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.     

A general relation between kink-exchange and kink-rotation

The normal correlation between spin and statistics is shown to be valid for arbitrary kinks, among them theSU(n) Skyrmions forn3. It is assumed in the proof that no gauge-ambiguity attaches to the values of the underlying scalar field, and that conversely each configuration of this field is represented quantum mechanically by a Hilbert subspace of dimension precisely one.Supported in part by NSF Grant No. PHY 83-18350     

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

Development and critical comparison of greener flow procedures for nitrite determination in natural waters

Two greener procedures for flow-injection spectrophotometric determination of nitrite in natural waters were developed and critically compared. Replacement of toxic reagents, waste minimization and treatment were exploited to attend the standards of clean chemistry. The flow system was designed with solenoid micro-pumps in order to minimize reagent consumption and waste generation. The first procedure is based on the Griess diazo-coupling reaction with sulfanilamide and N-(1-naphthyl)ethylenediamine (NED) yielding an azo dye, followed by photodegradation of the low amount of waste generated based on the photo-Fenton reaction. The second procedure is based on the formation of iodine from nitrite and iodide in acid medium in order to avoid the use of toxic reagents. For Griess method, linear response was achieved up to 1.0 mg L^− 1, described by the equation A = − 0.007 + 0.460C (mg L^− 1), r = 0.999. The detection limit was estimated as 8 μg L^− 1 at the 99.7% confidence level and the coefficient of variation was 0.8% (n = 20). The sampling rate was estimated as 108 determinations per hour. The consumption of the most toxic reagent (NED) is reduced 55-fold and 20-fold in comparison to batch method and flow injection with continuous reagent addition, respectively. A colorless residue was obtained by in-line photodegradation with reduction of 87% of the total organic carbon content. The results obtained for natural water samples were in agreement with those achieved by the reference method at the 95% confidence level. For the nitrite–iodide method, linear response was observed up to 2.0 mg L^− 1, described by the equation A = − 0.024 + 0.148C (mg L^− 1), r = 0.999. The detection limit was estimated as 25 μg L^− 1 at the 99.7% confidence level and the coefficient of variation was 0.6% (n = 20). The sampling rate was estimated as 44 determinations per hour. Despite avoiding the use of toxic reagents, the nitrite–iodide method presented worst performance in terms of selectivity and sensitivity.     

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).