19F-detected dual-optimized inverted 1JCC 1,n-ADEQUATE

Modification of the recently reported ¹⁹F-detected 1,1-ADEQUATE experiment that incorporates dual-optimization to selectively invert a wide range of ¹J_CC correlations in a 1,n-ADEQUATE experiment is reported. Parameters for the dual-optimization segment of the pulse sequence were modified to accommodate the increased size of ¹J_CC homonuclear coupling constants of poly- and perfluorinated molecules relative to protonated molecules to allow broadband inversion of the ¹J_CC correlations. The observation and utility of isotope shifts are reported for the first time for 1,1- and 1,n-ADEQUATE correlations.     

Melt spinning of propylene carbonate‐plasticized poly(acrylonitrile)‐co‐poly(methyl acrylate)

The primary use of poly(acrylonitrile) (PAN) fibers, commonly referred to as acrylic fibers, is in textile applications like clothing, furniture, carpets, and awnings. All commercially available PAN fibers are processed by solution spinning; however, alternative, more cost‐effective processes like melt spinning are still highly desired. Here, the melt spinning of PAN‐co‐poly(methyl acrylate) (PMA) plasticized with propylene carbonate (PC) at 175°C is reported. The use of methyl acrylate (MA) as comonomer and PC as an external plasticizer renders the approach a combination of internal and external plasticization. Various mixtures of PAN and PC used in this work were examined by rheology, subjected to melt spinning, followed by discontinuous and continuous washing, respectively. The best fibers were derived from a PAN‐co‐PMA copolymer containing 8.1 mol‐% of MA having a number‐average molecular weight M _n of 34 000 g/mol, spun in the presence of 22.5 wt.‐% of PC. The resulting fibers were analyzed by scanning electron microscopy and wide‐angle X‐ray scattering (WAXS), and were subjected to mechanical testing.     

Voltammetric Study and Rapid Quantification of Resorcinol in Hair Dye and Biological Samples Using Ultrasensitive Maghemite/MWCNT Modified Carbon Paste Electrode

Increased concern over the risk resorcinol (RS) pose to ecology and humans, led to its position in European Union Category 1 list of endocrine disruptors. Legal measures restricted RS utilization and hence crucial to monitor its levels in the environment. Herein we report development of highly efficient and economically viable electrochemical sensor for quantitative determination of RS based on 77Maghemite/MultiWall Carbon Nanotube (M/MWCNT) modified carbon paste electrode. M/MWCNT was synthesized via strategic IR irradiation for the first time, a promising approach to overcome other complicated chemical routes. Powder X‐ray diffraction (PXRD), Transmission electron microscopy (TEM), Field emission scanning electron microscopy (FESEM) and Energy dispersive X‐ray (EDX) were used for characterization. Using Differential Pulse Voltammetry (DPV), we report the lowest detection limit at 0.02 μM. The potential application of the sensor was accomplished as a result of excellent recoveries made from real samples fortified with RS. Results indicated the proficiency of the sensor reliable for rapid, onsite monitoring of RS water contamination and in biological matrices.     

Aerodynamic optimization of the flat-plate leading edge for experimental studies of laminar and transitional boundary layers

This work is concerned with the design of a leading edge for a flat-plate model used to study laminar and transitional boundary layers. For this study, the flow over the complete boundary-layer model, including leading edge, flat section, and trailing-edge flap, is modeled. The effect of important geometrical features of the leading edge on the resulting pressure distribution, starting from the well-known symmetric modified super ellipse, is investigated. A minimal pressure gradient on the measurement side of the plate is achieved using an asymmetrical configuration of modified super ellipses, with a thickness ratio of 7/24. An aerodynamic shape optimization is performed to obtain a novel leading edge shape that greatly reduces the length of the non-zero pressure gradient region and the adverse pressure gradient region compared to geometries defined by ellipses. Wind tunnel testing is used to validate the numerical solutions.     

Stability of algebraic multigrid for Stokes problems

An investigation is made of the performance of algebraic multigrid (AMG) solvers for the discrete Stokes problem. The saddle‐point formulations are based on the direct enforcement of the fundamental conservation laws in discrete spaces and subsequently stabilised with the aid of a regular splitting of the diffusion operator. AMG solvers based on an independent coarsening of the fields (the unknown approach) and also on a common coarsening (the point approach) are investigated. Both mixed‐order and equal‐order interpolations are considered. The dependence of convergence on the ‘degree of coarsening’ is investigated by studying the ‘convergence versus coarsening’ characteristics and their variation with mesh resolution. They show a consistency in shape, which reveals two distinct performance zones, one convergent the other divergent. The transition from the convergent to the divergent zones is discontinuous and occurs at a critical coarsening factor that is largely mesh independent. It signals a breakdown in the stability of the smoothing at the coarser levels of coarse grid approximation. It is shown that the previously observed, mesh‐dependent, scaling of convergence factors, which had suggested inconsistencies in the coarse grid approximation, is not a reliable marker of inconsistency. It is an indirect consequence of the breakdown in the stability of smoothing. For stable smoothing, reduction factors are shown to be largely mesh independent. The ability of mixed‐order interpolation to permit stable smoothing and therefore to deliver mesh‐independent convergence is explained. Two expedient options are suggested for obtaining mesh‐independent convergence for those AMG codes that are based on an equal‐order interpolation. Copyright © 2012 John Wiley & Sons, Ltd.     

Nonstandard Finite Difference Schemes for Differential Equations

This paper gives an introduction to nonstandard finite difference methods useful for the construction of discrete models of differential equations when numerical solutions are required. While the general rules for such schemes are not precisely known at the present time, several important criterion have been found. We provide an explanation of their significance and apply them to several model ordinary and partial differential equations. The paper ends with a discussion of several outstanding problems in this area and other related issues.     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

Chiral aminocyclopentene-based cycloaddition strategies to bicyclic [3.3.0] rings

Two cycloaddition methods were applied to chiral protected aminocyclopentenes 2 and 9 and provided novel bicyclic products 3 and 4 in good yields. The explanation for the observed stereochemistry was based on the sterically encumbered β-face forcing the cycloadditions to occur on the α-face of the cyclopentene ring. The stereochemistry of 4 was confirmed by X-ray of the fumarate salt 10 and showed the trans-relationship between the newly formed ring and the chiral –NHBoc group.