An entropy-based uncertainty principle for a locally compact abelian group

We classify all functions on a locally compact, abelian group giving equality in an entropy inequality generalizing the Heisenberg Uncertainty Principle. In particular, for functions on a real line, we proof a conjecture of Hirschman published in 1957.     

Dielectrophoretic force on a sphere near a planar boundary

The small gap distance separating a spherical colloidal particle in electrophoretic motion from a planar nonconducting surface is a required parameter for calculating its electrophoretic mobility. In the presence of an externally applied electric field, this gap distance is determined by balancing the van der Waals, electrical double layer interaction, and gravitational forces with a dielectrophoretic (DEP) force. Here, the DEP force was determined analytically by integration of the Maxwell stress over the surface of the particle. The account of this force showed that its previous omission from the analysis always resulted in underpredicted gap distances. Furthermore, the DEP force dominated under conditions of low particle density or high electric field strength and led to much higher gap distances on the order of a few microns. In one particular case, a combination of low particle density and small particle size produced two possible equilibrium gap distances for the particle. However, the particle was unstable in the second equilibrium position when subjected to small perturbations. In general, larger particles had smaller gap sizes. The effects of four other parameters on gap distance were studied, and gap distances were found to increase with lower particle density, higher electric field strength, higher particle and wall zeta potentials, and lower Hamaker constants. Retardation effects on van der Waals attraction were considered.     

Vacancy ion-exclusion chromatography of carboxylic acids on a weakly acidic cation-exchange resin

In this preliminary study, a new approach to ion-exclusion chromatography is proposed to overcome the relatively poor conductivity detection response which occurs in ion-exclusion chromatography when acids are added to the eluent in order to improve peak shape. This approach, termed vacancy ion-exclusion chromatography, requires the sample to be used as eluent and a sample of water to be injected onto a weakly acidic cation-exchange column (TSKgel OApak-A). Vacancy peaks for each of the analytes appear at the retention times of these analytes. Highly sensitive conductivity detection is possible and sharp, well-shaped peaks are produced, leading to efficient separations. Retention times were found to be affected by the concentration of the analytes in the eluent, and also by the presence of an organic modifier such as methanol in the eluent. Detection limits for oxalic, formic, acetic, propionic, butyric and valeric acids were 0.1, 0.2, 0.3, 0.3, 0.4 and 0.5 microM, respectively, and linear ranges for some acids extended over two orders of magnitude. Precision values for retention times were 0.21% and for peak areas were <1.90%. The vacancy ion-exclusion chromatography method was found to give detection responses four to 10 times higher than conventional ion-exclusion chromatography using sulfuric acid eluent and two to five times higher than conventional ion-exclusion chromatography using benzoic acid eluent.     

Molecular dynamics averaging of Xe chemical shifts in liquids

The Xe nuclear magnetic resonance chemical shift differences that afford the discrimination between various biological environments are of current interest for biosensor applications and medical diagnostic purposes. In many such environments the Xe signal appears close to that in water. We calculate average Xe chemical shifts (relative to the free Xe atom) in solution in eleven liquids: water, isobutane, perfluoro-isobutane, n-butane, n-pentane, neopentane, perfluoroneopentane, n-hexane, n-octane, n-perfluorooctane, and perfluorooctyl bromide. The latter is a liquid used for intravenous Xe delivery. We calculate quantum mechanically the Xe shielding response in Xe-molecule van der Waals complexes, from which calculations we develop Xe (atomic site) interpolating functions that reproduce the ab initio Xe shielding response in the complex. By assuming additivity, these Xe-site shielding functions can be used to calculate the shielding for any configuration of such molecules around Xe. The averaging over configurations is done via molecular dynamics (MD). The simulations were carried out using a MD technique that one of us had developed previously for the simulation of Henry's constants of gases dissolved in liquids. It is based on separating a gaseous compartment in the MD system from the solvent using a semipermeable membrane that is permeable only to the gas molecules. We reproduce the experimental trends in the Xe chemical shifts in n-alkanes with increasing number of carbons and the large chemical shift difference between Xe in water and in perfluorooctyl bromide. We also reproduce the trend for a given solvent of decreasing Xe chemical shift with increasing temperature. We predict chemical shift differences between Xe in alkanes vs their perfluoro counterparts.     

Ion-exclusion chromatography with conductimetric detection of aliphatic carboxylic acids on a weakly acidic cation-exchange resin by elution with benzoic acid-beta-cyclodextrin

In this study, an aqueous solution consisting of benzoic acid with low background conductivity and beta-cyclodextrin (beta-CD) of hydrophilic nature and the inclusion effect to benzoic acid were used as eluent for the ion-exclusion chromatographic separation of aliphatic carboxylic acids with different pKa values and hydrophobicity on a polymethacrylate-based weakly acidic cation-exchange resin in the H+ form. With increasing concentration of beta-cyclodextrin in the eluent, the retention times of the carboxylic acids decreased due to the increased hydrophilicity of the polymethacrylate-based cation-exchange resin surface from the adsorption of OH groups of beta-cyclodextrin. Moreover, the eluent background conductivity decreased with increasing concentration of beta-cyclodextrin in 1 mM benzoic acid, which could result in higher sensitivity for conductimetric detection. The ion-exclusion chromatographic separation of carboxylic acids with high resolution and sensitivity was accomplished successfully by elution with a 1 mM benzoic acid-10 mM cyclodextrin solution without chemical suppression.     

