Abstract: Gielis transformations, with their origin in botany, are used to define square waves and trigonometric functions of higher order. They are rewritten in terms of Chebyshev polynomials. The origin of both, a uniform descriptor and the origin of orthogonal polynomials, can be traced back to a letter of Guido Grandi to Leibniz in 1713 on the mathematical description of the shape of flowers. In this way geometrical description and analytical tools are seamlessly combined.

Abstract: The discovery of antibiotics represented one of the greatest breakthroughs in medicine. Their success combined with an increasing intensive use is apparently bound to be also their undoing. This is due to the development of acquired antibiotic resistance, leading to inefficient antibiotherapy and even to the impossibility of treatment and death. The development and spread of antibiotic resistance are fueled by the widespread presence of trace levels of antibiotics residue, in various media, from environment to aliments. One of the solutions is the rigorous monitoring of the levels of antibiotics, which in term requires an almost constant development of new, more accessible analytical methods, especially screening methods, capable of decentralized analysis. In this direction, the electrochemical detection of antibiotics represents a very viable alternative. In this context, the aim of this thesis was to develop new electrochemical methods for the detection of antibiotics by employing and expanding on several strategies, like biomimetic sensors and electrochemical fingerprinting. Five studies were described in this thesis, that can be roughly divided in three categories, based on the analytical strategy employed. The first group is represented by direct electrochemical methods. The second group focuses on the use of biomimetic elements, molecularly imprinted polymers and aptamers. The hyphenation of electrochemical methods with other analytical methods was explored in the last group. In the last study, included in this group, the singlet oxygen-based photoelectrochemical approach was used for the detection of a phenolic antibiotic, rifampicin. The originality of the thesis consists in the testing and development of new approaches to various strategies used in electrochemical detection, revealing new insights in the field of electrochemical detection of antibiotics. The complex electrochemical fingerprint and the mechanism of the electrochemical oxidation were created and investigated, respectively, for the antibiotic vancomycin. New sensitive nanoplatforms were prepared by employing and combining new protocols. Additionally, important contributions were brought through the study involving the singlet oxygen-based detection of rifampicin. We demonstrated how a photocatalyst can exhibit analyte selectivity by strongly interacting with a complex phenolic compound, rifampicin. Summing up, the studies presented in this thesis will have an important impact in the field of electrochemical detection of antibiotics.

Abstract: The Dirichlet problem for the Laplace equation in normal-polar annuli is addressed by using a suitable Fourier-like technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.

Abstract: Composition of bed, core and suspended sediments collected from Krishna River sediments were studied and the observations are discussed in the light of other Indian rivers, world's average river suspended particles, surficial rock and soils. The contents of V, Cr, Co, Ni, Cu and Zn in the suspended particles are higher in the Krishna River than in the world's average, indicating pollution inputs. Suspended sediments are enriched (5 to 10 times) in all the elements considered relative to bed sediments. Downstream profile and metal/Al ratios of the elements indicate that the mobility of elements within the basin is controlled by basin geology, size and mineralogical characteristics. Good correlations observed for a number of elements point out to their common sink in the clay fraction of the sediments. There is no systematic variation with depth for the major elements and most of the elements are considerably higher compared to estuarine or Bay of Bengal sediments.

Abstract: Since the introduction of the sustainability challenge, scientists disagree over the interpretation of the term sustainability. Weak and strong sustainability are the two main interpretations of sustainability, which are opposing each other. Some researchers stated that the interpretation of the term depends on the context; others disagree pointing out that it always implies the meaning of continuation. The term sustainability can be used as attribute, which adds a certain characteristic to the noun. If something can be attributed as being sustainable, it can also be unsustainable. The sustainability challenge consists of shifting from the current unsustainable towards a sustainable system. This paper outlines that the weak sustainability term is illegitimate, as it leads to a contradiction with the acknowledged assumption that the current state is unsustainable. This contradiction is revealed through an analysis of the occurrence of decoupling in agriculture: Agricultural land use could be decoupled from agricultural production, but only with the trade-off of massive increases in fertilizer, pesticide, energy and water usage. This paper outlines an inherent inconsistency within the ongoing discussion about the interpretation of sustainability. Through identifying the invalidity of the weak sustainability interpretation the focus can be shifted form the discourse to the sustainability challenge itself.