Surfaces of Constant Mean Curvature Bounded by Two Planar Curves

In this paper we study constant mean curvature compact surfaces with two Jordan curves in parallel planes as boundary and we investigate the point at which the surface inherits the symmetries of its boundary.     

Time Delay and Short-Range Scattering in Quantum Waveguides

Although many physical arguments account for using a modified definition of time delay in multichannel-type scattering processes, one can hardly find rigorous results on that issue in the literature. We try to fill in this gap by showing, both in an abstract setting and in a short-range case, the identity of the modified time delay and the Eisenbud-Wigner time delay in waveguides. In the short-range case we also obtain limiting absorption principles, state spectral properties of the total Hamiltonian, prove the existence of the wave operators and show an explicit formula for the S-matrix. The proofs rely on stationary and commutator methods. Communicated by Yosi Avron submitted 12/04/05, accepted 13/05/05     

The twist coefficient of periodic solutions of a time-dependent Newton's equation

This paper gives sufficient conditions for the existence of periodic solutions of twist type of a time-dependent differential equation of the second order. The concept of periodic solution of twist type is defined in terms of the corresponding Birkhoff normal form and, in particular, implies that the solution is Lyapunov stable. Some applications to nonlocal problems are given.     

Branch and win: OR tree search algorithms for solving combinatorial optimisation problems

Currently, most combinatorial optimisation problems have to be solved, if the optimum solution is sought, using general techniques to explore the space of feasible solutions and, more specifically, through exploratory enumerative procedures in trees and search graphs. We propose Branch and Win, a general formulation for understanding and synthesising the different tree search procedures that have been presented in the literature of operations research as well as in that of artificial intelligence. Several general ideas are also presented, whose application allows designing new hybrid search algorithms, in order to implement the procedure.     

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.     

Pyridinium N-heteroarylaminides: synthesis of N-heteroaryltetramines based on 1,6-bis(phenoxy)hexane and 1,3-bis(phenoxymethyl)benzene

The synthesis of a set of new N-heteroaryltetramines is reported. A regioselective alkylation on the N-exo nitrogen of pyridinium N-(heteroaryl)aminide with the corresponding tetrabromo compounds, followed by a clean N-N bond reduction of the corresponding tetra-salts, allowed an easy and general method to obtain N,N′,N″,N?-tetrakis(2-heteroaryl)tetramines.     

Stereochemical analysis of 3,4-methylenedioxymethamphetamine and its main metabolites by gas chromatography/mass spectrometry

3,4-Methylenedioxymethamphetamine (MDMA, ecstasy) is consumed as the racemate but some metabolic steps are enantioselective. In addition, chiral properties are preserved during MDMA biotransformation. A quantitative analytical methodology using gas chromatography/mass spectrometry (GC/MS) to determine enantioselective disposition in the body of MDMA and its main metabolites including 3,4-methylenedioxyamphetamine (MDA), 4-hydroxy-3-methoxymethamphetamine (HMMA), and 4-hydroxy-3-methoxyamphetamine (HMA) was developed. Plasma and urine samples were collected from a male volunteer. The analysis of MDMA, MDA, and 4-hydroxy-3-methoxy metabolites by GC/MS required a two-step derivatization procedure. The first step consisted of derivatization of the amine with enantiomerically pure Mosher's reagent ((R)-MTPCl). Triethylamine was used as a base to neutralize hydrochloric acid formed during the reaction allowing quantitative derivatization, which resulted in a substantial improvement in the sensitivity of the method compared with other previously described techniques. Further treatment with ammonium hydroxide was required since both amine and hydroxyl groups underwent derivatization in the reaction. Ammonium hydroxide breaks bonds formed with hydroxyl groups without affecting amine derivatives. The second derivatization step using hexamethyldisilazane was needed for metabolites containing phenol residues. This derivatization method permitted the stereochemically specific study of MDMA and its main monohydroxylated metabolites by GC/MS. A detailed study of the chemical reactions involved in the derivatization steps was indispensable to develop a straightforward, sensitive, and reproducible method for the analysis of the parent drug compound and its metabolites.