N. Limić

Theory of scattering on highly singular potentials

SummaryIt has been shown that potentials repulsive at the origin with a singularity higher than I/x2 lead to the same analytic properties of theS matrix in the variablek as the potential with the finite first absolute momentum. There is a difference in the behaviour of theS matrix fork → ∞ in thek-plane and in the analyticity properties in thel-plane. In general theS matrix will have an essential singularity at the infinitely distant point of thek-plane and it is a meromorphic function ofl.RiassuntoSi è dimostrato che i potenziali ripulsivi ail’origine con una singolarità di ordine più elevato di 1/x2 portano alle stesse proprietà analitiche della matriceS nella variabilek che ha il potenziale cou il primo momento assoluto finito. C’è una differenza nel comportamento della matriceS perk → ∞ nel pianok e nelle proprietà di analiticità nel pianol. In generale la matriceS dirà una singolarità essenziale in un punto infinitamente distante nel pianok ed è una funzione meromorfica dil.

Environmental influence on trace element levels in human hair

Trace element content of human hair depends on many factors. It has been shown by a large number of investigators that environmental factors play an important role. Elements from air particulates, water, shampoo or other media get incorporated into the hair structure. Here a model is proposed in which different contributions to trace element levels in human hair are factorized and the environmental contribution to the radial and longitudinal concentration profiles can be calculated. With the proper understanding of environmental contamination, hair analysis has better chances of being used as a diagnostic tool.

Estimation of diffuse inputs to a coastal sea: Solution to an inverse modelling problem

Abstract An important contribution to the input of substances in coastal waters is made by diffuse sources. A method is presented that allows estimation of the total input rate and contribution of each of several diffuse inflows. As an example, measurements of currents and salinity in the Punat Bay (the Adriatic Sea) are used to reconstruct the total current field and to estimate the wash-out rate of water. By using a two-dimensional transport model and measurements of total concentrations of lead in both water and sediment, sedimentation rate and input are estimated. Finally, the reliability of the results is discussed.

Reconstruction of a concentration field in a coastal sea

Abstract Based on measurements of currents and concentrations of a chemical species (nutrient, pollutant), two control problems are solved in order to estimate turbulent dispersion coefficient, extinction coefficient and background concentration. Furthermore, a concentration field is reconstructed in a coastal sea. The two problems are analysed for the Rijeka Bay on the northeastern coast of the Adriatic Sea. The parameters are estimated for summer and winter seasons. During summer, the mean horizontal turbulent dispersion coefficient is 1·45 10 4 cm 2 s −1 and the background concentration of total phosphorus is 0·11 μg—at P l −1 . For winter period the estimation gave 1·1 10 4 cm 2 s −1 and 0·2 μg—at P l −1 respectively. The reliability of the estimation procedures and of estimated values are also discussed.

The occurrence of trace elements in coal

Abstract The standard comparison of relationships of trace element concentrations in coal is based on a comparison of mean values of elemental concentrations. This method is extended by including some functions of covariances among trace element concentrations. In the proposed method, the comparison is based on: the pattern of the mass spectrum of mean values of concentrations; the spectrum of the covariance matrix; the eigenvectors of the covariance matrix; and the order of eigenvectors. The method has been applied to the coal of the Istrian coal basin and the same genesis of the elements calcium, sulphur, iron, titanium and vanadium throughout the considered coal seam has been established.

A method to estimate diffuse inflow of fresh water into a coastal sea

A method is presented to estimate the total inflow rate of a diffuse source of fresh water into a small bay. The method relies on an estimation of the residual current field and on measurements of salinity in the coastal sea. The method is applied to the estimation of freshwater inflow rate during summer into a small bay in the Adriatic Sea.

Incorporation of trace elements from environment into the hair structure

A model describing the incorporation of trace elements from environment into the hair structure is presented. Model predictions for radial and longitudinal concentration profiles are given. Comparison with elemental data is satisfactory.

A minimization problem in residual current modelling

Abstract An interpolation of residual currents is modelled by a variational principle, fitting the data measured at several points in a region and at all points of the boundary. The model can be interpreted by means of the least-squares estimation with a given covariance function for vorticities.

Analytic structure in

The asymptotic behaviour in the λ-plane of solutions of the Schrödinger equation for scattering on singular potentials is investigated. The asymptotic behaviour of the Jost functions and theS-matrix is obtained. Furthermore, the general analytic form in the λ-plane of the Jost functions and theS-matrix is established. Some properties of the distribution of poles of theS-matrix are proved.

\lambda

SummaryThe existence of the wave operators and the scattering operator for the scattering on highly singular spherically symmetric potentials that are repulsive at the origin is shown. The eigenfunction expansion in terms of the eigenfunctions of the Hamiltonian is derived using the analytic properties of the solution of the Schrödinger equation.RiassuntoSi mostra l’esistenza degli operatori d’onda e degli operatori di scattering per lo scattering di potenziali molto singolari a simmetria sferica che sono repulsivi all’origine-Si deduce lo sviluppo dell’autofunzione in funzione delle autofunzioni dell’hamiltoniano, facendo uso delle proprietà analitiche della soluzione dell’equazione di Schrödinger.