A Model Equation Illustrating Subcritical Instability to Long Waves in Shear Flows

A model equation somewhat more general than Burger's equation has been employed by Herron [1] to gain insight into the stability characteristics of parallel shear flows. This equation, namely, u_t + uu_y = u_xx + u_yy, has an exact solution U(y) = ?2tanh y. It was shown in [1] that this solution is linearly stable, and more recently, Galdi and Herron [3] have proved conditional stability to finite perturbations of sufficiently small initial amplitude using energy methods. The present study utilizes multiple-scaling methods to derive a nonlinear evolution equation for a long-wave perturbation whose amplitude varies slowly in space and time. A transformation to the heat-conduction equation has been found which enables this amplitude equation to be solved exactly. Although all disturbances ultimately decay due to diffusion, it is found that subcritical instability is possible in that realistic disturbances of finite initial amplitude can amplify substantially before finally decaying. This behavior is probably typical of perturbations to shear flows of practical interest, and the results illustrate deficiencies of the energy method.     

Stereocontrolled Synthesis of Vinyl Boronates and Vinyl Silanes via Atom‐Economical Ruthenium‐Catalyzed Alkene–Alkyne Coupling

The synthesis of vinyl boronates and vinyl silanes was achieved by employing a Ru‐catalyzed alkene–alkyne coupling reaction of allyl boronates or allyl silanes with various alkynes. The double bond geometry in the generated vinyl boronates can be remotely controlled by the juxtaposing boron‐ and silicon groups on the alkyne substrate. The synthetic utility of the coupling products has been demonstrated in a variety of synthetic transformations, including iterative cross‐coupling reactions, and a Chan‐Lam‐type allyloxylation followed by a Claisen rearrangement. A sequential one‐pot alkene‐alkyne‐coupling/allylation‐sequence with an aldehyde to deliver a highly complex α‐silyl‐β‐hydroxy olefin with a handle for further functionalization was also realized.     

Construction of a New Class of Tetracycline Lead Structures with Potent Antibacterial Activity through Biosynthetic Engineering

Antimicrobial resistance and the shortage of novel antibiotics have led to an urgent need for new antibacterial drug leads. Several existing natural product scaffolds (including chelocardins) have not been developed because their suboptimal pharmacological properties could not be addressed at the time. It is demonstrated here that reviving such compounds through the application of biosynthetic engineering can deliver novel drug candidates. Through a rational approach, the carboxamido moiety of tetracyclines (an important structural feature for their bioactivity) was introduced into the chelocardins, which are atypical tetracyclines with an unknown mode of action. A broad‐spectrum antibiotic lead was generated with significantly improved activity, including against all Gram‐negative pathogens of the ESKAPE panel. Since the lead structure is also amenable to further chemical modification, it is a platform for further development through medicinal chemistry and genetic engineering.     

Real-time mass-spectrometric study of the chemistry initiated by infrared-laser photolysis: CF2Cl2

The infrared-laser photolysis/mass-spectrometric (ILP/MS) technique was used to monitor directly in real time the free-radical and stable reactants and products present in the reactive system initiated by the multiphoton-induced dissociation of CF₂Cl₂. It was found that contrary to conclusions based on final-products analyses, the C₂F₄ observed as a final product in this system is not formed solely through the recombination of: CF₂ radicals, but rather C₂F₄ is produced in a complex series of secondary reactions.     

Acuchem: A computer program for modeling complex chemical reaction systems

Acuchem is a program for solving the system of differential equations describing the temporal behavior of spatially homogeneous, isothermal, multicomponent chemical reaction systems. It is designed to provide modelers, data evaluators, and laboratory scientists with an easy to use program for modeling complex chemical reactions, and for presenting the results in tabular or graphical form. The program is described and some examples of its application given. Acuchem is designed to operate on the IBM Personal Computer family and other compatible microcomputers, and is available in a compiled version on a floppy disk.     

Methyl thiirane: Kinetic gas-phase titration of sulfur atoms in SX OY systems

The reaction SO + SO →l S + SO₂(2) was studied in the gas phase by using methyl thiirane as a titrant for sulfur atoms. By monitoring the C₃H₆ produced in the reaction \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm S} + {\rm CH}_3\hbox{---} \overline {{\rm CH\hbox{---}CH}_2\hbox{---} {\rm S}} \to {\rm S}_2 + {\rm C}_3 {\rm H}_6 (7) $\end{document}, we determined that k₂ ? 3.5 × 10^?15 cm³/s at 298 K.     

Quasiconformal Deformations and Volume Growth

We determine when a metric measure space admits a uniformizingdensity which has Ahlfors regular volume growth. A characterizationof uniformizing conformal densities in terms of doubling anda lifting procedure are the key ingredients in our presentation.We also furnish an application characterizing metric doublingmeasures. 2000 Mathematics Subject Classification 30C65 (primary),20F67, 30F45, 51F99 (secondary).     

1-[Ferrocenyl(hydroxy)methyl]-1,7-dicarba<Emphasis Type="Italic">-closo</Emphasis>-dodecaborane: Synthesis and X-ray crystal structure

The synthesis and molecular structure of the novel 1-[ferrocenyl(hydroxy)methyl]-1,7-dicarba-closo-dodecaborane (1) is described. Compound 1 was synthesized from reaction of m-carborane and ferrocene carboxaldehyde using n-butyllithium (n-BuLi) or tetrabutylammonium fluoride (TBAF) in THF in 45% and 36% yield, respectively. Compound 1 consists of a ferrocene molecule tethered to m-carborane through a methylhydroxy bridge. The crystal structure of 1 was determined by single crystal X-ray diffraction analysis. Crystal data: 1 [Fe(C₅H₅)(C₅H₄-CH₂O-1,7-C₂B₁₀H₁₂)], formula weight = 359.17, crystallized in orthorhombic system, space group Pna2 ₁ with a=19.698(4) ?, b=10.709(2) ?, c=8.520(2) ?, and V=1797.3(7) ?³ and Z=4. Refined to R ₁=0.043 for 4124 observed reflections with I/σ>2σ(I). The compound was crystallized as racemic twins in a ratio of 73(2)/27(2). The unsubstituted Cp ring was disordered and modeled as two conformations in a 53(3)/47(3) ratio. Intermolecular hydrogen bonding was observed from the hydrogen of the meta-carbon on the carborane cluster towards the hydroxyl oxygen.     

Diffusion properties of cortical and pericortical tissue: regional variations, reliability and methodological issues

Characterizing the diffusion properties of cortical tissue is complicated by intersubject variability in the relative locations of gyri and sulci. Here we extend methods of measuring the average diffusion properties of gyral and sulcal structures after they have been aligned to a common template of cortical surface anatomy. Diffusion tensor image (DTI) data were gathered from 82 young subjects and co-registered with high-resolution T1 images that had been inflated and co-registered to a hemispherically unified spherical coordinate system based on FreeSurfer. We analyzed fractional anisotropy (FA), mean diffusivity (MD) and the novel quantity of cortical primary diffusion direction (cPDD) at five surfaces parallel to the white/gray junction, spanning approximately 5 mm from the pial surface into white matter. FA increased with increasing depth, whereas MD and cPDD were reduced. There were highly significant and reliable regional differences in FA, MD and cPDD as well as systematic differences between cortical lobes and between the two hemispheres. The influence of nearby cortical spinal fluid (CSF), local cortical curvature and thickness, and sulcal depth was also investigated. We found that FA correlated significantly with cortical curvature and sulcal depth, while MD was strongly influenced by nearby CSF. The measurement of FA, MD and cPDD near the cortical surface clarifies the organization of fiber projections to and from the cortex.