Cel The aim of this project is the development of methods, based on potential theory, analysis on Riemann surfaces and constructive approximation, to attack long-standing quantum-mechanical problems such as those posed by the use of the density-functional theory in physical systems. New statements of problems will be studied to develop the mathematical theory and to design new strategies for the exact solution of some specific physical problems. In particular, the determination of fundamental and/or experimentally measurable quantities (information entropies, kinetic and exchange energies, etc.) of fermionic systems (atoms, nuclei, neutron stars) can be attacked by modern methods of potential theory with external fields of harmonic functions together with the recently discovered techniques of special functions (e.g. orthogonal polynomials with varying measures and hyperelliptic functions). At the end of the project an accurate determination of the information entropy of the two simplest physical systems will have been obtained (harmonic oscillator and hydrogen atom), at least for moderate n but also for n tending to infinity (which corresponds to the Rydberg states). From these results a conjecture improving the Bialynick-Birula Mycielski inequality will be formulated. The meaning of entropy for orthogonal polynomials will be understood and, in particular, the ability to formulate and prove the asymptotic results for orthogonal polynomials on the interval [-1,1] only in terms of the behaviour of the norm of the monic orthogonal polynomials and the mutual energy of the zero distribution measure and the measure p2 (X) dp(x) describing the size of the polynomials. Regarding rational approximation, the most relevant results for Pade approximation to Hermite-Pade approximation for vector functions and also for matrix functions will be extended. In particular, for the approximation of Markov functions (the general Markov system) the relevant convergence results for at least some important Markov systems will be obtained. Finally, for Sobolev orthogonal polynomials the proper method of treating continuous Sobolev orthogonality will be found. For discrete Sobolev orthogonality one can still work with operator theory involving band matrices, but a new technique is needed for continuous Sobolev orthogonality. Presumably a differential-difference operator is needed, and it is expected that such an operator can be identified. Program(-y) IC-INTAS - International Association for the promotion of cooperation with scientists from the independent states of the former Soviet Union (INTAS), 1993- Temat(-y) 21 - Mathematics Zaproszenie do składania wniosków Data not available System finansowania Data not available Koordynator Universidad de Granada Wkład UE Brak danych Adres Avenida Fuentenueva 18071 Granada Hiszpania Zobacz na mapie Koszt całkowity Brak danych Uczestnicy (5) Sortuj alfabetycznie Sortuj według wkładu UE Rozwiń wszystko Zwiń wszystko Katholieke Universiteit Leuven Belgia Wkład UE Brak danych Adres 3001 Heverlee - Leuven Zobacz na mapie Koszt całkowity Brak danych Moscow State University M.V. Lomonosov Rosja Wkład UE Brak danych Adres 119899 Moscow Zobacz na mapie Koszt całkowity Brak danych Russian Academy of Sciences Rosja Wkład UE Brak danych Adres 117966 Moscow Zobacz na mapie Koszt całkowity Brak danych Russian Academy of Sciences Rosja Wkład UE Brak danych Adres 125047 Moscow Zobacz na mapie Koszt całkowity Brak danych Universidad Carlos III de Madrid Hiszpania Wkład UE Brak danych Adres 28911 Leganés Zobacz na mapie Koszt całkowity Brak danych