Gilmore, R.
The Wizard of Quarks
A Fantasy of Particle Physics
2001. XIII, 202 pp. Hardcover
0-387-95071-0
Thousands of readers who were delighted by the adventures and science content of Alice in
Quantumland are in for another treat. This time physicist Robert Gilmore takes us on a journey with Dorothy, following the yellow building block road through the land of the Wizard of Quarks. Using characters and situations based on the Wizard of Oz story, we learn along the way about the
fascinating world of particle physics. Classes of particles, from quarks to leptons are shown in an
atomic garden, where atoms and molecules are produced. See how Dorothy, The Tin Geek, and
the Cowardly Lion experience the bizarre world of subatomic particles.
Contents: The Witch of Mass.- The Observant Scarecrow.- The Tin Geek.- The Confident Lion.- The Atomic Garden.- The Seed at the Heart of the World.- In the Kingdom of CERN.- The Field of the Weave of Light.- The Wizard of Quarks.- The Plaza of the Immortals.- A Weak Old Woman.- The Higgs of Maskervilles.
Greene, R.L., University of New Orleans, LA, USA
Classical Mechanics with Maple Corr. 2nd printing
2000. IX, 173 pp. 56 figs. Softcover
0-387-94512-1
Many problems in classical mechanics can now be readily solved using computers. This text
integrates Maple, a general-purpose symbolic computation program, into the traditional sophomore- or junior-level mechanics course. Intended primarily as a supplement to a standard text, it discusses all the topics usually covered in the course and shows how to solve problems using Maple and how to display solutions graphically to gain further insight. The text is self-contained and can also be used for self-study or as the primary text in a mechanics course.
"...this text is a valuable purchase for the undergraduate student in Physics or Mathematics as well
as the innovative lecturer." Australian & New Zealand Physicist
Contents: Introduction to Maple V.- Review of Introductory Mechanics.- Newtonian Dynamics of
Particles.- The Harmonic Oscillator.- Systems of Particles.- References.- Index.
Harville, D.A., IBM, Yorktown Heights, NY, USA
Matrix Algebra From a Statistician's Perspective
Corr. 3rd printing
2000. XVII, 630 pp. Hardcover
0-387-94978-X
A knowledge of matrix algebra is a prerequisite for the study of much of modern statistics,
especially the areas of linear statistical models and multivariate statistics. This reference book
provides the background in matrix algebra necessary to do research and understand the results in
these areas. Essentially self-contained, the book is best-suited for a reader who has had some
previous exposure to matrices.
Contents: Matrices.- Submatrices and partitioned matrices.- Linear dependence and
independence.- Linear spaces: Row and column spaces.- Trace of a (Square) Matrix.- Geometrical
considerations.- Linear systems.- Consistency and compatibility.- Inverse matrices.- Generalized
inverses.- Idempotent matrics.- Linear systems.- Projections and projection matrics.-
Determinants.- Linear, bilinear, and quadratic forms.- Matrix differentiation.- Kronecker products and the Vec and Vech operators.- Intersections and sums of subspaces.- Sums and differences of
matrics.- Minimization of a second-degree polynomial (in n variables) subject to linear constraints.-
The Moore-Penrose inverse.- Eigenvalues and eigenvectors.- Linear transformations.
Espedal, M.S., University of Bergen, Norway
Fasano, A., University of Florence, Italy
Mikelic, A., University of Lyon, Villeurbanne, France
Fasano, A., University of Florence, Italy (Ed.)Filtration in Porous Media and Industrial Application
Lectures given at the 4th Session of the Centro Internazionale Matematico
Estivo (C.I.M.E.) held in Cetraro, Italy, August 24-29, 1998
2000. VII, 218 pp. Softcover
3-540-67868-9
This book is devoted to the presentation of some flow problems in porous media having relevant
industrial applications. The main topics covered are: the manufacturing of composite materials, the
espresso coffee brewing process, the filtration of liquids through diapers, various questions about
flow problems in oil reservoirs and the theory of homogenization. The aim is to show that filtration
problems arising in very practical industrial context exhibit interesting and highly nontrivial
mathematical aspects. Thus the style of the book is mathematically rigorous, but specifically
oriented towards applications, so that it is intended for both applied mathematicians and
researchers in various areas of technological interest. The reader is required to have a good
knowledge of the classical theory of PDE and basic functional analysis.