Excited-state electron-transfer quenching by a series of water photoreduction mediators

Rate constants k_q for the quenching of the excited state of Ru(bipy)₃²⁺ by a series of viologen salts having different redox potential E_{$\text{1}\text{2}$} have been determined in deaerated aqueous solutions at pH = 5 by laser flash photolysis. The k_q values are found to decrease with increasing —E_{$\text{1}\text{2}$} and to correlate with the reaction free-energy change ΔG. Such a correlation is shown to be consistent with the Rehm—Weller model for electron-transfer reactions.     

Hydrogen activation on Mo-based sulfide catalysts,a periodic DFT study

Hydrogen adsorption on Mo[bond]S, Co[bond]Mo[bond]S, and Ni[bond]Mo[bond]S (10 1 macro 0) surfaces has been modeled by means of periodic DFT calculations taking into account the gaseous surrounding of these catalysts in working conditions. On the stable Mo[bond]S surface, only six-fold coordinated Mo cations are present, whereas substitution by Co or Ni leads to the creation of stable coordinatively unsaturated sites. On the stable MoS(2) surface, hydrogen dissociation is always endothermic and presents a high activation barrier. On Co[bond]Mo[bond]S surfaces, the ability to dissociate H(2) depends on the nature of the metal atom and the sulfur coordination environment. As an adsorption center, Co strongly favors molecular hydrogen activation as compared to the Mo atoms. Co also increases the ability of its sulfur atom ligands to bind hydrogen. Investigation of surface acidity using ammonia as a probe molecule confirms the crucial role of sulfur basicity on hydrogen activation on these surfaces. As a result, Co[bond]Mo[bond]S surfaces present Co[bond]S sites for which the dissociation of hydrogen is exothermic and weakly activated. On Ni[bond]Mo[bond]S surfaces, Ni[bond]S pairs are not stable and do not provide for an efficient way for hydrogen activation. These theoretical results are in good agreement with recent experimental studies of H(2)[bond]D(2) exchange reactions.     

NMR and UV studies of 3'-S-phosphorothiolate modified DNA in a DNA : RNA hybrid dodecamer duplex; implications for antisense drug design

High-resolution NMR spectroscopy has been used to establish the conformational consequences of the introduction of a single 3[prime or minute]-S-phosphorothiolate link in the DNA strand of a DNA : RNA hybrid. These systems are of interest as potential antisense therapeutic agents. Previous studies on similarly modified dinucleotides have shown that the conformation of the sugar to which the sulfur is attached shifts to the north (C(3[prime or minute])-endo/C(2[prime or minute])-exo). Comparisons made between NOESY cross-peak intensities, and coupling constants from PE-COSY spectra, for both non-modified and modified duplexes confirm that this conformational shift is also present in the double helical oligonucleotide system. In addition it is noted that in both the dinucleotides and the modified duplex, the conformation of the sugar ring 3[prime or minute] to the site of modification is also shifted to the north. That this pattern is observed in the small monomeric system as well as the larger double helix is suggestive of some pre-ordering of the sequences. The conclusion is supported by consideration of the (1)H chemical shifts of the heterocyclic bases near the site of the modification. The enhanced stability that these conformational changes should bring was confirmed by UV thermal melting studies. Subsequently a series of singly and doubly 3[prime or minute]-S-phosphorothiolate-modified duplexes were investigated by UV. The results are indicative of an additive effect of the modification with thermodynamic benefit being derived from alternate spacing of two modified linkers.     

Convexity preserving interpolation by algebraic curves and surfaces

The problem of interpolation by a convex curve to the vertices of a convex polygon is considered. A natural 1-parameter family ofC algebraic curves solving this problem is presented. This is extended to a solution, of a general Hermite-type problem, in, which the curve also interpolates to one or two prescribedtangents at any desired vertices of the polygon. The construction of these curves is a generalization of well known methods for generatingconic sections. Several properties of this family of algebraic curves are discussed. In addition, the method is generalized to convexC interpolation of strictly convex data sets inR ³ by algebraicsurfaces.     

FDA Quality assurance for radioactivity in foods and radiopharmaceuticals

Summary The Food and Drug Administration (FDA) has regulatory responsibility for radionuclides in foods and radiopharmaceuticals and must maintain an ongoing Quality Assurance Program. These Quality Control Programs involve the U.S. Environmental Protection Agency (EPA) [1, 2] and the National Institute of Standards and Technology (NIST) [3], who supply the necessary reference materials and standards to ensure that the measurements are accurate and reproduceable. Data from EPA (1987 to 1991) and from a NIST Blind Source study (1985 to 1991) show the results are accurate with an average variation from NIST values of 1.8% [4–10]. The use of standard materials with the same matrices as the samples being analyzed provides credibility to the measurements.