPMs) core was prepared by one-pot threecomponent Biginelli condensation and which was catalyzed by trifluoromethane sulfonic acid.The classical Bignelli reaction has been extended by the use of N-substituted benzoxazolyl semicarbazides and thiosemicarbazides and this method has the advantage of excellent yields and short reaction times.     

Majorana fermions in finite-size strips with in-plane magnetic fields

The European Physical Journal B - In this article we study the effects of disorder and long-range Coulomb interactions on triple-Weyl semimetals using renormalization group up to one-loop order. We...