A penalty method for numerically handling dispersive equations with incompatible initial and boundary data

This article is the numerical counterpart of a theoretical work in progress Qin and Teman, Applicable Anal (2011), 1–19, related to the approximation of evolution hyperbolic equations with incompatible data. The Korteweg‐de Vries and Schrödinger equations with incompatible initial and boundary data are considered here. For hyperbolic equations, the lack of regularity (compatibility) is known to produce large numerical errors which propagate throughout the spatial domain, destroying convergence. In this article, we numerically test the effectiveness of the penalty‐based method proposed in Qin and Teman, Applicable Anal (2011), 1–19, which replaces the hyperbolic equations with incompatible data by a system with compatible data. We observe that convergence is increased. As explained in the text, in the case of the Schrödinger equation, the impact of incompatible (nonregular) data is most severe, and the authors are not aware of any other method that can handle such severe incompatible data. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011     

Focused ion beam preparation of samples for X‐ray nanotomography

The preparation of hard material samples with the necessary size and shape is critical to successful material analysis. X‐ray nanotomography requires that samples are sufficiently thin for X‐rays to pass through the sample during rotation for tomography. One method for producing samples that fit the criteria for X‐ray nanotomography is focused ion beam/scanning electron microscopy (FIB/SEM) which uses a focused beam of ions to selectively mill around a region of interest and then utilizes a micromanipulator to remove the milled‐out sample from the bulk material and mount it on a sample holder. In this article the process for preparing X‐ray nanotomography samples in multiple shapes and sizes is discussed. Additionally, solid‐oxide fuel cell anode samples prepared through the FIB/SEM technique underwent volume‐independence studies for multiple properties such as volume fraction, average particle size, tortuosity and contiguity to observe the characteristics of FIB/SEM samples in X‐ray nanotomography.     

Structures of Highly Twisted Amides Relevant to Amide N−C Cross‐Coupling: Evidence for Ground‐State Amide Destabilization

Herein, we show that acyclic amides that have recently enabled a series of elusive transition‐metal‐catalyzed N?C activation/cross‐coupling reactions are highly twisted around the N?C(O) axis by a new destabilization mechanism of the amide bond. A unique effect of the N‐glutarimide substituent, leading to uniformly high twist (ca. 90°) irrespective of the steric effect at the carbon side of the amide bond has been found. This represents the first example of a twisted amide that does not bear significant steric hindrance at the α‐carbon atom. The ¹⁵N NMR data show linear correlations between electron density at nitrogen and amide bond twist. This study strongly supports the concept of amide bond ground‐state twist as a blueprint for activation of amides toward N?C bond cleavage. The new mechanism offers considerable opportunities for organic synthesis and biological processes involving non‐planar amide bonds.     

Preparative access to medicinal chemistry related chiral alcohols using carbonyl reductase technology

Libraries of highly enantioenriched secondary alcohols in both enantiomeric forms were synthesised by enzymatic reduction of their parent ketones using selectAZyme? carbonyl reductase (CRED) technology. Commercially available CREDs were able to reduce a range of substrate classes efficiently and with very high enantioselectivity. Matching substrate classes to small subsets of CREDs enabled the fast development of preparative bioreductions and the rapid generation of 100–1500 mg samples of chiral alcohols in typically >95% ee and the majority in ?99.0% ee. The conditions for small scale synthesis were then scaled up to 0.5 kg to deliver one of the chiral alcohols, (S)-1-(4-bromophenyl)-2-chloroethanol, in 99.8% ee and 91% isolated yield.     

Determination of Some Organochlorine Compounds in the Atmosphere

Abstract

Since plastics are suspected to adsorb orthophosphate, disposable-tip pipettes have been checked to determine their ability to be used in orthophosphate calibration. No adsorption has been detected through an experiment of standard preparation with and without changing the pipette tip. That is, the pipettes appear to be convenient for orthophosphate calibration.     

Bio‐Inspired Formal Synthesis of Hirsutellones A–C Featuring an Electrophilic Cyclization Triggered by Remote Lewis Acid‐Activation

A bio‐inspired strategy was used to complete the formal synthesis of the antitubercular hirsutellone B and congeners A and C, through construction of its decahydrofluorene core from a linear polyene strand activated at both ends by a silyl enol ether and an allyl acetate. Our synthesis features a key electrophilic cyclization, starting with the remote activation (by [Yb(OTf)₃] or BF₃ ? OEt₂) of the allyl acetate and stereoselectively affording the C ring. This was followed by an intramolecular Diels–Alder reaction to get the tricyclic core of the natural product. The stereoselective reduction of the resulting ketone towards the formal intermediate was critical to the success of this strategy.     

Simplicity of eigenvalues in Anderson-type models

We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schrödinger operators, extending methods introduced by Simon for the discrete Anderson model. These methods work throughout the spectrum and are not restricted to the localization regime. We establish general criteria for the simplicity of eigenvalues which can be interpreted as separately excluding the absence of local and global symmetries, respectively. The criteria are applied to Anderson models with matrix-valued potential as well as with single-site potentials supported on a finite box.     

Reactions at Only One of Two Equivalent Functional Groups

A common problem encountered by synthetic chemists is to carry out a reaction at just one of two similar functional groups in the substrate molecule. Examples include protection/deprotection of just one hydroxyl group in a diol, addition to only one carbonyl of a diketone, etc. The problem, as depicted below, is to find conditions which maximize formation of the monoproduct (XP) while minimizing the amounts of diproduct (P₂) and starting material (X₂).