The book shows that doubly transitive or transitive t-parallelisms cannot exist unless the parallelism is a line parallelism. Along with the author’s other three books (Subplane Covered Nets, Foundations of Translation Planes, Handbook of Finite Translation Planes), this text forms a solid, comprehensive account of the complete theory of the geometries that are connected with translation planes in intricate ways. It explores how to construct interesting parallelisms and how general spreads of vector spaces are used to study and construct subgeometry partitions of projective spaces.

After C. Gardner, J. Greene, M. Kruskal et R. Miura [44] showed that this equation could be solved using the inverse scattering method and P. Lax [62] reinterpreted this method by his famous equation, many other deep observations have been made during the seventies, mainly by the Russian and the Japanese schools. In particular this theory was shown to be strongly connected with methods from algebraic geom- etry

It gives the elements required to develop a defect prevention system (DPS), and integrates the application of process control and problem analysis tools.

The second part explores several recent projects in which the 3Dhp code was used and illustrates how these applications have greatly driven the development of 3D hp technology. It encompasses acoustic and electromagnetic (EM) scattering problems, an analysis of complex structures with thin-walled components, and challenging simulations of logging tools. The book concludes with a look at the future of hp methods.

Spearheaded by a key developer of this technology with more than 20 years of research in the field, this self-contained, comprehensive resource will help readers overcome the difficulties in coding hp-adaptive elements.

First of all, we are indebted to all the authors for submitting their work, and to the referees for their help in the selec­ tion and for their generous contribution to the content of the articles. Many talks given during the CRM semester or at the conference focused on aspects of the following topics: abstract stable homotopy, model categories, homotopical localizations and cellular approximations, p-compact groups, mod­ ules over the Steenrod algebra, classifying spaces for proper actions of discrete groups, K-theory and other generalized cohomology theories, cohomology of fi­ nite and profinite groups, Hochschild homology, configuration spaces, Lusternik­ Schnirelmann category, stable and unstable splittings. Other talks treated multi­ disciplinary subjects related to quantum field theory, differential geometry, homo­ topical dynamics, tilings, and various aspects of group theory. In addition, an advanced course on Classifying Spaces and Cohomology of Groups was organized by the CRM in the days preceding the conference. Lecture notes from this course will be published by Birkhauser Verlag as the first volume of a newly created CRM Advanced Course series.

A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec­ trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of “starter” designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding “starter” designs.

The material has been well organized, stress being given to various definition and appropriate examples are worked out to comprehend logically in a coherent manner to the graduate students when the applications are encounter in their various specialization in engineering curriculum.