A Course on Elation Quadrangles

A Course on Elation Quadrangles

The notion of elation generalized quadrangle is a natural generalization to the theory of generalized quadrangles of the important notion of translation planes in the theory of projective planes. Almost any known class of finite generalized quadrangles can be constructed from a suitable class of elation quadrangles. In this book the author considers several aspects of the theory of elation generalized quadrangles. Special attention is given to local Moufang conditions on the foundational level, exploring, for instance, Knarr’s question from the 1990s concerning the very notion of elation quadrangles. All the known results on Kantor’s prime power conjecture for finite elation quadrangles are gathered, some of them published here for the first time. The structural theory of elation quadrangles and their groups is heavily emphasized. Other related topics, such as $p$-modular cohomology, Heisenberg groups, and existence problems for certain translation nets, are briefly touched. This book starts from scratch and is essentially self-contained. Many alternative proofs are given for known theorems. This course contains dozens of exercises at various levels, from very easy to rather difficult, and will stimulate undergraduate and graduate students to enter the fascinating and rich world of elation quadrangles. More accomplished mathematicians will find the final chapters especially challenging. A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

A Course on Elation Quadrangles

Generalized, Linear, and Mixed Models

Generalized, Linear, and Mixed Models

Wiley Series in Probability and Statistics

Generalized, Linear, and Mixed Models

Advanced Methods of Fatigue Assessments

Advanced Methods of Fatigue Assessments

In five chapters, this volume presents recent developments in fatigue assessment. In the first chapter, a generalized Neuber concept of fictitious notch rounding is presented where the microstructural support factors depend on the notch opening angle besides the loading mode. The second chapter specifies the notch stress factor including the strain energy density and J-integral concept while the SED approach is applied to common fillet welded joints and to thin-sheet lap welded joints in the third chapter. The forth chapter analyses elastic-plastic deformations in the near crack tip zone and discusses driving force parameters. The last chapter discusses thermomechanical fatigue, stress, and strain ranges.

Advanced Methods of Fatigue Assessments

Fractals and Universal Spaces in Dimension Theory

Fractals and Universal Spaces in Dimension Theory

Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods – the classical (separable metric) and the modern (not-necessarily separable metric). The classical theory is now well documented in several books. This monograph is the first book to unify the modern theory from 1960-2007. Like the classical theory, the modern theory fundamentally involves the unit interval. Unique features include: * The use of graphics to illustrate the fractal view of these spaces; * Lucid coverage of a range of topics including point-set topology and mapping theory, fractal geometry, and algebraic topology; * A final chapter contains surveys and provides historical context for related research that includes other imbedding theorems, graph theory, and closed imbeddings; * Each chapter contains a comment section that provides historical context with references that serve as a bridge to the literature. This monograph will be useful to topologists, to mathematicians working in fractal geometry, and to historians of mathematics. Being the first monograph to focus on the connection between generalized fractals and universal spaces in dimension theory, it will be a natural text for graduate seminars or self-study – the interested reader will find many relevant open problems which will create further research into these topics.

Fractals and Universal Spaces in Dimension Theory

SAS for Linear Models, Fourth Edition

SAS for Linear Models, Fourth Edition

This clear and comprehensive guide provides everything you need for powerful linear model analysis. Using a tutorial approach and plenty of examples, authors Ramon Littell, Walter Stroup, and Rudolf Freund lead you through methods related to analysis of variance with fixed and random effects. You will learn to use the appropriate SAS procedure for most experiment designs (including completely random, randomized blocks, and split plot) as well as factorial treatment designs and repeated measures. SAS for Linear Models, Fourth Edition, also includes analysis of covariance, multivariate linear models, and generalized linear models for non-normal data. Find inside: regression models; balanced ANOVA with both fixed- and random-effects models; unbalanced data with both fixed- and random-effects models; covariance models; generalized linear models; multivariate models; and repeated measures. New in this edition: MIXED and GENMOD procedures, updated examples, new software-related features, and other new material.

SAS for Linear Models, Fourth Edition

Algebraic Cobordism

Algebraic Cobordism

Following Quillen’s approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen’s theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications.

Algebraic Cobordism

Mastering Machine Learning with scikit-learn

Mastering Machine Learning with scikit-learn

This book examines machine learning models including logistic regression, decision trees, and support vector machines, and applies them to common problems such as categorizing documents and classifying images. It begins with the fundamentals of machine learning, introducing you to the supervised-unsupervised spectrum, the uses of training and test data, and evaluating models. You will learn how to use generalized linear models in regression problems, as well as solve problems with text and categorical features.,

You will be acquainted with the use of logistic regression, regularization, and the various loss functions that are used by generalized linear models. The book will also walk you through an example , that prompts you to label the most uncertain training examples. You will also use an unsupervised Hidden Markov Model to predict stock prices.

Mastering Machine Learning with scikit-learn