The Octagonal Pets

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 53,7 Mb
Release : 2014-07-03
Category : Mathematics
ISBN : 9781470415228

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The Octagonal PETs by Richard Evan Schwartz Pdf

A polytope exchange transformation is a (discontinuous) map from a polytope to itself that is a translation wherever it is defined. The 1-dimensional examples, interval exchange transformations, have been studied fruitfully for many years and have deep connections to other areas of mathematics, such as Teichmüller theory. This book introduces a general method for constructing polytope exchange transformations in higher dimensions and then studies the simplest example of the construction in detail. The simplest case is a 1-parameter family of polygon exchange transformations that turns out to be closely related to outer billiards on semi-regular octagons. The 1-parameter family admits a complete renormalization scheme, and this structure allows for a fairly complete analysis both of the system and of outer billiards on semi-regular octagons. The material in this book was discovered through computer experimentation. On the other hand, the proofs are traditional, except for a few rigorous computer-assisted calculations.

Author : Sandra Helene Straub
Publisher : Routledge
Page : 164 pages
File Size : 54,6 Mb
Release : 2019-06-04
Category : Psychology
ISBN : 9781351853958

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Pet Death by Sandra Helene Straub Pdf

In "Pet Death", Dr. Straub addresses issues and feelings commonly encountered after the death of a pet. Practical guidelines are provided for coping with feelings of loss and sorrow. Many questions arise from the difficult topic of euthanasia, and in this book, the medical aspect of this procedure is explained in plain language. "Are your other pets grieving?" and "Should I get another pet right away?" are other questions addressed. Dr. Straub and others openly share their personal accounts of pet loss.

Author : Thomas S. Muir
Publisher : Unknown
Page : 68 pages
File Size : 49,9 Mb
Release : 1877
Category : Electronic
ISBN : NLS:V000621961

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Two Tellings to Pet. (A Third Telling to Pet) by Thomas S. Muir Pdf

Author : Team Prabhat
Publisher : Prabhat Prakashan
Page : 573 pages
File Size : 46,6 Mb
Release : 2023-01-23
Category : Study Aids
ISBN : 9789390906697

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UPSSSC Uttar Pradesh Subordinate Services Selection Commission PET (Preliminary Eligibility Test) Group-C (Include Latest Solved Paper) by Team Prabhat Pdf

The Present Edition of “UPSSSC PET GROUP-C” has been carefully prepared to serve as a Complete Study Guide/Solved Papers for those aspirants who are preparing for UPSSSC PET (Preliminary Eligibility Test Group-C) conducted by Uttar Pradesh Subordinate Services Selection Commission. -This book contains Solved Papers of 2022 & 2021 including Shift 1& 2. -The subjects are arranged exactly as per the latest syllabus and pattern, to make it 100% convenient for the candidates. -This book gives you an idea of the questions asked in previous years' exams, and also what type of questions you should expect in the upcoming exam. -To summarize, this book serves as an ideal revision source for all candidates who are aspiring for different posts in UPSSSC PET GROUP-C such as Junior Assistant, Stenographer, Clerk, Forest Guard, Junior Engineer, Lekhpal, Boring Technician, Computer Operator, etc. Topics to be covered Indian History Geography Indian Economy Indian Constitution & Public Administration General Science Elementary Arithmetic Samanya Hindi General English Logic & Reasoning General Awareness Graphs & Tables Highlights of the book Analyzing the pattern of examination Practices Sets are a collection of useful exam questions Answers with explanations are available for all questions According to the prescribe syllabus and exam pattern

Author : Christopher L. Douglas, John Francis, André G. Henriques, Michael A. Hill
Publisher : American Mathematical Soc.
Page : 318 pages
File Size : 52,5 Mb
Release : 2014-12-04
Category : Mathematics
ISBN : 9781470418847

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Topological Modular Forms by Christopher L. Douglas, John Francis, André G. Henriques, Michael A. Hill Pdf

