Finitely generated simple algebras: A question of B. I. Plotkin

In his recent series of lectures, Prof. B. I. Plotkin discussed geometrical properties of the variety of associativeK-algebras. In particular, he studied geometrically noetherian and logically noetherian algebras and, in this connection, he asked whether there exist uncountably many simpleK-algebras with a fixed finite number of generators. We answer this question in the affirmative using both crossed product constructions and HNN extensions of division rings. Specifically, we show that there exist uncountably many nonisomorphic 4-generator simple Ore domains, and also uncountably many nonisomorphic division algebras having 2 generators as a division algebra. The first author is grateful to Professor B. I. Plotkin for communicating this problem to him and for stimulating conversations.     

A geometrical constraint for capillary jet breakup

The formation of thinning filaments is commonly observed previously to the break-up of a very viscous jet. This paper shows that a fluid under capillary forces cannot break-up through the uniform collapse of a filament.     

Rapid and efficient synthesis of optically active pyrazoles under solvent-free conditions

2-Formyl glycals undergo rapid condensation with arylhydrazines under solvent-free conditions to give the corresponding optically pure 4-substituted pyrazoles in good yields with high selectivity. The stereochemistry of the products was assigned by various NMR experiments.     

An N,N′-diaryl urea based conjugated polymer model system

An N,N′-diphenyl urea was designed as a model system for aggregation phenomenon in poly(phenyleneethynylenes) (PPEs). The unmethylated N,N′-diphenyl urea adopts an open, unfolded conformation in which the two diphenyl acetylene fluorophores are far enough away, mimicking the unaggregated state. Dimethylation forces the aromatic surfaces together into π-π contact, mimicking the aggregated state of PPEs. Analogous to bulk PPEs, this model system shows dramatic differences in quantum yield between the folded and unfolded states, with the unfolded urea having greater than 400-fold higher fluorescence quantum yield than its folded equivalent.     

Sulfobetaine‐containing diblock and triblock copolymers via reversible addition‐fragmentation chain transfer polymerization in aqueous media

A novel bifunctional acrylamido‐based reversible addition–fragmentation chain transfer (RAFT) chain‐transfer agent (CTA), N,N′‐ethylenebis[2‐(thiobenzoylthio)propionamide] (CTA2), has been synthesized and used for the controlled free‐radical polymerization of N,N‐dimethylacrylamide (DMA). A comparative study of CTA2 and the monofunctional CTA N,N‐dimethyl‐s‐thiobenzoylthiopropionamide (CTA1) has been conducted. Polymerizations mediated by CTA1 result in poly(N,N‐dimethylacrylamide) (PDMA) homopolymers with unimodal molecular weight distributions, whereas CTA2 yields unimodal, bimodal, and trimodal distributions according to the extent of conversion. The multimodal nature of the PDMAs has been attributed to termination events and/or chains initiated by primary radicals. The RAFT polymerization of DMA with CTA2 also results in a prolonged induction period that may be attributed to the higher local concentration of dithioester functionalities early in the polymerization. A series of ω‐ and α,ω‐dithioester‐capped PDMAs have been prepared in organic media and subsequently employed as macro‐CTAs for the synthesis of diblock and triblock copolymers in aqueous media with the zwitterionic monomer 3‐[2‐(N‐methylacrylamido)‐ethyldimethylammonio] propane sulfonate (MAEDAPS). Additionally, an ω‐dithioester‐capped MAEDAPS homopolymer has been used as a macro‐CTA for the block polymerization of DMA. To our knowledge, this is the first example of a near‐monodisperse, sulfobetaine‐containing block copolymer prepared entirely in aqueous media. The diblock and triblock copolymers form aggregates in pure water that can be dissociated by the addition of salt, as determined by ¹H NMR spectroscopy and dynamic light scattering. In pure water, highly uniform, micellelike aggregates with hydrodynamic diameters of 71–93 nm are formed. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1262–1281, 2003     

Nonreciprocity of losses and shift of the zero point in a laser gyroscope

Results of calculations of intensities, losses, and frequencies of counterpropagating waves in a ring resonator containing a weakly nonlinear active medium and an aperture are given. It is shown that inequalities of frequencies and intensities of generation of counterpropagating waves occur in such a resonator. The behavior of these inequalities is determined by the nonreciprocity of frequency-dependent losses of the counterpropagating waves.     

Hydrogen generation in nitric acid solutions of plutonium

Summary Literature data on the radiolytic generation of hydrogen in nitric acid solutions of plutonium are used to construct a model that predicts G(H₂) as a function of the nitric acid and plutonium concentrations. The model indicates that G(H₂) decreases with increasing concentration of nitric acid, in agreement with most experimental observations. The effect of the plutonium concentration on G(H₂) is secondary to the effect of the acid concentration. An equation for interpolating Gvalues for total gas is included.     

Investigation into the ROMP copolymerization of peptide‐ and PEG‐functionalized norbornene derivatives

The ring‐opening metathesis polymerizations (ROMP), using RuCl₂ (PCy₃)₂CHPh, of a series of peptide‐functionalized norbornene derivatives have been investigated. Incorporation of a PEG‐monomer was found to prevent premature precipitation of polymer strands during the course of polymerization reactions and yield water compatible polymers in high conversions. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3178–3190, 2007