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

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.     

Study of the feasibility of focused microwave-assisted soxhlet extraction of N-methylcarbamates from soil

A fast microwave-assisted dansylation procedure has been developed for the derivatization of N-nitrosamines prior to high-performance liquid chromatography determination. N-Nitrosomorpholine, N-nitrosodimethylamine, N-nitrosodiethylamine, N-nitrosopyrrolidine and N-nitrosopiperidine are first denitrosated by hydrobromic acid-acetic acid to produce secondary amines, which are then quantitatively dansylated in 5 min using radiation power of 378 W and a maximum pressure of 1.4 bar inside the reactor. The reaction mixture is separated on a C18 column with acetonitrile-water (55:45, v/v) as mobile phase with fluorimetric detection at 531 nm (excitation at 339 nm). The detection limits range from 8 to 75 pg for N-nitrosomorpholine and N-nitrosodiethylamine, respectively. The method was applied to study the recoveries of N-nitrosamines in beer and their determination in cigarette smoke.     

Theoretical study of alkyl-pi and aryl-pi interactions. Reconciling theory and experiment

Quantum mechanical and quantum mechanical/molecular mechanical calculations in conjunction with continuum solvation models have been used to analyze CH-pi interactions in model systems of aryl- and alkyl-aromatic interactions, as well as in a model folding system designed to study those interactions. High level calculations reproduced accurately the interaction of CH-pi interactions in both alkyl- and aryl-based model systems. Dispersion effects dominate the interaction, but the electrostatics term is also relevant for aryl CH-pi interactions. Theoretical calculations were also used to examine the influence of CH-pi interactions in determining the conformational flexibility of folding models. Finally, a critical comparison of the results obtained from high level calculations on model systems and the experimental data derived for folding models in apolar solvents was carried out, which allowed us to reconcile the apparent discrepancy found between both data.     

First‐order correlation‐kinetic contribution to Kohn–Sham exchange charge density function in atoms,using quantal density functional theory approach

Using the static exchange‐correlation charge density concept, the total integrated exchange‐charge density function is calculated within the nonrelativistic spin‐restricted exchange‐only (i) optimized effective potential model, and (ii) nonvariational local potential derived from the exchange‐only work potential within the quantal density functional theory, for the ground‐state isoelectronic series: Ga⁺, Zn, Cu^?; In⁺, Cd, Ag^?; and Tl⁺, Hg, Au^?. The difference between the exchange charge density function derived from these potentials is employed to evaluate the first‐order correlation‐kinetic contribution to the integrated exchange charge density. This contribution is found to be important for both the intra‐ and inter‐shell regions. Screening effects on the contribution due to the nd¹⁰ (n = 3–5) subshells are discussed through comparisons with similar calculations on Ca, Sr, and Ba, wherein nd¹⁰ electrons are absent. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005