Keywords: Flows in porous media, free boundary problems, homogenization, flows in oil reservoirs,
numerical methods . Mathematics Subject Classification Numbers : 76S05, 76M50, 74A40, 35R35,
76M10
Contents: M. Espedal, K.H.Karlsen: Numerical solution of reservoir flow models based on large
time step operator splitting algorithms.- A. Fasano: Filtration problems in various industrial
processes.- A. Mikelic: Homogenization theory and applications to filtration through porous media.
Series: Lecture Notes in Mathematics.VOL. 1734
Fuchs, M., Universitat des Saarlandes, Saarbruken, Germany
Seregin, G., V.A. Steklov Mathematical Institute, St. Petersburg, RussiaVariational Methods for Problems from Plasticity Theory and
for Generalized Newtonian Fluids
2000. VI, 269 pp. Softcover
3-540-41397-9
Variational methods are applied to prove the existence of weak solutions for boundary value
problems from the deformation theory of plasticity as well as for the slow, steady state flow of
generalized Newtonian fluids including the Bingham and Prandtl-Eyring model. For perfect plasticity
the role of the stress tensor is emphasized by studying the dual variational problem in appropriate
function spaces. The main results describe the analytic properties of weak solutions, e.g.
differentiability of velocity fields and continuity of stresses. The monograph addresses researchers
and graduate students interested in applications of variational and PDE methods in the mechanics
of solids and fluids.
Keywords: variational problems, plasticity, generalized Newtonian fluids, regularity ofsolutions,
relexation and duality . MSC : 74C, 74G40, 74G65, 76A05, 76M30 ,49N15, 49N60, 35Q
Contents: Introduction
1 Weak solutions to boundary value problems in the deformation theory of perfect elastoplasticity
1.0. Preliminaries
1.1. The classical boundary value problem for the equilibrium state of a perfect elastoplastic body
and its primary functional formulation
1.2. Relaxation of convex variational problems in non reflexive spaces.
General construction
1.3. Weak solutions to variational problems of perfect elastoplasticity
2 Differentiability properties of weak solutions to boundary value problems in the deformation theory of plasticity
2.0. Preliminaries
2.1. Formulation of the main results
2.2. Approximation and proof of Lemma 2.1.1
2.3. Proof of Theorem 2.1.1 and local estimate of Caccioppoli-type for the stress tensor
2.4. Estimates for solutions of certain systems of PDE's with constant coeffcients
2.5. The main lemma and its iteration
2.6. Proof of Theorem 2.1.2
2.7. Open Problems
2.8. Remarks on the regularity of minimizers of variational functionals from the deformation theory of plasticity with power hardening
Appendix A
A.1 Density of smooth functions in spaces of tensor-valued functions
A.2 Density of smooth functions in spaces of vector-valued functions
A.3 Some properties of the space BD
A.4 Jensen's inequality
3 Quasi-static fluids of generalized Newtonian type
3.0. Preliminaries
3.1. Partial C1 regularity in the variational setting
3.2. Local boundedness of the strain velocity
3.3. The two-dimensional case
3.4. The Bingham variational inequality in dimensions two and three
3.5. Some open problems and comments concerning extensions
4 Fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening law
4.0. Preliminaries
4.1. Some functions spaces related to the Prandtl-Eyring fluid model
4.2. Existence of higher order weak derivatives and a Caccioppoli-type inequality
4.3. Blow-up: the proof of Theorem 4.1.1 for n=3
4.4. The two-dimensional case
4.5. Partial regularity for plastic materials with logarithmic hardening
4.6. A general class of constitutive relations
Appendix B
B.1 Density results
Notation and tools from functional analysis
Series: Lecture Notes in Mathematics.VOL. 1749