CONTENTS -- Preface -- Conference Committee -- A Time Dependent Inverse Problem in Photon Transport A. Belleni-Morante -- 1 Introduction -- 2 The mathematical model -- 3 Time-discretization procedures -- 4 Identification of the source -- 5 Concluding remarks -- References -- Torsionless Conformal Killing Tensors and Cofactor Pair Systems S. Benenti -- 1 Introduction -- 2 Notation and basic definitions -- 3 Elliptic-parabolic tensors on Rn -- 4 Commutation relations -- 5 Elliptic metric tensors -- 6 The torsion of E w.r. to E -- 7 Elliptic-parabolic tensors as conformal Killing tensors -- Acknowledgments -- References -- Sulle Distorsioni del Tipo Volterra Applicate a un Cilindro Iperelastico Cavo Omogeneo Trasversalmente Isotropo G. Caricato -- 1 Considerazioni preliminari -- 2 Le leggi costitutive. Le equazioni indefinite di equilibrio. -- 3 Determinazione di un insieme di soluzioni delle equazioni di equilibrio e delle relative condizioni al contorno -- 4 Genesi di una distorsione -- References -- Heat and Mass Transport in Non-Isothermal Partially Saturated Oil-Wax Solutions A . Fasano and M. Primicerio -- 1 Introduction -- 2 The basic model -- 3 Weak formulation -- 4 An alternative model -- 5 Analogy with fast chemical reaction problems -- 6 Conclusions -- References -- New Applications of a Versatile Liapunov Functional J. N. Flavin -- 1 Introduction -- 2 Steady, Unsteady, and Perturbation Problems. -- 3 Analogous Estimate for a Steady Diffusion Problem in a Right Cylinder -- 4 Closing remarks -- 5 Appendix -- References -- Remarks on the Propagation of Light in the Universe D. Galletto and B. Barberis -- 1 The Cosmological Principle -- 2 The Intrinsic Geometry of the Fluid u -- 3 The Metrics for u in polar coordinates in Cases S3 and PS3 -- 4 Case E3 and Hubble's Law -- 5 On the Metrics of u in Cases E3, S3 and PS3.

6 The Intervention of the Velocity of Light -- 7 The Velocity c and the Law of Composition for Velocities -- 8 The Law of Composition for Velocities and the Hubble Sphere -- 9 About Cosmography and the Deduction of the Function R(t) -- 10 The Local Character of Special Relativity in Cosmology -- 11 The Deduction of the Friedmann-Robertson-Walker Metric -- 12 The Deduction of (7.1) in the Relativistic Context. The Minkowski Metric -- References -- Thermodynamic Limit for Spin Glasses S. Graffi -- 1 Basic lexicon of classical statistical mechanics for spin systems -- 2 Phase transitions -- 3 Amorphous magnetic materials (spin glasses) -- 4 Thermodynamic limit -- References -- Rigid Motions in Celestial Mechanics. Keplerian Motions G. Grioli -- 1 Introduction -- 2 Kinematical Premises -- 3 Dynamics -- 4 Gyroscopic Case -- References -- Stability Switches on Four Types of Charateristic Equation with Discrete Delay Z. Ma and J. Li -- 1 Introduction -- 2 Equation P( ) + Q( )e- T = 0 -- 3 Equation P( ) + Q( )e -r + R( )e-2 r = 0 -- 4 Equation P(, r) + Q(, r)e-r = 0 -- 5 Equation P(, r ) + Q(, r)e-r + R(, r)e-2r = 0 -- References -- On the Best Value of the Critical Stability Number in the Anisotropic Magnetohydrodynamic Benard Problem M. Maiellaro -- 1 Introduction -- 2 Basic equations and linear Benard problem -- 3 Critical Rayleigh curves -- 4 Linear energy stability -- References -- A BGK-Type Model for a Gas Mixture with Reversible Reactions R. Monaco and M. Pandolfi Bianchi -- 1 Introduction -- 2 Kinetic equations and their properties -- 3 A BGK-type approach -- 3.1 Approximation of the elastic terms -- 3.2 Approximation of the inelastic terms -- 4 The BGK-type model -- 5 A numerical test -- Acknowledgments -- References -- Stabilizing Effects in Fluid Dynamics Problems G. Mulone -- 1 Introduction -- 2 The stability problem.

