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Shafarevich-Tate Groups (Frontiers in Mathematics)
by M.L. BrownThis monograph explores the finiteness and structure of Shafarevich-Tate groups of abelian varieties over global fields of any characteristic. Readers will better understand how the methods of Euler systems and Kolyvagin systems can be adapted to Heegner points and CM points. Also offered is a comprehensive overview of the most important classical and recent results on these objects. Shafarevich-Tate Groups will be a valuable resource to those interested in this active area of research.
Shallow and Deep Learning Principles: Scientific, Philosophical, and Logical Perspectives
by Zekâi ŞenThis book discusses Artificial Neural Networks (ANN) and their ability to predict outcomes using deep and shallow learning principles. The author first describes ANN implementation, consisting of at least three layers that must be established together with cells, one of which is input, the other is output, and the third is a hidden (intermediate) layer. For this, the author states, it is necessary to develop an architecture that will not model mathematical rules but only the action and response variables that control the event and the reactions that may occur within it. The book explains the reasons and necessity of each ANN model, considering the similarity to the previous methods and the philosophical - logical rules.
Shallow Learning vs. Deep Learning: A Practical Guide for Machine Learning Solutions (The Springer Series in Applied Machine Learning)
by Ömer Faruk Ertuğrul Josep M. Guerrero Musa YilmazThis book explores the ongoing debate between shallow and deep learning in the field of machine learning. It provides a comprehensive survey of machine learning methods, from shallow learning to deep learning, and examines their applications across various domains. Shallow Learning vs Deep Learning: A Practical Guide for Machine Learning Solutions emphasizes that the choice of a machine learning approach should be informed by the specific characteristics of the dataset, the operational environment, and the unique requirements of each application, rather than being influenced by prevailing trends. In each chapter, the book delves into different application areas, such as engineering, real-world scenarios, social applications, image processing, biomedical applications, anomaly detection, natural language processing, speech recognition, recommendation systems, autonomous systems, and smart grid applications. By comparing and contrasting the effectiveness of shallow and deep learning in these areas, the book provides a framework for thoughtful selection and application of machine learning strategies. This guide is designed for researchers, practitioners, and students who seek to deepen their understanding of when and how to apply different machine learning techniques effectively. Through comparative studies and detailed analyses, readers will gain valuable insights to make informed decisions in their respective fields.
Shallow Water Hydraulics
by Oscar Castro-Orgaz Willi H. HagerThis book presents the theory and computation of open channel flows, using detailed analytical, numerical and experimental results. The fundamental equations of open channel flows are derived by means of a rigorous vertical integration of the RANS equations for turbulent flow. In turn, the hydrostatic pressure hypothesis, which forms the core of many shallow water hydraulic models, is scrutinized by analyzing its underlying assumptions. The book’s main focus is on one-dimensional models, including detailed treatments of unsteady and steady flows. The use of modern shock capturing finite difference and finite volume methods is described in detail, and the quality of solutions is carefully assessed on the basis of analytical and experimental results.The book’s unique features include:• Rigorous derivation of the hydrostatic-based shallow water hydraulic models• Detailed treatment of steady open channel flows, including the computation of transcritical flow profiles• General analysis of gate maneuvers as the solution of a Riemann problem• Presents modern shock capturing finite volume methods for the computation of unsteady free surface flows• Introduces readers to movable bed and sediment transport in shallow water models• Includes numerical solutions of shallow water hydraulic models for non-hydrostatic steady and unsteady free surface flowsThis book is suitable for both undergraduate and graduate level students, given that the theory and numerical methods are progressively introduced starting with the basics. As supporting material, a collection of source codes written in Visual Basic and inserted as macros in Microsoft Excel® is available. The theory is implemented step-by-step in the codes, and the resulting programs are used throughout the book to produce the respective solutions.
Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
by Jordan EllenbergFrom the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything. <P><P>How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real. <P><P>If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel. <P><P>Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how. <P><P><b>A New York Times Bestseller</b>
Shape (Math Counts: Updated Editions)
by Henry PluckroseAn introduction to capacity for the youngest readers!Math Counts series introduces young readers (grades K-3) to early math concepts. Real-world examples and corresponding photos make math concepts easy to grasp.Squares, triangles, circles... Shapes are all around us.
