A comparison result for a class of quasilinear elliptic partial differential equations

A comparison theorem and a uniqueness corollary for positive solutions to the equation

on the closure of a bounded open set are found. The important hypotheses on the nonlinear coefficients are that each p_i is positive and monotone increasing in u while q is monotone decreasing in u. An application is made to equations arising in the theory of chemical reactors.     

Synthesis of Carbapenems Containing Peptidoglycan Mimetics and Inhibition of the Cross-Linking Activity of a Transpeptidase of l,d Specificity

The carbapenem class of β-lactams has been optimized against Gram-negative bacteria producing extended-spectrum β-lactamases by introducing substituents at position C2. Carbapenems are currently investigated for the treatment of tuberculosis as these drugs are potent covalent inhibitors of l,d -transpeptidases involved in mycobacterial cell wall assembly. The optimization of carbapenems for inactivation of these unusual targets is sought herein by exploiting the nucleophilicity of the C8 hydroxyl group to introduce chemical diversity. As β-lactams are structure analogs of peptidoglycan precursors, the substituents were chosen to increase similarity between the drug and the substrate. Fourteen peptido-carbapenems were efficiently synthesized. They were more effective than the reference drug, meropenem, owing to the positive impact of a phenethylthio substituent introduced at position C2 but the peptidomimetics added at position C8 did not further improve the activity. Thus, position C8 can be modified to modulate the pharmacokinetic properties of highly efficient carbapenems.     

Syntheses of 3-Chloro-7-[(Chlorocarbonyl)Methoxy]-4-Methylcoumarin

Two efficient syntheses of 3-chloro-7-[(chlorocarbonyl)methoxy]-4-methylcoumarin are described, one utilizing traditional chemistry starting from 3-chloro-7-hydroxy-4-methylcoumarin, while the other uses a novel reagent, sulfuryl chloride/thionyl chloride, in a one-pot reaction starting from 7-(carboxymethoxy)-4-methylcoumarin.     

One-Step Generalized Estimating Equations With Large Cluster Sizes

Medical studies increasingly involve a large sample of independent clusters, where the cluster sizes are also large. Our motivating example from the 2010 Nationwide Inpatient Sample (NIS) has 8,001,068 patients and 1049 clusters, with average cluster size of 7627. Consistent parameter estimates can be obtained naively assuming independence, which are inefficient when the intra-cluster correlation (ICC) is high. Efficient generalized estimating equations (GEE) incorporate the ICC and sum all pairs of observations within a cluster when estimating the ICC. For the 2010 NIS, there are 92.6 billion pairs of observations, making summation of pairs computationally prohibitive. We propose a one-step GEE estimator that (1) matches the asymptotic efficiency of the fully iterated GEE; (2) uses a simpler formula to estimate the ICC that avoids summing over all pairs; and (3) completely avoids matrix multiplications and inversions. These three features make the proposed estimator much less computationally intensive, especially with large cluster sizes. A unique contribution of this article is that it expresses the GEE estimating equations incorporating the ICC as a simple sum of vectors and scalars.     

Molecular Design Principles for Near‐Infrared Absorbing and Emitting Indolizine Dyes

Desirable components for dye‐sensitzed solar cell (DSC) sensitizers and fluorescent imaging dyes include strong donating building blocks coupled with well‐balanced acceptor functionalities for absorption beyond the visible range. We have evaluated the effects of increasing acceptor strengths and incorporation of dye morphology controlling groups on molar absorptivity and absorption breadth with indolizine donor‐based dyes. Indolizine‐based D –A and D –π–A sensitizers incorporating bis‐rhodanine, tricyanofuran (TCF), and cyanoacrylic acid functionalities were analyzed for performance in DSC devices. The TCF derivatives were also evaluated as near‐infrared (NIR)‐emissive materials with the AH25 emissions extending past 1000 nm.     

Construction of the 17-Thiasteroid Ring System by the Diene-Sulfur Dioxide Cycloaddition Reaction

Abstract

We recently showed² that the steroid ring system can be constructed with a phosphorus atom replacing a carbon in the D-ring by the cycloaddition of a phosphorus (III) halide with a diene that is a vinyl dihydrophenanthrene derivative, such as (1). The phosphine oxide (3) resulting from the hydrolysis of the initial cycloadduct (2) has some resemblance to the hormone equilenin, which also has rings A and B in naphthalene form.