Optimal bounds for ratios of eigenvalues of one-dimensional Schrödinger operators with Dirichlet boundary conditions and positive potentials

Consider the Schrödinger equation –u+V(x)u=u on the intervalI, whereV(x)0 forxI and where Dirichlet boundary conditions are imposed at the endpoints ofI. We prove the optimal bound

Application of strategically designed sample composition to the rapid analytical screening of milk samples for polychlorinated biphenyls

Strategically designed sample composition (SSC) is a new technique that decreases the number of analytical determinations needed in routine screening to as few as the number of original sample specimens while providing information that is specific to them. Although this new technique has been applied to environmental studies, this paper describes its first application to food safety studies. Contamination of milk samples with polychlorinated biphenyls (PCBs) was chosen as a case study to show the usefulness and potential of the SSC technique with a fast analytical procedure that involves saponification of the samples and solid-phase microextraction of the PCBs. A total of 20 sample specimens can be analyzed in 11 determinations with excellent predictions of the positive samples and the concentration levels of the contaminants. The robustness of the strategy was investigated and demonstrated.     

In vitro determination of the release kinetics of peptides and free amino acids during the digestion of food proteins

The kinetics of peptide release during in vitro digestion of 4 protein sources (casein, cod protein, soy protein, and gluten) were investigated. Samples were sequentially hydrolyzed with pepsin (30 min) and pancreatin (2, 4, or 6 h) in a dialysis cell with continuous removal of digestion products. Nondialyzed digests were fractionated by ion-exchange chromatography and ultrafiltration. Animal proteins were digested at a greater rate than plant proteins. Target amino acids of specific enzymes appeared more rapidly in the dialyzed fractions when compared to other amino acids. Throughout the hydrolysis, nondialyzed digests contained a higher proportion of peptide mixtures with basic-neutral properties. Except for gluten, peptide fractions with molecular weights that exceeded 10 kDa (basic-neutral, BN > 10) were rapidly hydrolyzed during the first 2 h of pancreatin digestion. The kinetics of release and the composition of peptide fractions were different when the protein sources were compared. The analysis of amino acids revealed that threonine and proline proportions were relatively high in BN > 10 and in peptide fractions with molecular weight between 10-1 kDa (BN 10-1), while tyrosine, phenylalanine, lysine, and arginine predominated in the low molecular weight (<1 kDa) fractions. More resistant peptides were generally rich in proline and glutamic acid. The role of in vitro digestion assays in dietary protein quality evaluation is discussed.     

Cycloaddition reactions of 2-vinylthiophen

Cycloaddition reactions between 2-vinylthiophen and the dienophiles maleic anhydride, dimethyl acetylenedicarboxylate,' methyl propiolate, and methyl acrylate, are reported. Products include simple benzo[b]thiophen carboxylates (6, 13, 17) and reduced derivatives (3, 4, 18). The acetylenic dienophiles also gave a dihydrobenzthienyl-acrylate (16) or -fumarate (11), and the dithienylcyclohexene esters (7) and (14).     

Thiocarbonyl rhodium complexes with tricyclohexylphosphine and other nitrogen and phosphorus donor ligands

Summary The preparation of the covalent Rh(OCIO₃)(CS)(PCy₃)₂ and Rh(OClO₃)(CS)(PPh₃)(PCy₃) perchlorato complexes is described, These complexes react with mono- or bidentate nitrogen donor ligands to give new cationic complexes of the [Rh(CS)(PCY₃)₂L]ClO4 and [Rh(CS)(PPh,)(PCy₃)L]ClO₄ types,     

Highly conjugated p-quinonoid pi-extended tetrathiafulvalene derivatives: a class of highly distorted electron donors

A new class of pi-extended TTF-type electron donors (11 a-c) has been synthesized by Wittig-Horner olefination of bianthrone (9) with 1,3-dithiole phosphonate esters (10 a-c). In cyclic voltammetry experiments, donors 11 a-c reveal a single, electrochemically irreversible oxidation-yielding the corresponding dicationic products-at relatively low oxidation potentials (approximately 0.7-0.8 V). Theoretical calculations, performed at the DFT level (B3 P86/6-31 G*), predict a highly-folded C(2h) structure for 11 a. In the ground state, the molecule adopts a double saddle-like conformation to compensate the steric hindrance. The calculations suggest that the intramolecular charge transfer associated with the HOMO-->LUMO transition is responsible for an absorption band observed above 400 nm. While the radical cation 11 a*+ retains the folded C(2h) structure predicted for the neutral molecule as the most stable conformation, the dication 11 a(2+) has a fully aromatic D(2) structure, formed by an orthogonal 9,9'-bianthryl central unit to which two singly-charged dithiole rings are attached. The drastic conformational changes that compounds 11 undergo upon oxidation account for their electrochemical properties. By means of pulse radiolysis measurements, radical-induced one-electron oxidation of 11 a-c was shown to lead to the radical cation species (11 a-c*+), which were found to disproportionate with generation of the respective dication species (11 a-c(2+)) and the neutral molecules (11 a-c).     

Relaxation processes in room temperature ionic liquids: the case of 1-butyl-3-methyl imidazolium hexafluorophosphate

A detailed investigation on the nature of the relaxation processes occurring in a typical room temperature ionic liquid (RTIL), namely, 1-butyl-3-methyl imidazolium hexafluorophosphate ([bmim][PF(6)]), is reported. The study was conducted using both elastic and inelastic neutron scattering over a wide temperature range from 10 to 400 K, accessing the dynamic features of both the liquid and glassy amorphous states. In this study, the inelastic fixed energy scan technique has been applied for the first time to this class of materials. Using this technique, the existence of two relaxation processes below the glass transition and a further diffusive process occurring above the glass-liquid transition are observed. The low temperature processes are associated with methyl group rotation and butyl chain relaxation in the glassy state and have been modeled in terms of two Debye-like, Arrhenius activated processes. The high temperature process has been modeled in terms of a Kohlraush-Williams-Watts relaxation, with a distinct Vogel-Fulcher-Tamman temperature dependence. These results provide novel information that will be useful in rationalizing the observed structural and dynamical behavior of RTILs in the amorphous state.     

Synthesis of novel 2,5-dihydro-1,5,2-diazaphosphinines from primary enamine phosphonates and from alkyl phosphonates

A simple method for the preparation of phosphorus-containing pyrimidine analogues such as 2,5-dihydro-2-ethoxy-1,5,2-diazaphosphinine 2-oxides 9, 12-15 and adducts 3, 10 is described. Dihydrophosphinines 9, 12-15 are prepared from primary enamine phosphonates and nitriles or from phosphonates and nitriles in the presence of base, while highly stable hydrogen-bonded amine-dihydro-diazaphosphinine adducts 3, 10 are obtained by the addition of amine to dihydrophosphinines 9 or by reaction of alkylphosphonates with nitriles in the presence of LDA.