The Shape and Size of the Earth: A Historical Journey from Homer to Artificial Satellites
by Dino BoccalettiThis book describes in detail the various theories on the shape of the Earth from classical antiquity to the present day and examines how measurements of its form and dimensions have evolved throughout this period. The origins of the notion of the sphericity of the Earth are explained, dating back to Eratosthenes and beyond, and detailed attention is paid to the struggle to establish key discoveries as part of the cultural heritage of humanity. In this context, the roles played by the Catholic Church and the philosophers of the Middle Ages are scrutinized. Later contributions by such luminaries as Richer, Newton, Clairaut, Maupertuis, and Delambre are thoroughly reviewed, with exploration of the importance of mathematics in their geodetic enterprises. The culmination of progress in scientific research is the recognition that the reference figure is not a sphere but rather a geoid and that the earth’s shape is oblate. Today, satellite geodesy permits the solution of geodetic problems by means of precise measurements. Narrating this fascinating story from the very beginning not only casts light on our emerging understanding of the figure of the Earth but also offers profound insights into the broader evolution of human thought.
Shape and Space: Activities for Children with Mathematical Learning Difficulties
by Mel LeverFirst Published in 2003. Routledge is an imprint of Taylor & Francis, an informa company.
Shape in Medical Imaging: International Workshop, ShapeMI 2024, Held in Conjunction with MICCAI 2024, Marrakesh, Morocco, October 6, 2024, Proceedings (Lecture Notes in Computer Science #15275)
by Christian Wachinger Beatriz Paniagua Shireen Elhabian Gijs Luijten Jan EggerThis book constitutes the proceedings of the International Workshop on Shape in Medical Imaging, ShapeMI 2024, which took place in Marrakesh, Morocco, on October 6, 2024, held in conjunction with MICCAI 2024. The 16 full papers included in this book were carefully reviewed and selected from 24 submissions. They focus on shape and spectral analysis, geometric learning and modeling algorithms, and application-driven research.
The Shape of a Life: One Mathematician's Search for the Universe's Hidden Geometry
by Shing-Tung Yau Steve NadisA Fields medalist recounts his lifelong effort to uncover the geometric shape—the Calabi-Yau manifold—that may store the hidden dimensions of our universe.Harvard geometer Shing-Tung Yau has provided a mathematical foundation for string theory, offered new insights into black holes, and mathematically demonstrated the stability of our universe. In this autobiography, Yau reflects on his improbable journey to becoming one of the world’s most distinguished mathematicians. Beginning with an impoverished childhood in China and Hong Kong, Yau takes readers through his doctoral studies at Berkeley during the height of the Vietnam War protests, his Fields Medal–winning proof of the Calabi conjecture, his return to China, and his pioneering work in geometric analysis. This new branch of geometry, which Yau built up with his friends and colleagues, has paved the way for solutions to several important and previously intransigent problems.With complicated ideas explained for a broad audience, this book offers not only insights into the life of an eminent mathematician, but also an accessible way to understand advanced and highly abstract concepts in mathematics and theoretical physics.“The remarkable story of one of the world’s most accomplished mathematicians . . . Yau’s personal journey—from escaping China as a youngster, leading a gang outside Hong Kong, becoming captivated by mathematics, to making breakthroughs that thrust him on the world stage—inspires us all with humankind’s irrepressible spirit of discovery.” —Brian Greene, New York Times–bestselling author of The Elegant Universe“An unexpectedly intimate look into a highly accomplished man, his colleagues and friends, the development of a new field of geometric analysis, and a glimpse into a truly uncommon mind.” —The Boston Globe“Engaging, eminently readable. . . . For those with a taste for elegant and largely jargon-free explanations of mathematics, The Shape of a Life promises hours of rewarding reading.” —American Scientist
The Shape of Content: Creative Writing in Mathematics and Science
by Chandler Davis Marjorie Wikler Senechal Jan ZwickyThis book is a collection of creative pieces-poems, short stories, essays, play excerpts-that give shape to mathematical and scientific content. This book portrays by example how various people work creatively with ideas from mathematics and other sciences. Creative writing about the content of mathematics and science is rare, and creative writing
The Shape of Data: Geometry-Based Machine Learning and Data Analysis in R
by Colleen M. Farrelly Yaé Ulrich GabaThis advanced machine learning book highlights many algorithms from a geometric perspective and introduces tools in network science, metric geometry, and topological data analysis through practical application.Whether you&’re a mathematician, seasoned data scientist, or marketing professional, you&’ll find The Shape of Data to be the perfect introduction to the critical interplay between the geometry of data structures and machine learning.This book&’s extensive collection of case studies (drawn from medicine, education, sociology, linguistics, and more) and gentle explanations of the math behind dozens of algorithms provide a comprehensive yet accessible look at how geometry shapes the algorithms that drive data analysis.In addition to gaining a deeper understanding of how to implement geometry-based algorithms with code, you&’ll explore:Supervised and unsupervised learning algorithms and their application to network data analysisThe way distance metrics and dimensionality reduction impact machine learningHow to visualize, embed, and analyze survey and text data with topology-based algorithmsNew approaches to computational solutions, including distributed computing and quantum algorithms
The Shape of Inner Space: String Theory and the Geometry of the Universe's Hidden Dimensions
by Shing-Tung Yau Steve NadisString theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe.Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau's penetrating thinking on where we've been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
The Shape of Space (Chapman & Hall/CRC Pure and Applied Mathematics #249)
by Jeffrey R. WeeksMaintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.