The theory of topological modular forms is an intricate blend of classical algebraic modular forms and stable homotopy groups of spheres. The construction of this theory combines an algebro-geometric perspective on elliptic curves over finite fields with techniques from algebraic topology, particularly stable homotopy theory. It has applications to and connections with manifold topology, number theory, and string theory. This book provides a careful, accessible introduction to topological modular forms. After a brief history and an extended overview of the subject, the book proper commences with an exposition of classical aspects of elliptic cohomology, including background material on elliptic curves and modular forms, a description of the moduli stack of elliptic curves, an explanation of the exact functor theorem for constructing cohomology theories, and an exploration of sheaves in stable homotopy theory. There follows a treatment of more specialized topics, including localization of spectra, the deformation theory of formal groups, and Goerss-Hopkins obstruction theory for multiplicative structures on spectra. The book then proceeds to more advanced material, including discussions of the string orientation, the sheaf of spectra on the moduli stack of elliptic curves, the homotopy of topological modular forms, and an extensive account of the construction of the spectrum of topological modular forms. The book concludes with the three original, pioneering and enormously influential manuscripts on the subject, by Hopkins, Miller, and Mahowald.

Author : Charlotte Hardouin,Jacques Sauloy,Michael F. Singer
Publisher : American Mathematical Soc.
Page : 171 pages
File Size : 53,9 Mb
Release : 2016-04-27
Category : Difference and functional equations -- Difference equations -- Linear equations
ISBN : 9781470426552

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Galois Theories of Linear Difference Equations: An Introduction by Charlotte Hardouin,Jacques Sauloy,Michael F. Singer Pdf

This book is a collection of three introductory tutorials coming out of three courses given at the CIMPA Research School “Galois Theory of Difference Equations” in Santa Marta, Columbia, July 23–August 1, 2012. The aim of these tutorials is to introduce the reader to three Galois theories of linear difference equations and their interrelations. Each of the three articles addresses a different galoisian aspect of linear difference equations. The authors motivate and give elementary examples of the basic ideas and techniques, providing the reader with an entry to current research. In addition each article contains an extensive bibliography that includes recent papers; the authors have provided pointers to these articles allowing the interested reader to explore further.

Author : Ruy Exel
Publisher : American Mathematical Soc.
Page : 321 pages
File Size : 45,6 Mb
Release : 2017-09-20
Category : Banach spaces
ISBN : 9781470437855

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Partial Dynamical Systems, Fell Bundles and Applications by Ruy Exel Pdf

Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of “partiality”. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener–Hopf algebras and graph C*-algebras.

Author : Tushar Das,David Simmons,Mariusz Urbański
Publisher : American Mathematical Soc.
Page : 281 pages
File Size : 55,7 Mb
Release : 2017-04-14
Category : Geometry, Hyperbolic
ISBN : 9781470434656

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Geometry and Dynamics in Gromov Hyperbolic Metric Spaces by Tushar Das,David Simmons,Mariusz Urbański Pdf

This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 196 pages
File Size : 46,6 Mb
Release : 2017-04-20
Category : Dynamical systems and ergodic theory
ISBN : 9781470435141

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The Projective Heat Map by Richard Evan Schwartz Pdf

This book introduces a simple dynamical model for a planar heat map that is invariant under projective transformations. The map is defined by iterating a polygon map, where one starts with a finite planar -gon and produces a new -gon by a prescribed geometric construction. One of the appeals of the topic of this book is the simplicity of the construction that yet leads to deep and far reaching mathematics. To construct the projective heat map, the author modifies the classical affine invariant midpoint map, which takes a polygon to a new polygon whose vertices are the midpoints of the original. The author provides useful background which makes this book accessible to a beginning graduate student or advanced undergraduate as well as researchers approaching this subject from other fields of specialty. The book includes many illustrations, and there is also a companion computer program.

Author : A. Shen,V. A. Uspensky,N. Vereshchagin
Publisher : American Mathematical Society
Page : 511 pages
File Size : 54,9 Mb
Release : 2022-05-18
Category : Mathematics
ISBN : 9781470470647

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Kolmogorov Complexity and Algorithmic Randomness by A. Shen,V. A. Uspensky,N. Vereshchagin Pdf

Looking at a sequence of zeros and ones, we often feel that it is not random, that is, it is not plausible as an outcome of fair coin tossing. Why? The answer is provided by algorithmic information theory: because the sequence is compressible, that is, it has small complexity or, equivalently, can be produced by a short program. This idea, going back to Solomonoff, Kolmogorov, Chaitin, Levin, and others, is now the starting point of algorithmic information theory. The first part of this book is a textbook-style exposition of the basic notions of complexity and randomness; the second part covers some recent work done by participants of the “Kolmogorov seminar” in Moscow (started by Kolmogorov himself in the 1980s) and their colleagues. This book contains numerous exercises (embedded in the text) that will help readers to grasp the material.

