Lower semicontinuous solutions of the Bellman equation for the minimum time problem

The minimum time problem associated with a nonlinear control system is considered, and the unicity of the lower semicontinuous solution of the corresponding Bellman equation is investigated. A main tool in our approach is the Kruzkov transformation that enables us to work on ⁿ –{0}, where {0} is the target set, instead of the unknown reachable set.This research was carried out while the first author was visiting the Department of Mathematics, University of Genova, Genova, Italy.     

Mono- and diiodocyclophosphamide as possible internal standards for cyclophosphamide quantification: characterization by ion trap multi-stage mass spectrometry and effects of iodine-chlorine substitution on the fragmentation pattern

Hospital personnel involved in antineoplastic drug preparation and administration to patients are exposed to large amounts of these drugs. Labour legislation indicates the necessity of planning monitoring strategies aimed at prevention and/or reduction of drug exposure. Monitoring strategies consist of quantitative determinations of indicators, present in environmental and biological matrices. Among the antineoplastic drugs widely used, cyclophosphamide (CP) has been identified as a suitable indicator of potential exposure to mixtures of antineoplastic drugs. Many literature methods for quantitative analysis of CP involve either liquid (LC) or gas chromatography (GC) with mass spectrometry (MS), both of which require use of a suitable internal standard. The present work focuses on the synthesis of mono- and diiodocyclophosphamide (CPI and CPI(2)) to be used as internal standard. These compounds were analyzed by GC/EI-MS/MS and LC/ESI-MS(n) using ion trap mass spectrometry. The product ion mass spectra are interpreted in terms of proposed structures of fragment ions. Iodine-chlorine substitution resulted in a weakening of the carbon-halogen bond with a noteworthy influence on the ion fragmentation processes. The proposed suitability of CPI and CPI(2) as internal standards was based on similarities to CP as regards ionization and fragmentation processes. The results obtained suggest that CPI could be used as internal standard for CP quantification by LC/ESI-MS/MS, and CPI(2) for GC/EI-MS/MS analyses.     

Small-angle neutron scattering of ionic perfluoropolyether micellar solutions: role of counterions and temperature

This paper reports a small-angle neutron scattering (SANS) characterization of perfluoropolyether (PFPE) aqueous micellar solutions with lithium, sodium, cesium and diethanol ammonium salts obtained from a chlorine terminated carboxylic acid and with two perfluoroisopropoxy units in the tail (n(2)). The counterion and temperature effects on the micelle formation and micellar growth extend our previous work on ammonium and potassium salts n(2) micellar solutions. Lithium, sodium, cesium and diethanol ammonium salts are studied at 0.1 and 0.2 M surfactant concentration in the temperature interval 28-67 degrees C. SANS spectra have been analyzed by a two-shell model for the micellar form factor and a screened Coulombic plus steric repulsion potential for the structure factor in the frame of the mean spherical approximation of a multicomponent system reduced to a generalized one component macroions system (GOCM). At 28 degrees C, for all the salts, the micelles are ellipsoidal with an axial ratio that increases from 1.6 to 4.2 as the counterion volume increases. The micellar core short axis is 13 A and the shell thickness 4.0 A for the alkali micelles, and 14 and 5.1 A for the diethanol ammonium micelles. Therefore, the core short axis mainly depends on the surfactant tail length and the shell thickness on the carboxylate polar head. The bulky diethanol ammonium counterion solely influences the shell thickness. Micellar charge and average aggregation number depend on concentration, temperature and counterion. At 28 degrees C, the fractional ionization decreases vs the counterion volume (or molecular weight) increase at constant concentration for both C = 0.1 M and C = 0.2 M. The increase of the counterion volume leads also to more ellipsoidal shapes. At C = 0.2 M, at 67 degrees C, for sodium and cesium micelles the axial ratio changes significantly, leading to spherical micelles with a core radius of 15 A, lower average aggregation number, and larger fractional ionization.     

Latex Fractionation by Sedimentation and Colloidal Crystallization: The Case of Poly(styrene-co-acrylamide)

Poly(styrene-co-acrylamide) (PS-AAM) latex was prepared, fractionated by sedimentation under gravity, and characterized by PCS, infrared spectra, secondary and backscattered electron imaging in the scanning electron microscope, and electron spectroscopy imaging in an analytical transmission electron microscope. Three latex fractions were obtained. The lower fraction was opalescent and its particles were the more uniform, concerning size, chemical composition, and topochemical features. This lower fraction was still further fractionated by zonal centrifugation in a density gradient, yielding two fractions with similar macrocrystal-forming abilities but different sizes and chemical compositions. These results confirm those previously obtained for the PS-HEMA latex. Copyright 2000 Academic Press.     

Chemometric Strategies to Develop a Nanocomposite Electrode for Simultaneous Determination of Ascorbic Acid,Dopamine, and Uric Acid

A simple and sensitive method for simultaneously measuring dopamine (DA), ascorbic acid (AA), and uric acid (UA) using a poly(1‐aminoanthracene) and carbon nanotubes nanocomposite electrode is presented. The experimental parameters for composite film synthesis as well as the variables related to simultaneous determination of DA, AA, and UA were optimized at the same time using fractional factorial and Doehlert designs. The use of carbon nanotubes and poly(1‐aminoanthracene) in association with a cathodic pretreatment led to three well‐defined oxidation peaks at potentials around ?0.039, 0.180 and 0.351 V (vs. Ag/AgCl) for AA, DA, and UA, respectively. Using differential pulse voltammetry, calibration curves for AA, DA, and UA were obtained over the range of 0.16–3.12×10^?3 mol L^?1, 3.54–136×10^?6 mol L^?1, and 0.76–2.92×10^?3 mol L^?1, with detection limits of 3.95×10^?5 mol L^?1, 2.90×10^?7 mol L^?1, and 4.22×10^?5 mol L^?1, respectively. The proposed method was successfully applied to determine DA, AA, and UA in biological samples with good results.     

Derivation of the Gross-Pitaevskii equation for condensed bosons from the Bogoliubov-de Gennes equations for superfluid fermions

We derive the time-independent Gross-Pitaevskii equation at zero temperature for condensed bosons, which form as bound-fermion pairs when the mutual fermionic attractive interaction is sufficiently strong, from the strong-coupling limit of the Bogoliubov-de Gennes equations that describe superfluid fermions in the presence of an external potential. Three-body corrections to the Gross-Pitaevskii equation are also obtained by our approach. Our results are relevant to the recent advances with ultracold fermionic atoms in a trap.