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Grothendieck Duality and Base Change

Grothendieck Duality and Base Change
Author: Brian Conrad
Publisher: Springer
Total Pages: 302
Release: 2003-07-01
Genre: Mathematics
ISBN: 354040015X

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Grothendieck's duality theory for coherent cohomology is a fundamental tool in algebraic geometry and number theory, in areas ranging from the moduli of curves to the arithmetic theory of modular forms. Presented is a systematic overview of the entire theory, including many basic definitions and a detailed study of duality on curves, dualizing sheaves, and Grothendieck's residue symbol. Along the way proofs are given of some widely used foundational results which are not proven in existing treatments of the subject, such as the general base change compatibility of the trace map for proper Cohen-Macaulay morphisms (e.g., semistable curves). This should be of interest to mathematicians who have some familiarity with Grothendieck's work and wish to understand the details of this theory.


Basic Duality

Basic Duality
Author: Payman Sattari
Publisher:
Total Pages: 50
Release: 2019-09-06
Genre:
ISBN: 9781691314058

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As a foundation for the spiritual conversation we will have later in the Language of Truth series, Basic Duality presents a new philosophy of physics. It describes the bridge between material and immaterial aspects of energy, the nature of "yin" and "yang" or the masculine and feminine forces, and the basic "zero" and "one" relationship that underlies all things in the physical universe. A highly complex topic presented through the lens of logic and with a great economy of words, this work was written with the layperson in mind.


The Fundamental Duality of Nature

The Fundamental Duality of Nature
Author: Richard Zindell
Publisher: AuthorHouse
Total Pages: 70
Release: 2011-07-28
Genre: Science
ISBN: 1463420730

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Every generation marvels at the complexity of our universe. Each of us has to decide whether present scientific theories adequately explains the way nature works and how the panoramic view of the heavens on display each night came to be. The ongoing discovery of new data from more precise instrumentation, forces ongoing change to all current theories. We need to take a closer look at exactly what nature has to work with. All that our senses allow us to experience comes from the interactions of nature's fundamental duality.


Self-dual Partial Differential Systems and Their Variational Principles

Self-dual Partial Differential Systems and Their Variational Principles
Author: Nassif Ghoussoub
Publisher: Springer Science & Business Media
Total Pages: 352
Release: 2008-10-08
Genre: Mathematics
ISBN: 0387848975

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This text is intended for a beginning graduate course on convexity methods for PDEs. The generality chosen by the author puts this under the classification of "functional analysis". The book contains new results and plenty of examples and exercises.


The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering

The Numerical Method of Lines and Duality Principles Applied to Models in Physics and Engineering
Author: Fabio Silva Botelho
Publisher: CRC Press
Total Pages: 295
Release: 2024-02-06
Genre: Mathematics
ISBN: 1003848478

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The book includes theoretical and applied results of a generalization of the numerical method of lines. A Ginzburg-Landau type equation comprises the initial application, with detailed explanations about the establishment of the general line expressions. Approximate numerical procedures have been developed for a variety of equation types, including the related algorithms and software. The applications include the Ginzburg-Landau system in superconductivity, applications to the Navier-Stokes system in fluid mechanics and, among others, models in flight mechanics. In its second and final parts, the book develops duality principles and numerical results for other similar and related models. The book is meant for applied mathematicians, physicists and engineers interested in numerical methods and concerning duality theory. It is expected the text will serve as a valuable auxiliary project tool for some important engineering and physics fields of research.


A Complete Guide to the Soul

A Complete Guide to the Soul
Author: Patrick Harpur
Publisher: Random House
Total Pages: 258
Release: 2010-06-03
Genre: Psychology
ISBN: 1407063294

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Who am I? What's my life's purpose? Where am I going when I die? These questions lie at the heart of all our lives, yet clear answers seem hard to come by. A Complete Guide to the Soul explains that answers can in fact be found in a secret history that runs like quicksilver through Western culture, from philosophy and alchemy, to poetry and modern psychology. This hidden tradition places our soul at the centre of the universe and shows us how to recover a sense of meaning that so many of us have lost today. In this important book, Patrick Harpur explores the nature of our soul, as well as its destiny. He unpacks the myths that surround it and shows how it may actually be the very fabric of reality. And he explains that, not until we have a clear understanding of this invisible part of ourselves, can we discover the answers to many of our questions about existence and human nature. Ultimately, this knowledge could help us find our true place within the world in which we live.


Essential Difference

Essential Difference
Author: James Blachowicz
Publisher: State University of New York Press
Total Pages: 330
Release: 2012-08-02
Genre: Philosophy
ISBN: 1438443331

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Finalist for the 2015 John N. Findlay Award in Metaphysics presented by the Metaphysical Society of America Is metaphysics possible? This book argues that the greatest threat to its viability derives from a self-destructive formalism. If what is essential to the nature of physical entities are the properties they have in common (as formalism holds), the inevitable result will be a reductionist collapse—leaving only "being" or physical "matter" or some other underlying ground. In Essential Difference, James Blachowicz first constructs a one-to-one historical parallel between the modern crisis surrounding formalism (Hume/Kant/Hegel) and the ancient version (Parmenides/Plato/Aristotle), focusing on the principles of differentiation and individuation that underlie Aristotle's and Hegel's antireductionist programs. He then proposes a contemporary metaphysical theory of emergence in the context of recent philosophy of science. This theory, founded on the principle of the nonderivability of actual states from possible states, holds that the differences among physical, biological, and mental phenomena are essential to any metaphysics. Essential Difference is the only focused treatment of this problem and is itself essential for any understanding of the nature of metaphysics.


Knowledge, Language and Silence

Knowledge, Language and Silence
Author: Anna Brożek
Publisher: BRILL
Total Pages: 403
Release: 2015-12-22
Genre: Philosophy
ISBN: 9004312676

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Izydora Dąmbska (1904-1982) was a Polish philosopher; a student of Kazimierz Twardowski, and his last assistant. Her output consists of almost 300 publications. The main domains of her research were semiotics, epistemology and broadly understood methodology as well as axiology and history of philosophy. Dąmbska’s approach to philosophical problems reflected tendencies that were characteristic of the Lvov-Warsaw School. She applied high methodological standards but has never limited the domain of analyzed problems in advance. The present volume includes twenty-eight translations of her representative papers. As one of her pupils rightly wrote: “Dąmbska’s works may help everyone [...] to think clearly. Her attitude of an unshaken philosopher may help anyone to hold oneself straight, and, if necessary, to get up after a fall”.


Duality by Design

Duality by Design
Author: Nuno Gil
Publisher: Cambridge University Press
Total Pages: 443
Release: 2019-11-28
Genre: Business & Economics
ISBN: 1108473164

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Using Africa as a context for research, new conceptual framing is proposed to make sense of the challenges of designing effective organizations to pursue socio-economic development.


The Basic Writings of C.G. Jung

The Basic Writings of C.G. Jung
Author: C. G. Jung
Publisher: Princeton University Press
Total Pages: 598
Release: 1990
Genre: Psychology
ISBN: 0691019029

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Originally published: New York: Random House, 1959.