Mathematics in Industrial Problems

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 Partial solution 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.