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This book provides comprehensive analysis of dynamical systems in tropical geometry, which include the author's significant discoveries and pioneering contributions. Tropical geometry is a kind of dynamical scale transform which connects real rational dynamics with piecewise linear one presented by max and plus algebras. A comparison method is given which estimates orbits corresponding to different rational dynamics by reduction to the piecewise linear dynamics.

Both rational and piecewise linear dynamics appear in many important branches of mathematics. Tropical geometry can play a...

In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure.

The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory...

This book will discuss and cover standard treatments and advances in some of the most controversial topics in cerebrovascular surgery traversing the whole arena, including open and interventional surgeries. They will be discussed with case scenarios, bail out strategies and complication handling, followed by advances in the subject. Some of the best academic cereberovascular physician will author these chapters with their vast experience. The book will be of particular benefit to neurosurgeons, neurologists, and radiologists. It will be particularly targeting residents, young and...

If you have not heard about cohomology, this book may be suited for you. Fundamental notions in cohomology for examples, functors, representable functors, Yoneda embedding, derived functors, spectral sequences, derived categories are explained in elementary fashion. Applications to sheaf cohomology are given. Also cohomological aspects of D-modules and of the computation of zeta functions of the Weierstrass family are provided.

Liberalizing Lynching: Building a New Racialized State seeks to explain the seemingly paradoxical relationship between the American liberal regime and the illiberal act of lynching. Drawing on legal cases, congressional...