Positivity in Natural Sciences
Many problems in natural sciences require a notion of positivity: only non-negative densities, population sizes or probability make sense in real life. This imposes certain constrains in the modelling but also, coupled with metric structure of underlying
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C.I.M.E. means Centro Internazionale Matematico Estivo, that is, International Mathematical Summer Center. Conceived in the early fifties, it was born in 1954 and made welcome by the world mathematical community where it remains in good health and spirit. Many mathematicians from all over the world have been involved in a way or another in C.I.M.E.’s activities during the past years. So they already know what the C.I.M.E. is all about. For the benefit of future potential users and cooperators the main purposes and the functioning of the Centre may be summarized as follows: every year, during the summer, Sessions (three or four as a rule) on different themes from pure and applied mathematics are offered by application to mathematicians from all countries. Each session is generally based on three or four main courses (24−30 hours over a period of 6-8 working days) held from specialists of international renown, plus a certain number of seminars. A C.I.M.E. Session, therefore, is neither a Symposium, nor just a School, but maybe a blend of both. The aim is that of bringing to the attention of younger researchers the origins, later developments, and perspectives of some branch of live mathematics. The topics of the courses are generally of international resonance and the participation of the courses cover the expertise of different countries and continents. Such combination, gave an excellent opportunity to young participants to be acquainted with the most advance research in the topics of the courses and the possibility of an interchange with the world famous specialists. The full immersion atmosphere of the courses and the daily exchange among participants are a first building brick in the edifice of international collaboration in mathematical research. C.I.M.E. Director Pietro ZECCA Dipartimento di Energetica “S. Stecco” Università di Firenze Via S. Marta, 3 50139 Florence Italy e-mail: [email protected]
C.I.M.E. Secretary Elvira MASCOLO Dipartimento di Matematica Università di Firenze viale G.B. Morgagni 67/A 50134 Florence Italy e-mail: [email protected]
For more information see CIME’s homepage: http://www.cime.unifi.it CIME’s activity is supported by: – Istituto Nationale di Alta Mathematica “F. Severi” – Ministero dell’Istruzione, dell’Università e della Ricerca
Jacek Banasiak · Vincenzo Capasso Mark A.J. Chaplain · Mirosław Lachowicz Jacek Mie¸kisz
Multiscale Problems in the Life Sciences From Microscopic to Macroscopic
Lectures given at the Banach Center and C.I.M.E. Joint Summer School held in Be¸dlewo, Poland September 4–9, 2006 Editors: Vincenzo Capasso Mirosław Lachowicz
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Authors and Editors Jacek Banasiak
Mark A.J. Chaplain
School of Mathematical Sciences University of Kwa-Zulu-Natal (Westville) Private Bag X54001 Durban 4000 South Africa [email protected]
The SIMBIOS Centre Division of Mathematics University of Dundee Dundee DD1 4HN Scotland [email protected]
Vincenzo Capasso
Mirosław Lachowicz Jacek Mie¸kisz
Department of Mathematics & ADAMSS (Centre for Advanced App
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