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

In this chapter a short overview will be given regarding the physics of semiconductors and some properties of the Boltzmann equation that is the starting point for describing the semiclassical transport of charge carriers.

Band Structure and Boltzmann Equation

Optimization of homogeneous emitter and thin-film solar cells

High-field phenomena in submicron electron devices cannot be described satisfactorily within the framework of the drift-diffusion models that do not include energy as a dynamical variable and are valid only in the quasi-stationary limit, while most hydrodynamical models suffer from serious theoretical drawbacks due to the ad hoc treatment of the closure problem [1]. Here we employ a moment approach, previously introduced in [2, 3] (see also [4] for a complete review) in which the closure procedure is based on the maximum entropy principle while the conduction bands are described by the Kane dispersion relation. The electrons in GaAs are considered as a mixture of two fluids, one representing the electrons in the Γ -valley and the other the electrons in the four equivalent L-valleys. The model comprises the balance equations of electron density, energy density, velocity and energy flux for both populations, coupled to the Poisson equation for the electric potential. We will give only a brief sketch of the model. For more details the interested reader is referred to [5]. One assumes that the conduction band is described in the neighborhood of each minimum (valley) by the Kane dispersion relation approximation

Gunn Oscillations Described by the MEP Hydrodynamical Model of Semiconductors

Heat Generation and Dissipation

Starting from the quantum Liouville equation for the density operator and applying the Weyl quantization, Wigner equations for the longitudinal and transversal optical and acoustic phonons are deduced. The equations are valid for any solid, including 2D crystals like graphene. With the use of Moyal’s calculus and its properties the pseudo-diﬀerential operators are expanded up to the second order in ~ . The phonon-phonon collision operators are modelled in a BGK form and describe the relaxation of the Wigner functions to a local equilibrium function, depending on a local equilibrium temperature which is deﬁnite according to [1]. An energy transport model is obtained by using the moment method with closures based on a quantum version of the Maximum Entropy Principle. An explicit form of the thermal conductivity with quantum correction is obtained under a suitable scaling.

Vittorio Romano

Papers

Band Structure and Boltzmann Equation

Optimization of homogeneous emitter and thin-film solar cells

Gunn Oscillations Described by the MEP Hydrodynamical Model of Semiconductors

Heat Generation and Dissipation

Wigner equations for phonons transport and quantum heat flux