Exact propagator beyond and at caustics for isotropic time-dependent coupled and driven oscillators

Through a sequence of transformations we relate the propagator for the system of isotropic time-dependent, coupled and driven oscillators with time-varying mass, with those of free particles. We then derive the wave functions and the propagator beyond and at caustics. Finally we study a particular case which appears in quantum optics. © 1990.

Exact solution for a three-dimensional three-body problem with harmonic interactions

The three-dimensional three-body problem with non-equal masses interacting through pairwise harmonic forces of non-equal strengths is analysed. It is shown that the Jacobi coordinates per se do not decouple this problem but lead to the problem of two coupled three-dimensional harmonic oscillators which becomes exactly soluble through the use of an additional coordinate set.

Exact solutions related to nonminimal gravitational coupling

We obtain exact analytic solutions for a typical autonomous dynamical system, related to the problem of a vector field nonminimally coupled to gravity. © 1995.

Quark-meson coupling model with constituent quarks: Exchange and pionic effects

The binding energy of nuclear matter including exchange and pionic effects is calculated in a quark-meson coupling model with massive constituent quarks. As in the case with elementary nucleons in QHD, exchange effects are repulsive. However, the coupling of the mesons directly to the quarks in the nucleons introduces a new effect on the exchange energies that provides an extra repulsive contribution to the binding energy. Pionic effects are not small. Implications of such effects on observables are discussed. © 1998 Published by Elsevier Science B.V. All rights reserved.

Interaction of mercury(II) with humic substances from the Rio Negro (Amazonas State, Brazil) by means of an ion exchange procedure

The aquatic humic substances (HS) investigated in this study with respect to their binding capability towards mercury(II) were isolated from the river Rio Negro, Amazonas State - Brazil, by means of the adsorbent XAD 8. Labile/inert fractions of inorganic Hg(II) complexes formed with these HS were characterized using an ion-exchange batch and column technique, respectively, based on Chelite S. This collector exhibits high Hg(II) distribution coefficients, Kd, up to the order of 104 decreasing, however, in the case of small Hg(II)/HS ratios (< 0.1 μg Hg(II) / mg HS). The influence of different complexation parameters (ratio of Hg(II)/HS, pH, contact time, complexing time) relevant for Hg(II) binding in aquatic environments was assessed. The Hg(II) lability in dissolved HS is mainly influenced by the mass ratio of Hg(II)/HS and the ageing of Hg(II)-HS species formed. This is particularly obvious in the case of low Hg(II) loading of HS where slow transformation processes of freshly formed Hg(II)-HS species significantly decrease their lability, leading to incomplete recoveries (< 20%) of the total Hg(II) bound to HS.

Renormalization of the one-pion-exchange interaction

A renormalization scheme for the nucleon-nucleon (NN) interaction based on a subtracted T-matrix equation is proposed and applied to the one-pion-exchange potential supplemented by contact interactions. The singlet and triplet scattering lengths are given to fix the renormalized strengths of the contact interactions. With only one scaling parameter (μ), the results show an overall very good agreement with neutron-proton data, particularly for the observables related to the triplet channel. The agreement is qualitative in the 1 S0 channel. Between the low-energy NN observables we have examined, the mixing parameter of the 3S1-3D1 states is the most sensitive to the scale. The scheme is renormalization group invariant for μ → ∞. © 1999 Elsevier Science B.V. All rights reserved.

Determination of mercury in agroindustrial samples by flow-injection cold vapor atomic absorption spectrometry using ion exchange and reductive elution

A flow-injection system with a Chelite-S® cationic resin packed minicolumn is proposed for the determination of trace levels of mercury in agroindustrial samples by cold vapor atomic absorption spectrometry. Improved sensitivity and selectivity are attained since mercuric ions are on-line concentrated whereas other potential interferents are discarded. With on-line reductive elution procedure, concentrated hydrochloric acid could be replaced by 10% w/v SnCl2, in 6 M HCl as eluent. The reversed-intermittent stream either carries the atomic mercury, to the flow cell in the forward direction or removes the residue from reactor/gas liquid separator to a discarding flask in the opposite direction. Concentration and volume of reagent, acidity, flow rates, commutation times and potential interfering species were investigated. For 120 s preconcentration time, the proposed system handles about 25 samples h-1 (50.0 500 ng l-1), consuming about 10 ml sample and 5 mg SnCl2 per determination. The detection limit is 0.8 ng l-1 and the relative standard deviation (RSD) (n = 12) of a 76.7 ng l-1 sample is about 5%. Results are in agreement with certified value of standard materials at 95% confidence level and good recoveries (97-128%) of spiked samples were found. (C) 2000 Elsevier Science B.V.

Exact solvability of potentials with spatially dependent effective masses

We discuss the relationship between exact solvability of the Schroedinger equation, due to a spatially dependent mass, and the ordering ambiguity. Some examples show that, even in this case, one can find exact solutions. Furthermore, it is demonstrated that operators with linear dependence on the momentum are nonambiguous. (C) 2000 Elsevier Science B.V.

Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Minimization of lead and copper interferences on spectrophotometric determination of cadmium using electrolytic deposition and ion-exchange in multi-commutation flow system

A new strategy for minimization of Cu2+ and Pb2+ interferences on the spectrophotometric determination of Cd2+ by the Malachite green (MG)-iodide reaction using electrolytic deposition of interfering species and solid phase extraction of Cd2+ in flow system is proposed. The electrolytic cell comprises two coiled Pt electrodes concentrically assembled. When the sample solution is electrolyzed in a mixed solution containing 5% (v/v) HNO3, 0.1% (v/v) H2SO4 and 0.5 M NaCl, Cu2+ is deposited as Cu on the cathode, Pb2+ is deposited as PbO2 on the anode while Cd2+ is kept in solution. After electrolysis, the remaining solution passes through an AG1-X8 resin (chloride form) packed minicolumn in which Cd2+ is extracted as CdCl4/2-. Electrolyte compositions, flow rates, timing, applied current, and electrolysis time was investigated. With 60 s electrolysis time, 0.25 A applied current, Pb2+ and Cu2+ levels up to 50 and 250 mg 1-1, respectively, can be tolerated without interference. For 90 s resin loading time, a linear relationship between absorbance and analyte concentration in the 5.00-50.0 μg Cd 1-1 range (r2 = 0.9996) is obtained. A throughput of 20 samples per h is achieved, corresponding to about 0.7 mg MG and 500 mg KI and 5 ml sample consumed per determination. The detection limit is 0.23 μg Cd 1-1. The accuracy was checked for cadmium determination in standard reference materials, vegetables and tap water. Results were in agreement with certified values of standard reference materials and with those obtained by graphite furnace atomic absorption spectrometry at 95% confidence level. The R.S.D. for plant digests and water containing 13.0 μg Cd 1-1 was 3.85% (n = 12). The recoveries of analyte spikes added to the water and vegetable samples ranged from 94 to 104%. (C) 2000 Elsevier Science B.V.

Integrability and conformal symmetry in higher dimensions: A model with exact hopfion solutions

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two-dimensional target space. Requiring the existence of lagrangean and the stability of static solutions singles out a class of models which have an additional conformal symmetry. That is used to explain the existence of an ansatz leading to solutions with non-trivial Hopf charges. © SISSA/ISAS 2002.

Interfacial concentrations of chloride and bromide and selectivity for ion exchange in vesicles prepared with dioctadecyldimethylammonium halides, lipids, and their mixtures

The local concentrations of chloride, Cl b, and bromide, Br b, in the interface of vesicles prepared with dioctadecyldimethylammonium chloride, DODAC, or bromide, DODAB, dipalmitoylphosphatidylcholine, DPPC, dimyristoylphosphatidylcholine, DMPC, and mixtures of DMPC, DPPC, and DODAC were determined by chemical trapping by analyzing product yields from spontaneous dediazoniation of vesicle-bound 2,6-dimethyl-4-hexadecylbenzenediazonium ion. The values of Cl b and Br b in DODAC and DODAB vesicles increase with vesicle size, in agreement with previous data showing that counterion dissociation decreases with vesicle size. Addition of tetramethylammonium chloride displaces bromide from the DODAB vesicular interface. The value for the selectivity constant for Br/Cl exchange at the DODAB vesicular interface obtained by chemical trapping was ∼2.0, well within values obtained for comparable amphiphiles. In vesicles of DPPC the values of Cl b were very sensitive to the nature of the cation and decreased in the order Ca 2+ > Mg 2+ > Li + > Na + > K + = Cs + = Rb + ≥ +. The effect of the cation becomes more important as temperature increases above the phase transition temperature, T m, of the lipid. The values of Cl b increased sigmoidally with the mol % of DODAC in vesicles prepared with DODAC/lipid mixtures. In sonicated vesicles prepared with DODAC and DMPC (or DPPC), the values of Cl b reach local concentrations measured for the pure amphiphile at 80 mol % DODAC. These results represent the first extensive study of local concentration of ions determined directly by chemical trapping in vesicles prepared with lipids, synthetic ampliiphiles, and their mixtures.

Classes of exact wave functions for general time-dependent Dirac Hamiltonians in 1+1 dimensions

The construction of two classes of exact solutions for the most general time-dependent Dirac Hamiltonian in 1+1 dimensions was discussed. The extension of solutions by introduction of a time-dependent mass was elaborated. The possibility of existence of a generalized Lewis-Riesenfeld invariant connected with such solutions was also analyzed.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

Euclidean 4d exact solitons in a Skyrme type model

We introduce a Skyrme type, four-dimensional Euclidean field theory made of a triplet of scalar fields n→, taking values on the sphere S2, and an additional real scalar field φ, which is dynamical only on a three-dimensional surface embedded in R4. Using a special ansatz we reduce the 4d non-linear equations of motion into linear ordinary differential equations, which lead to the construction of an infinite number of exact soliton solutions with vanishing Euclidean action. The theory possesses a mass scale which fixes the size of the solitons in way which differs from Derrick's scaling arguments. The model may be relevant to the study of the low energy limit of pure SU(2) Yang-Mills theory. © 2004 Elsevier B.V. All rights reserved.