Derivation of soil screening values for metals in Portuguese natural soil

The increasing human activity has been responsible by profound changes and a constinuos degradation of the soil compartment in all the European territory. Some European policies are appearing focusing soil’s protection and the management of contaminated sites, in order to recover land for other uses. To regulate the risk assessment and the management of contaminated soils, many European member states adopted soil guideline values, as for example soil screnning values (SSV).These values are particularly useful for the the first tier of the Ecological Risk Assessment (ERA) processes of contaminated sites,especially for a first screening of sites requiring a more site-specific evaluation. Hence, the approriate definition of regional SSVs will have relevant economic impacts in the management of contaminated sites. Portugal is one of European Member States that still lack these soil guideline values. In this context, this study gaves a remarkable contribution in the generation of ecotoxicological data for soil microbiological parameters, terrestrial plants and invertebrates for the derivation of SSVs for uranium (U), cadmium (Cd) and copper (Cu), using a Portuguese natural soil, representative of a dominant type of soil in the Portuguese territory. SSVs were derived based on two methods proposed by the the Technical Guidance Document for Risk Assessment of the European Commission; namely the assessment factor method (AF) and the species sensitivity distribution (SSD) method (with some adaptations). The outputs of both methods were compared and discussed. Further, this study laid the foundation for a deeper reflection about the cut-off (hazard concentration for a given percentage of species - HCps) to be estimated from the SSDs, and to be selected for the derivation of SSVs, with the adequate level of protection. It was proven that this selection may vary for different contaminants, however a clear justification should be given, in each case. The SSvs proposed in this study were for: U (151.4 mg U kg-1dw), Cd (5.6 mg Cd kg-1dw), and Cu (58.5 mg Cu kg-1dw) These values should now be tested for their descriminating power of soils with different levels of contamination. However, this studies clarifies the approach that should be followed for the derivation of SSVs for other metals and organic contaminants, and for other dominant types of Portuguese natural soils.

Numerical and combinatorial applications of generalized Appell polynomials

This thesis studies properties and applications of different generalized Appell polynomials in the framework of Clifford analysis. As an example of 3D-quasi-conformal mappings realized by generalized Appell polynomials, an analogue of the complex Joukowski transformation of order two is introduced. The consideration of a Pascal n-simplex with hypercomplex entries allows stressing the combinatorial relevance of hypercomplex Appell polynomials. The concept of totally regular variables and its relation to generalized Appell polynomials leads to the construction of new bases for the space of homogeneous holomorphic polynomials whose elements are all isomorphic to the integer powers of the complex variable. For this reason, such polynomials are called pseudo-complex powers (PCP). Different variants of them are subject of a detailed investigation. Special attention is paid to the numerical aspects of PCP. An efficient algorithm based on complex arithmetic is proposed for their implementation. In this context a brief survey on numerical methods for inverting Vandermonde matrices is presented and a modified algorithm is proposed which illustrates advantages of a special type of PCP. Finally, combinatorial applications of generalized Appell polynomials are emphasized. The explicit expression of the coefficients of a particular type of Appell polynomials and their relation to a Pascal simplex with hypercomplex entries are derived. The comparison of two types of 3D Appell polynomials leads to the detection of new trigonometric summation formulas and combinatorial identities of Riordan-Sofo type characterized by their expression in terms of central binomial coefficients.