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Math Everywhere Deterministic and Stochastic Modelling in Biomedecine, Economics and Industry Contents List of Contributors ......................................................................................... XV Introduction Willi Jäger............................................................................................................ 1 Part I Deterministic and Stochastic Systems Coupled Dynamics and Quiescent Phases Karl P. Hadeler, Thomas Hillen ........................................................................ 7 Long Time Behavior of a System of Stochastic Differential Equations Modelling Aggregation Vincenzo Capasso, Daniela Morale, Matteo Ortisi ........................................ 25 Invariant Density Estimation for Multidimensional Diffusions Annamaria Bianchi ...................................................................................... 39 First Contact Distribution Function Estimation for a Partially Observed Dynamic Germ-Grain Model with Renewal Dropping Process Marcello De Giosa ............................................................................................. 51 An Extension of the Kolmogorov-Avrami Formula to Inhomogeneous Birth-and-Growth Processes Martin Burger, Vincenzo Capasso, Alessandra Micheletti............................ 63 On the Generalized Geometric Densities of Random Closed Sets. An Application to Growth Processes Vincenzo Capasso, Elena Villa ...................................................................... 77 The Multiparameter Fractional Brownian Motion Erick Herbin, Ely Merzbach ............................................................................ 93 Filtering of Multiparameter Processes: Theory and Applications Alberto Carabarin-Aguirre, B. Gail Ivanoff, Adriana Jordan ....................... 103 IFSM Representation of Brownian Motion with Applications to Simulation Stefano Maria Iacus, Davide La Torre .......................................................... 115 Iterated Function Systems on Multifunctions Davide La Torre, Franklin Mendivil, Edward R. Vrscay ............................... 125 Part II Mathematical Problems in Biology, Medicine and Ecology Stochastic Modeling and Estimation in a Neutron Lifetime Experiment Grace L. Yang, Kevin J. Coakley..................................................................... 141 The Transport of Specific Monoclonal Antibodies in Tumour Cords Alessandro Bertuzzi, Antonio Fasano, Alberto Gandolfi, Carmela Sinisgalli.......................................................................................................... 151 Structural Adaptation in Normal and Cancerous Vasculature Philip K. Maini, Tomas Alarcón, Helen M. Byrne, Markus R. Owen, James Murphy.............................................................................................165 Approximation of 2D and 3D Models of Chemotactic Cell Movement in Vasculogenesis Fausto Cavalli, Andrea Gamba, Giovanni Naldi, Matteo Semplice ............. 179 Homogenization Closure For A Two-Dimensional Effective Model Describing Fluid-Structure Interaction in Blood Flow Andro Mikelie, Suncica Canic ........................................................................... 193 Pattern Formation in Butterfly Wings: Experiments and Models Toshio Sekimura............................................................................................. 207 Stabilization for a Reaction-Diffusion System in Epidemiology Sebastian Anita........................................................................................... 219 Global Stability of Equilibria for a Metapopulation S­I­S Model Francesca Arrigoni, Andrea Pugliese ............................................................ 229 State Feedback Control of the Glucose-Insulin System Pasquale Palumbo, Andrea De Gaetano ...................................................... 241 An Algal Allelopathic Competition with Internal and External Toxic Compounds Paolo Fergola, Marianna Cerasuolo ............................................................ 253 Subsoil Decontamination with Biological Techniques: a Bio-Fluid Dynamics Problem Filippo Notarnicola........................................................................................... 265 Part III Mathematical Problems in Industry and Economics Modelling and Optimizing Batch Processes in the Chemical Industry Rainer E. Burkard, Johannes Hatzl............................................................279 Kinetics of Nucleation and Growth: Classical Nucleation and Helium Bubbles in Nuclear Materials Luis Bonilla, Ana Carpio, John C. Neu ......................................................... 291 Polymer Crystallization Processes Giacomo Aletti, Diane Saada........................................................................ 309 Optimal Marketing Decision in a Duopoly: A Stochastic Approach Luigi De Cesare, Andrea Di Liddo ................................................................ 325 Appendix. Color Plates.................................................................................. 335