Author : Alexandru Buium
Publisher : American Mathematical Society
Page : 357 pages
File Size : 40,9 Mb
Release : 2023-11-20
Category : Mathematics
ISBN : 9781470475772

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Foundations of Arithmetic Differential Geometry by Alexandru Buium Pdf

The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.

Author : Jared Speck
Publisher : American Mathematical Soc.
Page : 544 pages
File Size : 47,7 Mb
Release : 2016-12-07
Category : Differential equations, Nonlinear
ISBN : 9781470428570

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Shock Formation in Small-Data Solutions to 3D Quasilinear Wave Equations by Jared Speck Pdf

In 1848 James Challis showed that smooth solutions to the compressible Euler equations can become multivalued, thus signifying the onset of a shock singularity. Today it is known that, for many hyperbolic systems, such singularities often develop. However, most shock-formation results have been proved only in one spatial dimension. Serge Alinhac's groundbreaking work on wave equations in the late 1990s was the first to treat more than one spatial dimension. In 2007, for the compressible Euler equations in vorticity-free regions, Demetrios Christodoulou remarkably sharpened Alinhac's results and gave a complete description of shock formation. In this monograph, Christodoulou's framework is extended to two classes of wave equations in three spatial dimensions. It is shown that if the nonlinear terms fail to satisfy the null condition, then for small data, shocks are the only possible singularities that can develop. Moreover, the author exhibits an open set of small data whose solutions form a shock, and he provides a sharp description of the blow-up. These results yield a sharp converse of the fundamental result of Christodoulou and Klainerman, who showed that small-data solutions are global when the null condition is satisfied. Readers who master the material will have acquired tools on the cutting edge of PDEs, fluid mechanics, hyperbolic conservation laws, wave equations, and geometric analysis.

Author : Jason P. Bell,Dragos Ghioca,Thomas J. Tucker
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 40,9 Mb
Release : 2016-04-20
Category : Arithmetical algebraic geometry
ISBN : 9781470424084

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The Dynamical Mordell–Lang Conjecture by Jason P. Bell,Dragos Ghioca,Thomas J. Tucker Pdf

The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.

Author : Steve Y. Oudot
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 48,9 Mb
Release : 2017-05-17
Category : Electronic
ISBN : 9781470434434

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Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot Pdf

Persistence theory emerged in the early 2000s as a new theory in the area of applied and computational topology. This book provides a broad and modern view of the subject, including its algebraic, topological, and algorithmic aspects. It also elaborates on applications in data analysis. The level of detail of the exposition has been set so as to keep a survey style, while providing sufficient insights into the proofs so the reader can understand the mechanisms at work. The book is organized into three parts. The first part is dedicated to the foundations of persistence and emphasizes its connection to quiver representation theory. The second part focuses on its connection to applications through a few selected topics. The third part provides perspectives for both the theory and its applications. The book can be used as a text for a course on applied topology or data analysis.

Author : Benoit Fresse
Publisher : American Mathematical Soc.
Page : 532 pages
File Size : 50,5 Mb
Release : 2017-04-21
Category : Algebraic topology -- Homotopy theory -- Rational homotopy theory
ISBN : 9781470434816

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Homotopy of Operads and Grothendieck-Teichmuller Groups by Benoit Fresse Pdf

The Grothendieck–Teichmüller group was defined by Drinfeld in quantum group theory with insights coming from the Grothendieck program in Galois theory. The ultimate goal of this book is to explain that this group has a topological interpretation as a group of homotopy automorphisms associated to the operad of little 2-discs, which is an object used to model commutative homotopy structures in topology. This volume gives a comprehensive survey on the algebraic aspects of this subject. The book explains the definition of an operad in a general context, reviews the definition of the little discs operads, and explains the definition of the Grothendieck–Teichmüller group from the viewpoint of the theory of operads. In the course of this study, the relationship between the little discs operads and the definition of universal operations associated to braided monoidal category structures is explained. Also provided is a comprehensive and self-contained survey of the applications of Hopf algebras to the definition of a rationalization process, the Malcev completion, for groups and groupoids. Most definitions are carefully reviewed in the book; it requires minimal prerequisites to be accessible to a broad readership of graduate students and researchers interested in the applications of operads.