Ecofriendly synthesis and biological evaluation of 4-(4-nitro-phenyl)-2-phenyl-1,4-dihydro-benzo[4,5]imidazo[1,2-a]pyrimidine-3-carboxylic acid ethyl ester derivatives as an antitubercular agents

An ecofriendly route has been investigated for the synthesis of 4-(4-nitro-phenyl)-2-phenyl-1,4-dihydro-benzo[4,5]imidazo[1,2-a]pyrimidine-3-carboxylic acid ethyl ester derivatives by one-pot, three-component condensation of ethyl benzoylacetate, aromatic aldehydes, and 2-amino benzimidazole using 260?mol% of citric acid as reaction mediator. Citric acid is an inexpensive, nontoxic, and green medium with smoothly activates the rate of reaction. The synthesized compounds were assessed for in vitro antimycobacterial activity against Mycobacterium tuberculosis H₃₇RV strain using the microplate alamar blue assay (MABA). The results indicate that among all the synthesized compound series, P-4 and P-9 compounds illustrate effective activity with a minimum inhibitory concentration of 25?µg/ml.     

Modified extended BDF scheme for the discontinuous Galerkin solution of unsteady compressible flows

In this paper, a high‐order DG method coupled with a modified extended backward differentiation formulae (MEBDF) time integration scheme is proposed for the solution of unsteady compressible flows. The objective is to assess the performance and the potential of the temporal scheme and to investigate its advantages with respect to the second‐order BDF. Furthermore, a strategy to adapt the time step and the order of the temporal scheme based on the local truncation error is considered. The proposed DG‐MEBDF method has been evaluated for three unsteady test cases: (i) the convection of an inviscid isentropic vortex; (ii) the laminar flow around a cylinder; and (iii) the subsonic turbulent flow through a turbine cascade. Copyright © 2014 John Wiley & Sons, Ltd.     

Confined crystallization of polymers within anodic aluminum oxide templates

In this article, a review of recent literature on confined crystallization within nanoporous anodic aluminum oxide (AAO) templates is presented. For almost all infiltrated polymeric materials, crystal orientation within the nanopores is a function of pore diameter. T_c and T_m usually decrease and are a function of pore size. When no pore interconnection remains, the crystallization occur at large supercoolings in heterogeneity free environments. Hence, the nucleation mechanism changes from heterogeneous to surface or homogeneous nucleation. The crystallization kinetics of infiltrated polymers should be close to first order, since in confined environments nucleation is the determining step of the overall crystallization and Avrami indexes (n) of ～1 (or lower in some cases) should be obtained. Examples are provided where these conditions have been met and first order kinetics (n = 1) were measured as opposed to higher orders (n = 3?4) for the same polymer in the bulk. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1179–1194     

Exact WKB analysis of a Schrödinger equation with a merging triplet of two simple poles and one simple turning point,II — Its relevance to the Mathieu equation and the Legendre equation

We develop the exact WKB analysis of an M2P1T (merging two simple poles and one simple turning point) Schrödinger equation. In Part II, using a WKB-theoretic transformation to the algebraic Mathieu equation constructed in Part I, we calculate the alien derivative of its Borel transformed WKB solutions at each fixed singular point relevant to the simple poles through the analysis of Borel transformed WKB solutions of the Legendre equations. In the course of the calculation of the alien derivative we make full use of microdifferential operators whose symbols are given by the infinite series that appear in the coefficients of the algebraic Mathieu equation and the Legendre equation.     

Measurement of Large Dipolar Couplings of a Liquid Crystal with Terminal Phenyl Rings and Estimation of the Order Parameters

NMR spectroscopy is a powerful means of studying liquid‐crystalline systems at atomic resolutions. Of the many parameters that can provide information on the dynamics and order of the systems, ¹H–¹³C dipolar couplings are an important means of obtaining such information. Depending on the details of the molecular structure and the magnitude of the order parameters, the dipolar couplings can vary over a wide range of values. Thus the method employed to estimate the dipolar couplings should be capable of estimating both large and small dipolar couplings at the same time. For this purpose, we consider here a two‐dimensional NMR experiment that works similar to the insensitive nuclei enhanced by polarization transfer (INEPT) experiment in solution. With the incorporation of a modification proposed earlier for experiments with low radio frequency power, the scheme is observed to enable a wide range of dipolar couplings to be estimated at the same time. We utilized this approach to obtain dipolar couplings in a liquid crystal with phenyl rings attached to either end of the molecule, and estimated its local order parameters.     

High‐performance liquid chromatographic separations of stereoisomers of chiral basic agrochemicals with polysaccharide‐based chiral columns and polar organic mobile phases

The separation of the stereoisomers of 23 chiral basic agrochemicals was studied on six different polysaccharide‐based chiral columns in high‐performance liquid chromatography with various polar organic mobile phases. Along with the successful separation of analyte stereoisomers, emphasis was placed on the effect of the chiral selector and mobile phase composition on the elution order of stereoisomers. The interesting phenomenon of reversal of enantiomer/stereoisomer elution order function of the polysaccharide backbone (cellulose or amylose), type of derivative (carbamate or benzoate), nature, and position of the substituent(s) in the phenylcarbamate moiety (methyl or chloro) and the nature of the mobile phase was observed. For several of the analytes containing two chiral centers all four stereoisomers were resolved with at least one chiral selector/mobile phase combination.     

(2‐Aminopyrimidine‐κN1)aqua(pyridine‐2,6‐dicarboxylato‐κ3O2,N,O6)copper(II): X‐ray and DFT calculated structure

In the title compound, [Cu(C₇H₃N₂O₄)(C₄H₅N₂)(H₂O)], (I), pyridine‐2,6‐dicarboxylate (pydc²⁻), 2‐aminopyrimidine and aqua ligands coordinate the Cu^II centre through two N atoms, two carboxylate O atoms and one water O atom, respectively, to give a nominally distorted square‐pyramidal coordination geometry, a common arrangement for copper complexes containing the pydc²⁻ ligand. Because of the presence of Cu...X_bridged contacts (X = N or O) between adjacent molecules in the crystal structures of (I) and three analogous previously reported compounds, and the corresponding uncertainty about the effective coordination number of the Cu^II centre, density functional theory (DFT) calculations were used to elucidate the degree of covalency in these contacts. The calculated Wiberg and Mayer bond‐order indices reveal that the Cu...O contact can be considered as a coordination bond, whereas the amine group forming a Cu...N contact is not an effective participant in the coordination environment.     

Square function estimates on layer potentials for higher‐order elliptic equations

In this paper we establish square‐function estimates on the double and single layer potentials for divergence form elliptic operators, of arbitrary even order 2m , with variable t‐independent coefficients in the upper half‐space. This generalizes known results for variable‐coefficient second‐order operators, and also for constant‐coefficient higher‐order operators.     

On the dynamics of a third order Newton's approximation method

We provide an answer to a question raised by S. Amat, S. Busquier, S. Plaza on the qualitative analysis of the dynamics of a certain third order Newton type approximation function , by proving that for functions f twice continuously differentiable and such that both f and its derivative do not have multiple roots, with at least four roots and infinite limits of opposite signs at , has periodic points of any prime period and that the set of points a at which the approximation sequence does not converge is uncountable. In addition, we observe that in their Scaling Theorem analyticity can be replaced with differentiability.