Books in the Mathematical Society Of Japan Memoirs series

Although the Monte Carlo method is used in so many fields, its mathematical foundation has been weak until now because of the fundamental problem that a computer cannot generate random numbers. This book presents a strong mathematical formulation of the Monte Carlo method which is based on the theory of random number by Kolmogorov and others and that of pseudorandom number by Blum and others. As a result, we see that the Monte Carlo method may not need random numbers and pseudorandom numbers may suffice. In particular, for the Monte Carlo integration, there exist pseudorandom numbers which serve as complete substitutes for random numbers.

With developments in semiconductor technology, several mathematical models have been established to analyze and to simulate the behavior of electron flow in semiconductor devices. This title provides a study of mathematical research on semiconductor equations.

This book is a self-contained exposition on the Bohr Jessen limit theorem. This limit theorem, which is concerned with the behavior of the Riemann zeta function (s) on the line Re s =, where 1/2