3 Nonlinear stability results in the BQnard problems: Rionero's contributions and some new results -- Acknowledgments -- References -- An Alternative Kinematics for Multilattices M. Pitteri -- 1 Introduction -- 2 Preliminaries -- 3 Multilattice kinematics -- 4 Phase changes in a wt-nbhd -- 5 The case of -quartz -- Acknowledgments -- References -- On Contact Powers and Null Lagrangian Fluxes P. Podio Guidugli and G. Vergara Caffarelli -- 1 Introduction -- 2 Contact Interactions and Stress in Simple Cauchy Bodies -- 2.1 Standard Doctrine -- 2.2 Contact Power, Distance Power, and Contact Flux -- 2.3 Weak Notions of Contact Force and Stress -- 3 Contact Flux and Stress(es) Associated with an Energy -- 3.1 Grade-I Elasticity -- 3.2 Grade-2 Elasticity -- 3.3 Gradient Theories in General -- 4 Contact Flux and Stress(es) Associated with Null Lagrangians -- 4.1 Grade-1 Null Lagrangaans -- 4.2 Grade-2 Null Lagrangians -- Acknowledgments -- References -- Models of Cellular Populations with Different States of Activity M. Primicerio and F. Talamucci -- 1 Introduction -- 2 Mass conservation -- 3 Modelling the problem -- 3.1 Production and destruction -- 3.2 Mass fluxes -- 4 Closing the problem -- 4.1 Momentum balance -- 4.2 Specific assumptions -- 5 A different approach -- 5.1 Nonlocal interactions -- 5.2 Chemical potential -- 5.3 A numerical simulation -- References -- Flows of a Fluid with Pressure Dependant Viscosities Between Rotating Parrallel Plates K. R. Rajagopal and K. Kannan -- 1 Introduction -- 2 Equations of Motion -- 2.1 Flow between two plates rotating about non-coincident axes. -- 2.2 Torsional Flow -- References -- Control Aspects in Gas Dynamics P. Renno -- 1 Introduction -- 2 Basic properties of the fundamental solution -- 3 Linear evolution and explicit behavior -- 4 Estimates for non linear problems -- References.

A Functional Framework for Applied Continuum Mechanics G. Romano and M. Diaco -- 1 Structural model -- 2 Green's formula -- 3 Bilateral constraints -- 4 Korn's inequality -- 5 Basic theorems -- 6 Boundary value problems -- References -- Global Existence, Stability and Nonlinear Wave Propagation in Binary Mixtures of Euler Fluids T. Ruggeri -- 1 Introduction -- 2 Qualitative Analysis -- 2.1 Local well posedness -- 2.2 The Kawashima condition -- 2.3 Global Existence and stability of constant state -- 2.4 Kawashima Condition for the mixture -- 3 Acceleration Waves -- 4 Shock Waves -- 4.1 Sonic Shock -- 4.2 Diffusive Shock -- 4.3 Characteristic Shock -- Acknowledgments -- References -- Exchange of Stabilities in Porous Media and Penetrative Convection Effects B. Straughan -- 1 Introduction -- 2 Energy stability: theory and development -- 3 Energy stability and porous convection -- Acknowledgments -- References -- Effects of Adaptation on Competition among Species D. Lacitignola and C. Tebaldi -- 1 Introduction and the Model -- 2 Differentiation among species by carrying capacity -- 3 Differentiation among species by carrying capacity and intrinsic growth rate -- 4 Conclusions -- References -- Wasserstein Metric and Large-Time Asymptotics of Nonlinear Diffusion Equations J. A . Carrillo and G. Toscani -- 1 Introduction -- 2 Extremal distributions and Wasserstein-type metrics -- 3 Porous medium equations -- 4 Nonlinear friction equations -- 5 Nonlinear friction equations with viscosity -- 6 Degenerate convection-diffusion equations -- 7 Conclusions -- Acknowledgments -- References -- Opening Talks -- Acknowledgements.