A finite element formulation for global linear stability analysis of a nominally two‐dimensional base flow

A stabilized finite element method, to carry out the linear stability analysis of a two‐dimensional base flow to three‐dimensional perturbations that are periodic along span, is presented. The resulting equations for the time evolution of the disturbance requires a solution to the generalized eigenvalue problem. The analysis is global in nature and is also applicable to non‐parallel flows. Equal‐order‐interpolation functions for velocity and pressure are utilized. Stabilization terms are added to the Galerkin formulation to admit the use of equal‐order‐interpolation functions and to eliminate node‐to‐node oscillations that might arise in advection‐dominated flows. The proposed formulation is tested on two flow problems. First, the mode transitions in the circular Couette flow are investigated. Two scenarios are considered. In the first one, the outer cylinder is at rest, while the inner one spins. Two linearly unstable modes are identified. The primary mode is real and represents the axisymmetric Taylor vortices. The second mode is complex and consists of spiral vortices. For the counter‐rotating cylinders, the primary transition is via the appearance of spiral vortices. Excellent agreement with results from earlier studies is observed. The formulation is also utilized to investigate the parallel and oblique modes of vortex shedding past a cylinder for the Re = 100 flow. It is found that the flow is associated with a large number of unstable oblique shedding modes. The parallel mode of vortex shedding is a special case of this family of modes and is associated with the largest growth rate. Copyright © 2014 John Wiley & Sons, Ltd.     

A relation between multiplicity one and Böcherer’s conjecture

We show that a weak form of the generalized Böcherer conjecture implies multiplicity one for Siegel cusp forms of degree 2.     

Developments in Direct C?H Arylation of (Hetero)Arenes under Microwave Irradiation

This minireview describes the progress made in the development of direct C? H arylation approaches through the application of focused microwave irradiation. The synergistic combination of microwave‐assisted techniques with the rapidly evolving domain of C? H arylation has opened new vistas in the efficient synthesis of a diverse array of biologically important (hetero)arenes.     

Synthesis and Characterization of Novel Surfactant Molecules Based on Amphiphilic Polymers

Twelve amphiphilic polymers were synthesized using poly(ethylene glycols) (PEGs) of different molecular weights, viz. 300, 600 and1000 as hydrophilic block and aliphatic diacids namely glutaric acid, adipic acid, pimelic acid and suberic acid as hydrophobic block in presence of catalyst Conc. H₂SO₄. Synthesized polyesters were characterized by using ¹H-NMR, ¹³C-NMR and IR spectroscopy. Micellar sizes of the polymers were determined using Dynamic Light Scattering (DLS) which ranged from 127.5–354 nm. Transmission Electron Microscope (TEM) results confirm the findings of DLS. Critical Micelle Concentrations (CMC) of the synthesized polymers were determined using electrical conductivity meter which ranged from 112 to 155 mg L^?1.     

Single sensor for multiple analytes: fluorogenic detection of Al3+ in aqueous media and AcO− in organic media

A simple novel receptor, designed to have a combination of both oxygen and nitrogen-binding sites for metal ion and hydrogen bond donor sites for anion, was synthesised. The receptor has been explored for the selective detection of cation Al³⁺ over the other interfering metal ions and anion AcO^?  against a range of physiologically relevant anions in the fluorescence spectroscopy. The receptor shows a different response to aluminium and acetate in the emission spectra. The binding isotherm and detection limit demonstrate that the receptor is an excellent fluorometric probe for Al³⁺ and AcO^? .     

Determination of t,t-muconic acid in urine samples using a molecular imprinted polymer combined with simultaneous ethyl chloroformate derivatization and pre-concentration by dispersive liquid–liquid microextraction

The present communication describes the preparation and evaluation of a molecularly imprinted polymer (MIP) as a solid-phase extraction (SPE) sorbent and simultaneous ethyl chloroformate (ECF) derivatization and pre-concentration by dispersive liquid–liquid microextraction (DLLME) for the analysis of t,t-muconic acid (t,t-MA) in urine samples using gas chromatography–mass spectrometry. The imprinting polymer was prepared using methacrylic acid as a functional monomer, ethylene glycol dimethacrylate as a cross-linker, 2,2-azobisisobutyronitrile as the initiator and t,t-MA as a template molecule. The imprinted polymer was evaluated for its use as a SPE sorbent by comparing both imprinted and non-imprinted polymers in terms of the recovery of t,t-MA from urine samples. Molecular modelling studies were performed in order to estimate the binding energy and efficiency of the MIP complex formed between the monomer and the t,t-MA. Various factors that can affect the extraction efficiency of MIP, such as the loading, washing and eluting conditions, were optimized; other factors that can affect the derivatization and DLLME pre-concentration were also optimized. MIP in combination with ECF derivatization and DLLME pre-concentration for t,t-MA exhibits good linearity, ranging from 0.125 to 2 μg?mL^?1 (R ²?=?0.9971), with limit of detection of 0.037 μg?mL^?1 and limit of quantification of 0.109 μg?mL^?1. Intra- and inter-day precision was found to be <6 %. The proposed method has been proven to be effective and sensitive for the selective pre-concentration and determination of t,t-MA in urine samples of cigarette smokers.

Synthesis,Pharmacological, and Biological Screening of Novel Derivatives of Benzodiazepines

A series of novel 4‐(substituted phenyl)‐2‐(thiophen‐2‐yl)‐2,3‐dihydro‐1H‐benzo[b][1,4]diazepine have been synthesized from 3‐(substituted phenyl)‐1‐(thiophen‐2‐yl)prop‐2‐en‐1‐one. 3‐(Substituted phenyl)‐1‐(thiophen‐2‐yl)prop‐2‐en‐1‐one was prepared by condensing 2‐acetyl thiophene with various aromatic aldehydes in the presence of 20% NaOH as base. Different 3‐(substituted phenyl)‐1‐(thiophen‐2‐yl)prop‐2‐en‐1‐one on cyclization with o‐phenylenediamine in the presence of NaOH as base resulted in 4‐(substituted phenyl)‐2‐(thiophen‐2‐yl)‐2,3‐dihydro‐1H‐benzo[b][1,4]diazepine derivatives. The structures of synthesized compounds are confirmed by IR, ¹H NMR, mass spectra, and elemental analysis. All the compounds have been screened for their antimicrobial, analgesic, and anti‐inflammatory activities.