On the Uniqueness ofL 2-solutions in half-space of certain differential equations

Square integrable solutions to the equation{– ²/y² + P(D_x)+b(y)–}u(x, y) = f(x, y) are considered in the half-spacey>0, x ⁿ , whereP(D _x) is a constant coefficient operator. Under suitable conditions on lim_y0u(x, y), b(y), f(x, y) and , it is shown that suppu = suppf. This generalizes a result due to Walter Littman.Research partially supported by USNSF Grant 79-02538-A02.     

Electric field-controlled water permeation coupled to ion transport through a nanopore

We report molecular dynamics simulations of a generic hydrophobic nanopore connecting two reservoirs which are initially at different Na(+) concentrations, as in a biological cell. The nanopore is impermeable to water under equilibrium conditions, but the strong electric field caused by the ionic concentration gradient drives water molecules in. The density and structure of water in the pore are highly field dependent. In a typical simulation run, we observe a succession of cation passages through the pore, characterized by approximately bulk mobility. These ion passages reduce the electric field, until the pore empties of water and closes to further ion transport, thus providing a possible mechanism for biological ion channel gating.     

Rearrangement of epoxynitriles: a convenient homologation of acyclic and cyclic ketones to carboxylic acids

A convenient two-step homologation of both aliphatic and aromatic ketones to the corresponding carboxylic acid has been developed. First ketones were converted to epoxynitriles with the Darzens reaction. Second, a Lewis acid mediated rearrangement of these epoxynitriles with lithium bromide was achieved to give homologated secondary alkanoic acids (as well as aryl-alkanoic) in good yields. The mechanism and the scope of the rearrangement reaction were investigated. This strategy constitutes a two-step homologation of ketones to secondary carboxylic acids.     

Research applications of the Cambridge Structural Database (CSD)

Crystal structure data are of fundamental importance in a wide spectrum of scientific activities. This tutorial review summarises the principal application areas, so far, for the data from more than 300,000 crystal structures of small organic and metal-organic compounds that are stored in the Cambridge Structural Database (CSD). Direct use of the accumulated data is valuable in establishing standard molecular dimensions, determining conformational preferences and in the study of intermolecular interactions, all of which are crucial in structural chemistry and rational drug design. More recently, information derived from the CSD has been used to construct two dynamic libraries of structural knowledge: Mogul, which stores intramolecular information, and IsoStar, which stores information about intermolecular interactions. These electronic libraries provide information "at the touch of a button". In their turn, the libraries also serve as sources of structural knowledge for applications software that address specific problems in small-molecule and biological chemistry.     

Substitution-Inert Metal Complex Mobile Phases in Non-Suppressed Cation Chromatography

Substitution-inert metal complexes, [Co(edda)(H₂O)₂]⁺, (Co(edda)(en)]⁺, [Co(edda)(dmen)]⁺, [Co(en)₂-(gly)]²⁺, [Co(en)₂(acac)]²⁺, and [Co(trien)(gly)]²⁺ in their nitrate salt solutions are used as eluents in nonsuppressed cation chromatography (where edda = ethylenediamine-N,N′-diacetic acid, en = ethylenediamine, dmen = N,N′-dime-thylethylenediamine, gly = glycine, acac = acetylacetone, and trien = triethylenetetraamine). It is found that all the mono- and di-valent charged complexes can be used to separate alkali and alkaline earth metal cations, respectively. The separations for monovalent cations are sometimes comparable to those using ultrapure HNO₃ solutions. However, the divalent Ca²⁺ and Sr²⁺ ions cannot be resolved using the metal complex eluents. On the other hand, a selected, direct non-suppressed IC separation of zinc(II) and cadmium(II) ions is demonstrated for the first time using a substitution-inert metal complex eluent and a conductivity detector. Comparisons of these eluents with those reported previously, i. e. HNO₃ and ethylenediammonium salt solution are made and explanations are proposed to account for the different selectivities observed where possible. The future development of this technique is also briefly discussed.     

Fast-response system for signal acquisition and processing in electrothermal atomic absorption spectrometry

An electrothermal atomic absorption (a.a.) spectrometer is modified to allow accurate correlation of absorbance and pyrometrically measured temperature with time. To by-pass the slow electronics of the spectrometer, the signal is fed from the preamplifier immediately after the photomultipier tube to a 12-bit A/D converter mounted in a 320K IBM-PC microcomputer. The wall temperature of the graphite furnace, measured with an automatic optical pyrometer, is recorded simultaneously with absorbance by feeding the pyrometer output to a second channel of the A/D board. Fast deuterium-arac background correction is also done. Background-corrected absorbance, background absorbance and temperature are recorded at 60 Hz. A simple algorithm allowed experimental activation energies to be calculated automatically. All programming was in BASIC or PASCAL.