A note on tilde algebras

A closed setE is constructed so thatA∼(E) is an inseparable Banach space but its maximal ideal space isE. Supported in part by the National Science Foundation.     

A short and efficient synthesis of grisan

A three-step synthesis of grisan (spiro[benzofuran-2(3H)-1′-cyclohexane]), using methoxymethoxybenzene and 1-chloromethylcyclohexene as starting materials, is described.     

How Focusing Phenomena in the Instructional Environment Support Individual Students' Generalizations

This article sets forth a way of connecting the classroom instructional environment with individual students' generalizations. To do so, we advance the notion of focusing phenomena, that is, regularities in the ways in which teachers, students, artifacts, and curricular materials act together to direct attention toward certain mathematical properties over others. The construct of focusing phenomena emerged from an empirical study conducted during a 5-week unit on slope and linear functions in a high school classroom using a reform curriculum. Qualitative evidence from interviews with 7 students revealed that students interpreted the m value in y = b + mx as a difference rather than a ratio as a result of counterproductive generalization afforded by focusing phenomena. Classroom analysis revealed 4 focusing phenomena, which regularly directed students' attention to various sets of differences rather than to the coordination of quantities.     

Vibrational emission of NO2 from the reaction of NO with O3

Vibrational chemiluminescence in the Δν₁ = Δν₃ = ?1 band of NO₂ is observed both in the O + NO and O₃ + NO reactions and shown to be emitted by molecules with up to 11 000 cm^?1 of vibrational energy. Quenching rate constants of NO₂³ are estimated ranging from about 6 × 10^?14 for Ar to about 3 × 10^?12 cm³ s^?1 for NO₂. The ratio of vibrational to electronic emission is 0.06 ± 0.03 for O + NO and 5.3 ± 1.0 for O₃ + NO. It is suggested that vibrationally excited NO₂ is a major product of that channel of the O₃ + NO reaction which forms ground-state NO₂(²A₁) directly.     

Effect of solution chemistry on the surface charge of polymeric reverse osmosis and nanofiltration membranes

A streaming potential analyzer has been used to investigate the effect of solution chemistry on the surface charge of four commercial reverse osmosis and nanofiltration membranes. Zeta potentials of these membranes were analyzed for aqueous solutions of various chemical compositions over a pH range of 2 to 9. In the presence of an indifferent electrolyte (NaCl), the isoelectric points of these membranes range from 3.0 to 5.2. The curves of zeta potential versus solution pH for all membranes display a shape characteristic of amphoteric surfaces with acidic and basic functional groups. Results with salts containing divalent ions (CaCl₂, Na₂SO₄, and MgSO₄) indicate that divalent cations more readily adsorb to the membrane surface than divalent anions, especially in the higher pH range. Three sources of humic acid, Suwannee River humic acid, peat humic acid, and Aldrich humic acid, were used to investigate the effect of dissolved natural organic matter on membrane surface charge. Other solution chemistries involved in this investigation include an anionic surfactant (sodium dodecyl sulfate) and a cationic surfactant (dodecyltrimethylammonium bromide). Results show that humic substances and surfactants readily adsorb to the membrane surface and markedly influence the membrane surface charge.     

Quantum chemical modeling for 157 nm photolithography

In its continuing quest for smaller length scales, the electronics industry plans to introduce 157 nm as the next lithographic wavelength. Accordingly, there is a pressing need to develop photoresists that are more transparent, and pellicles that are both more transparent and more durable. With the advent and popularization of time-dependent density functional theory (TD-DFT), we now have a practical quantum chemical method for calculating excitation energies and transition moments in the vacuum ultraviolet (VUV) which can greatly assist in the scouting of highly transparent materials. We have performed TD-DFT calculations for a broad variety of fluorinated molecules and we will report calculated VUV photoabsorption spectra for a large family of model fluorohexanes. These calculations, which span a range from 1-fluorohexane to CH₃CF₂CF₂CF₂CF₂CH₃, illustrate some of the principles one may use to design low absorption polymeric materials.     

Reactions of methyltris(triarylphosphine)cobalt : I. Formation of biaryls

Methyltris(triarylphosphine)cobalt (Ar₃P)₃CoCH₃, decomposes in solutions of THF, benzene or chlorobenzene to yield biaryls. Coupling to biaryls occurs at the ring carbon originally bonded to phosphorus. Mixed biaryls are obtained from crossover reactions of complexes bearing different triarylphosphine ligands and reactions of complexes with free triarylphosphines.