Power series techniques are indispensable in many branches of mathematics, in particular in complex and in real analytic geometry, in commutative algebra, in algebraic geometry, in real algebraic geometry. The book covers in a comprehensive way and at an elementary level essentially all the theorems and techniques which are commonly used and needed in any of these branches. In particular it presents Rückert's complex nullstellensatz, Risler's real nullstellensatz, Tougerons' implicit function theorem, and Artin's approximation theorem, to name a few. Up to now a student of any of the subjects mentioned above usually had to learn about power series within the framework of the vast theory of the subject. The present book opens another path: One gets acquaintance with power series in a direct and elementary way, and then disposes of a good box of tools and examples to penetrate any of the subjects mentioned above, and also some others.

Unprecedented insight into the feminine body and on using its natural rhythms to heal, find balance and reconnect to our emotions. Your power lies in the rhythm of your menstrual cycle. Connect with your body on a deeper level to find healing, balance and wholeness. The menstrual cycle is a vital and vitalizing system in the female body, yet our understanding of and respect for this process is both limited and distorted. Few women really know about the physiology of their cycle, and many do not see it as an integral part of their health and wellbeing, let alone as a potential guide to emotional and spiritual empowerment. Wild Power tells a radical new story about feminine power. It reveals: · Your inner architecture and the path to power that is encoded in your body · How to tune in to the rhythm and changes of your menstrual cycle to realize the fullness and beauty of your authority · Three 'maps' to guide you through the energies, tasks and challenges presented as you journey through each cycle · How to work with your Inner Seasons to pace your energy, calm your nervous system and gain insight into your overall wellbeing · How to work with your cycle to channel spiritual forces, affirm your expression in the world and achieve a deep sense of belonging Written with humour, tenderness and practicality, and packed with women's stories and quotes throughout, Wild Power will restore women to wholeness and reinstate the full majesty and grace of the Feminine.

Careful presentation of fundamentals of the theory by one of the finest modern expositors of higher mathematics. Covers functions of real and complex variables, arbitrary and null sequences, convergence and divergence, Cauchy's limit theorem, more.

Multisummability is a method which, for certain formal power series with radius of convergence equal to zero, produces an analytic function having the formal series as its asymptotic expansion. This book presents the theory of multisummabi- lity, and as an application, contains a proof of the fact that all formal power series solutions of non-linear meromorphic ODE are multisummable. It will be of use to graduate students and researchers in mathematics and theoretical physics, and especially to those who encounter formal power series to (physical) equations with rapidly, but regularly, growing coefficients.

This book develops a theory of formal power series in noncommuting variables, the main emphasis being on results applicable to automata and formal language theory. This theory was initiated around 196O-apart from some scattered work done earlier in connection with free groups-by M. P. Schutzenberger to whom also belong some of the main results. So far there is no book in existence concerning this theory. This lack has had the unfortunate effect that formal power series have not been known and used by theoretical computer scientists to the extent they in our estimation should have been. As with most mathematical formalisms, the formalism of power series is capable of unifying and generalizing known results. However, it is also capable of establishing specific results which are difficult if not impossible to establish by other means. This is a point we hope to be able to make in this book. That formal power series constitute a powerful tool in automata and language theory depends on the fact that they in a sense lead to the arithmetization of automata and language theory. We invite the reader to prove, for instance, Theorem IV. 5. 3 or Corollaries III. 7. 8 and III. 7.- all specific results in language theory-by some other means. Although this book is mostly self-contained, the reader is assumed to have some background in algebra and analysis, as well as in automata and formal language theory.

Simple Ordinary Differential Equations may have solutions in terms of power series whose coefficients grow at such a rate that the series has a radius of convergence equal to zero. In fact, every linear meromorphic system has a formal solution of a certain form, which can be relatively easily computed, but which generally involves such power series diverging everywhere. In this book the author presents the classical theory of meromorphic systems of ODE in the new light shed upon it by the recent achievements in the theory of summability of formal power series.

My biggest adversary is out to take everything from me. My family. My business. My power.I have sworn to make him pay for his deceit, but first I must track him down.I own the biggest tech company in the world as a front for my criminal ways, but she has something I am missing.Amelia Becker.Brilliant. Beautiful. Brave.I am drawn to her. I cannot keep away. She consumes me.I want her to find him, but I need her to find me.TRIGGER WARNINGSubject matters like rape that may be dark and disturbing to some readers is included in this book.