Mathematics in Industrial Problems - Avner Friedman

. .

Biographie:
Anver Friedman is a Distinguished University Professor. He received his PH.D. degree in 1956 from the Hebrew University. His research interests include partial differential equations, both general mathematical theory as well as applications to models that arise in the physical and life sciences, in engineering, and in industry. Chiu-Yen Kao is an Associate Professor at Claremont McKenna College. Her area of expertise is in applied mathematics....

Sommaire:
1 Signal design problems in multi-channel data communication.- 1.1 General problems.- 1.2 A lower bound on MCT(d).- 1.3 Pulse amplitude modulation (PAM).- 1.4 References.- 2 Solitons in non-homogeneous medium.- 2.1 Optical fiber sensor; linear theory.- 2.2 Fiber optic sensor; nonlinear theory.- 2.3 Known recent results.- 2.4 Back to the open questions.- 2.5 References.- 3 Foam rheology.- 3.1 Equilibrium Structure.- 3.2 Future directions.- 3.3 References.- 4 Applications of large deviations to communications.- 4.1 Examples.- 4.2 Theory of large deviations.- 4.3 Applications.- 4.4 Open problems.- 4.5 References.- 5 Phase modulation in nonlinear optical medium.- 5.1 The model and the problem.- 5.2 Two numerical approaches.- 5.3 The full problem.- 5.4 References.- 6 Multiple solutions in semiconductor device modeling.- 6.1 The basic equations.- 6.2 Ohm's law.- 6.3 A p - n diode.- 6.4 The p - n - p and n - p - n transistors.- 6.5 Flip-flop and p - n - p - n junction.- 6.6 Open problems.- 6.7 References.- 7 Mathematical models for thermal imaging-an heuristic approach.- 7.1 The problem.- 7.2 Linear diffusion approach.- 7.3 An alternative approach.- 7.4 References.- 8 Graph spectra, connectivity, and spin glass models of associative memory.- 8.1 Evolution of neural network.- 8.2 Spin glasses.- 8.3 Results for neural networks.- 8.4 Open problems.- 8.5 References.- 9 Mathematical problems in electron beam lithography.- 9.1 The lithography steps.- 9.2 Mathematical issues.- 9.3 The proximity equation.- 9.4 Suggestions.- 9.5 References.- 10 A reaction-diffusion model of color negative film development.- 10.1 The development process.- 10.2 Homogenization problems.- 10.3 Edge enhancement.- 10.4 Solution of Problem (1).- 10.5 Solution of Problem (2).- 10.6 Partialsolution to problem (3).- 10.7 References.- 11 An inverse problem arising in the evolution of combustion aerosols.- 11.1 The model.- 11.2 Small coagulation.- 11.3 Partial solutions.- 11.4 References.- 12 Adaptive focused beamforming.- 12.1 The basic equations.- 12.2 The methods of AFB.- 12.3 Future directions.- 12.4 References.- 13 Optimal switching between a pair of Brownian motions.- 13.1 Optimal switching within a class of diffusion processes.- 13.2 Switching a pair of Brownian motions.- 13.3 Open problems.- 13.4 Solution of some of the problems.- 13.5 References.- 14 Mathematical models of latent image formation.- 14.1 The Hamilton-Bayer theory [1].- 14.2 The Monte Carlo Method.- 14.3 An alternate approach.- 14.4 References.- 15 Modeling problems in magneto-optic recording.- 15.1 An outline.- 15.2 Absorption of laser radiation.- 15.3 The heat generation.- 15.4 The magnetic energy effect.- 15.5 References.- 16 Shaped charge jets and subsonic free-surface flow theory.- 16.1 The model.- 16.2 The Chaplygin method.- 16.3 A variational approach.- 16.4 References.- 17 Electrophotographic system models.- 17.1 General description.- 17.2 Mathematical issues.- 17.3 References.- 18 Fluid models and other asymptotic limits with data and teletraffic applications.- 18.1 Asymptotics of closed product-form queueing networks.- 18.2 A fluid approximation.- 18.3 Stochastic fluid models.- 18.4 References.- 19 Solutions to problems from volume 1.- 19.1 References.