The Shape of Space: How To Visualize Surfaces And Three-dimensional Manifolds (Textbooks in Mathematics #Vol. 249)
by Jeffrey R. WeeksThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spaces—stretching students’ minds as they learn to visualize new possibilities for the shape of our universe. Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space. Features of the Third Edition: Full-color figures throughout "Picture proofs" have replaced algebraic proofs Simpler handles-and-crosscaps approach to surfaces Updated discussion of cosmological applications Intuitive examples missing from many college and graduate school curricula About the Author: Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.
Shape Optimization And Optimal Design
by John Cagnol Michael P. Polis Jean-Paul ZolésioThis volume presents developments and advances in modelling passive and active control systems governed by partial differential equations. It emphasizes shape analysis, optimal shape design, controllability, nonlinear boundary control, and stabilization. The authors include essential data on exact boundary controllability of thermoelastic plates with variable transmission coefficients.
Shape Optimization, Homogenization and Optimal Control: DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017 (International Series of Numerical Mathematics #169)
by Volker Schulz Diaraf SeckThe contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers.This workshop, held at the AIMS Center Senegal, March 13-16, 2017, has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the African Institute for Mathematical Sciences (AIMS) in Senegal, which is one of six centres of a pan-African network of centres of excellence for postgraduate education, research and outreach in mathematical sciences.
Shape Optimization Problems (Springer Optimization and Its Applications #164)
by Hideyuki AzegamiThis book provides theories on non-parametric shape optimization problems, systematically keeping in mind readers with an engineering background. Non-parametric shape optimization problems are defined as problems of finding the shapes of domains in which boundary value problems of partial differential equations are defined. In these problems, optimum shapes are obtained from an arbitrary form without any geometrical parameters previously assigned. In particular, problems in which the optimum shape is sought by making a hole in domain are called topology optimization problems. Moreover, a problem in which the optimum shape is obtained based on domain variation is referred to as a shape optimization problem of domain variation type, or a shape optimization problem in a limited sense. Software has been developed to solve these problems, and it is being used to seek practical optimum shapes. However, there are no books explaining such theories beginning with their foundations.The structure of the book is shown in the Preface. The theorems are built up using mathematical results. Therefore, a mathematical style is introduced, consisting of definitions and theorems to summarize the key points. This method of expression is advanced as provable facts are clearly shown. If something to be investigated is contained in the framework of mathematics, setting up a theory using theorems prepared by great mathematicians is thought to be an extremely effective approach. However, mathematics attempts to heighten the level of abstraction in order to understand many things in a unified fashion. This characteristic may baffle readers with an engineering background. Hence in this book, an attempt has been made to provide explanations in engineering terms, with examples from mechanics, after accurately denoting the provable facts using definitions and theorems.
Shape Up!: Fun with triangles and other polygons
by David A. AdlerUses cheese slices, pretzel sticks, a slice of bread, graph paper, a pencil, and more to introduce various polygons, flat shapes with varying numbers of straight sides.
Shapes: Squares (Concepts)
by Esther SarfattiToys are square! Foods are square! Squares are everywhere! Other books by this author are available in this library.
Shapes and Designs: Two-Dimensional Geometry (Connected Mathematics)
by Glenda Lappan Elizabeth Difanis Phillips James T. Fey Susan N. FrielThe contents of this book include: The Family of Polygons, Designing Polygons: The Angle Connection, Designing Triangles and Quadrilaterals, English/Spanish Glossary, etc.
Shapes and Designs: Two-Dimensional Geometry
by Glenda Lappan Elizabeth Difanis Phillips James T. Fey Susan N. FrielNIMAC-sourced textbook
Shapes and Designs, Two - Dimensional Geometry
by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis PhillipsNIMAC-sourced textbook
Shapes and Diffeomorphisms (Applied Mathematical Sciences #171)
by Laurent YounesThis book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control).The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chapters are suitable for a graduate course on shape analysis through the action of diffeomorphisms. Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching.
Shapes at the Park (The World Around You)
by Christianne JonesFrom rectangular ladders to circular rings and hexagonal picnic tables, the park is full of shapes! Finding shapes adds even more fun to a day at the park, and early learners will be fully engaged with the interactive, rhyming text and colorful photos in this picture book.