THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

https://www.chester.ac.uk/sites/files/chester/rep377.pdf

Analysis of Fractional Differential Equations

to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

Signal sequences: The limits of variation

New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations

Mathematical Problems in Semiconductor Physics

An exact closure is obtained of the 8-moment model for semiconductors based on the maximum entropy principle in the case of silicon semiconductors. The validity of the model is assessed, and comparisons with an approximate closure are presented and discussed.

Exact Maximum Entropy Closure of the Hydrodynamical Model for Si Semiconductors: The 8-Moment Case

In this paper we highlight the fact that the physical content of hyperbolic theories of relativistic dissipative fluids is, in general, much broader than that of the parabolic ones. This is substantiated by presenting an ample range of dissipative fluids whose behavior noticeably departs from Navier-Stokes'.

The Case for Hyperbolic Theories of Dissipation in Relativistic Fluids

A nanoscale double-gate MOSFET is simulated with an energy-transport subband model for semiconductors formulated starting from the moment system derived from the Schrodinger–Poisson–Boltzmann equations. The system is closed on the basis of the maximum entropy principle and includes scattering of electrons with acoustic and non-polar optical phonons. The proposed expression of the entropy combines quantum effects and semiclassical transport by weighting the contribution of each subband with the square modulus of the envelope functions arising from the Schrodinger–Poisson subsystem. The simulations show that the model is able to capture the relevant confining and transport features and assess the robustness of the numerical scheme.

Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle

A hydrodynamical model for electron transport in silicon semiconductors, free of any fitting parameters, has been formulated in [1,2] on the basis of the maximum entropy principle, by considering the energy band described by the Kane dispersion relation and by including electron-non polar optical phonon and electron-acoustic phonon scattering.

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Vittorio Romano

Papers

Mathematical Problems in Semiconductor Physics

Exact Maximum Entropy Closure of the Hydrodynamical Model for Si Semiconductors: The 8-Moment Case

The Case for Hyperbolic Theories of Dissipation in Relativistic Fluids

Numerical simulation of a double-gate MOSFET with a subband model for semiconductors based on the maximum entropy principle

Simulation of Submicron Silicon Diodes with a Non-Parabolic Hydrodynamical Model Based on the Maximum Entropy Principle