This volume grew out of two Simons Symposia on "Nonarchimedean and tropical geometry" which took place on the island of St. John in April 2013 and in Puerto Rico in February 2015. Each meeting gathered a small group of experts working near the interface between tropical geometry and nonarchimedean analytic spaces for a series of inspiring and provocative lectures on cutting edge research, interspersed with lively discussions and collaborative work in small groups. The articles collected he...

In Vibe, bestselling author Robyn Openshaw reveals the difference between low vibration emotions (fear, anger, inertia) and high vibration emotions (love, inner peace, gratitude) and helps you dramatically impact your physical and mental well-being by raising your vibrational frequencies.The great Austrian scientist Nikola Tesla is a household name among today’s scientific community, known for his finding that all matter has vibrational energy, or electric...

**OVER 1 MILLION COPIES SOLD!**"Kick bad mental habits and toughen yourself up."—Inc.Master your mental strength—revolutionary new strategies that work for everyone from homemakers to soldiers and teachers to CEOs. Read by author Amy Morin!Everyone knows that regular exercise and weight training lead to physical strength. But how do we strengthen ourselves mentally for the truly tough times? And what should...

No matter who you are, no matter where you are, no matter what your current circumstances, The Magic is going to change your entire life!Your life will change—as if by magic—with gratitude.In The Magic, Rhonda Byrne reveals life-changing knowledge about the power of gratitude that was hidden within a 2,000-year-old sacred text. Then, on an incredible 28-day journey, she teaches you how to apply this life-changing knowledge in your everyday...

Who are you? When you start to explore this question, you find outhow elusive it really is. Are you a physical body? A collection ofexperiences and memories? A partner to relationships? Each time you consider these aspects of yourself, you realize that there is much more to you than any of these can define. In The Untethered Soul,spiritual teacher Michael A. Singer explores the question of who we are and arrives at the conclusion that our identity is to be fou...

**#1 NEW YORK TIMES BESTSELLER • The “mercilessly entertaining” (Vanity Fair) instant classic “about the nature of identity and the terrible secrets that can survive and thrive in even the most intimate relationships” (Lev Grossman, Time “One of the Best Books of the Decade”)—now featuring never-before-published deleted scenesTHE NEW YORK TIMES’S BEST THRILLER OF THE CENTURY • ONE OF TIME'S 100 BEST MYSTERY AND THRILLER BOOKS OF ...

Fractal Delight is a collection of fractal based imagery with some 3D mixed in. These are the foundations for my video production whereby I play with colours and shapes before I embark on the task of creating an animation. They can be viewed on a tablet sideways or on a larger scale by downloading the PDF from Smashwords and rotating it 90 degrees as the pictures are mostly landscape. Kd.

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate thos...

The 2003 second volume of this account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard–Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant cycles follow. The main results of the second part are the generalized Noether–Lefschetz theorems, the generic triviality of the Abel–Jacobi maps, and m...

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface ...

Torsors, also known as principal bundles or principal homogeneous spaces, are ubiquitous in mathematics. The purpose of this book is to present expository lecture notes and cutting-edge research papers on the theory and applications of torsors and étale homotopy, all written from different perspectives by leading experts. Part one of the book contains lecture notes on recent uses of torsors in geometric invariant theory and representation theory, plus an introduction to the étale homotopy ...

This second edition of Mathematical Olympiad Treasures contains a stimulating collection of problems in geometry and trigonometry, algebra, number theory, and combinatorics. It encourages readers to think creatively about techniques and strategies for solving real-world problems, with new sections, revisions, and many more Olympiad-like problems at various levels of difficulty.The problems are clustered by topic into three self-contained chapters. The book begins with elem...