Abel Integral Equations


Book Description

In many fields of application of mathematics, progress is crucially dependent on the good flow of information between (i) theoretical mathematicians looking for applications, (ii) mathematicians working in applications in need of theory, and (iii) scientists and engineers applying mathematical models and methods. The intention of this book is to stimulate this flow of information. In the first three chapters (accessible to third year students of mathematics and physics and to mathematically interested engineers) applications of Abel integral equations are surveyed broadly including determination of potentials, stereology, seismic travel times, spectroscopy, optical fibres. In subsequent chapters (requiring some background in functional analysis) mapping properties of Abel integral operators and their relation to other integral transforms in various function spaces are investi- gated, questions of existence and uniqueness of solutions of linear and nonlinear Abel integral equations are treated, and for equations of the first kind problems of ill-posedness are discussed. Finally, some numerical methods are described. In the theoretical parts, emphasis is put on the aspects relevant to applications.




Born a Crime


Book Description

#1 NEW YORK TIMES BESTSELLER • More than one million copies sold! A “brilliant” (Lupita Nyong’o, Time), “poignant” (Entertainment Weekly), “soul-nourishing” (USA Today) memoir about coming of age during the twilight of apartheid “Noah’s childhood stories are told with all the hilarity and intellect that characterizes his comedy, while illuminating a dark and brutal period in South Africa’s history that must never be forgotten.”—Esquire Winner of the Thurber Prize for American Humor and an NAACP Image Award • Named one of the best books of the year by The New York Time, USA Today, San Francisco Chronicle, NPR, Esquire, Newsday, and Booklist Trevor Noah’s unlikely path from apartheid South Africa to the desk of The Daily Show began with a criminal act: his birth. Trevor was born to a white Swiss father and a black Xhosa mother at a time when such a union was punishable by five years in prison. Living proof of his parents’ indiscretion, Trevor was kept mostly indoors for the earliest years of his life, bound by the extreme and often absurd measures his mother took to hide him from a government that could, at any moment, steal him away. Finally liberated by the end of South Africa’s tyrannical white rule, Trevor and his mother set forth on a grand adventure, living openly and freely and embracing the opportunities won by a centuries-long struggle. Born a Crime is the story of a mischievous young boy who grows into a restless young man as he struggles to find himself in a world where he was never supposed to exist. It is also the story of that young man’s relationship with his fearless, rebellious, and fervently religious mother—his teammate, a woman determined to save her son from the cycle of poverty, violence, and abuse that would ultimately threaten her own life. The stories collected here are by turns hilarious, dramatic, and deeply affecting. Whether subsisting on caterpillars for dinner during hard times, being thrown from a moving car during an attempted kidnapping, or just trying to survive the life-and-death pitfalls of dating in high school, Trevor illuminates his curious world with an incisive wit and unflinching honesty. His stories weave together to form a moving and searingly funny portrait of a boy making his way through a damaged world in a dangerous time, armed only with a keen sense of humor and a mother’s unconventional, unconditional love.




Topological Data Analysis


Book Description

This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.




Abel’s Theorem in Problems and Solutions


Book Description

Do formulas exist for the solution to algebraical equations in one variable of any degree like the formulas for quadratic equations? The main aim of this book is to give new geometrical proof of Abel's theorem, as proposed by Professor V.I. Arnold. The theorem states that for general algebraical equations of a degree higher than 4, there are no formulas representing roots of these equations in terms of coefficients with only arithmetic operations and radicals. A secondary, and more important aim of this book, is to acquaint the reader with two very important branches of modern mathematics: group theory and theory of functions of a complex variable. This book also has the added bonus of an extensive appendix devoted to the differential Galois theory, written by Professor A.G. Khovanskii. As this text has been written assuming no specialist prior knowledge and is composed of definitions, examples, problems and solutions, it is suitable for self-study or teaching students of mathematics, from high school to graduate.




House Made of Dawn [50th Anniversary Ed]


Book Description

“Both a masterpiece about the universal human condition and a masterpiece of Native American literature. . . . A book everyone should read for the joy and emotion of the language it contains.” — The Paris Review A special 50th anniversary edition of the magnificent Pulitzer Prize-winning novel from renowned Kiowa writer and poet N. Scott Momaday, with a new preface by the author A young Native American, Abel has come home from war to find himself caught between two worlds. The first is the world of his father’s, wedding him to the rhythm of the seasons, the harsh beauty of the land, and the ancient rites and traditions of his people. But the other world—modern, industrial America—pulls at Abel, demanding his loyalty, trying to claim his soul, and goading him into a destructive, compulsive cycle of depravity and disgust. An American classic, House Made of Dawn is at once a tragic tale about the disabling effects of war and cultural separation, and a hopeful story of a stranger in his native land, finding his way back to all that is familiar and sacred.




Abel's Island


Book Description

William's Steig's Abel's Island tells the story of a mouse who gets swept away from his beloved wife—a truly timeless classic about life's simple pleasures. Abel's place in his familiar, mouse world has always been secure; he had an allowance from his mother, a comfortable home, and a lovely wife, Amanda. But one stormy August day, furious flood water carry him off and dump him on an uninhabited island. Despite his determination and stubborn resourcefulness--he tried crossing the river with boats and ropes and even on stepping-stones--Abel can't find a way to get back home. Days, then weeks and months, pass. Slowly, his soft habits disappear as he forages for food, fashions a warm nest in a hollow log, models clay statues of his family for company, and continues to brood on the problem of how to get across the river--and home. Abel's time on the island brings him a new understanding of the world he's separated from. Faced with the daily adventure of survival in his solitary, somewhat hostile domain, he is moved to reexamine the easy way of life he had always accepted and discovers skills and talents in himself that hold promise of a more meaningful life, if and when he should finally return to Mossville and his dear Amanda again. Abel's Island is a 1976 New York Times Book Review Notable Children's Book of the Year and Outstanding Book of the Year, and a 1977 Newbery Honor Book. It was adapted to a short animated film directed by Michael Sporn in 1988.




Abel on Analysis


Book Description




Environmental Oceanography: Topics and Analysis


Book Description

Environmental Oceanography: Towards a Sustainable Marine Environment is an interactive text and casebook designed to teach students about pressing marine environmental issues using critical thinking and basic math. The text uses an innovative approach to teaching environmental oceanography, consisting of marine environmental issues resented as self-contained analytical exercises, with information and questions on sustainability integrated throughout the text. Appropriate for a wide range of readers, Environmental Oceanography works well as a stand-alone text when supplemented with web-based activities, a lab-based course book, and as a supplement to main texts in oceanography and marine science for those instructors who would like to add an active learning focus to their course. Regardless of whether you are teaching a large or small course, Environmental Oceanography will engage and excite your students and prompt them to think critically about pressing environmental issues.




Statistical Analysis for High-Dimensional Data


Book Description

This book features research contributions from The Abel Symposium on Statistical Analysis for High Dimensional Data, held in Nyvågar, Lofoten, Norway, in May 2014. The focus of the symposium was on statistical and machine learning methodologies specifically developed for inference in “big data” situations, with particular reference to genomic applications. The contributors, who are among the most prominent researchers on the theory of statistics for high dimensional inference, present new theories and methods, as well as challenging applications and computational solutions. Specific themes include, among others, variable selection and screening, penalised regression, sparsity, thresholding, low dimensional structures, computational challenges, non-convex situations, learning graphical models, sparse covariance and precision matrices, semi- and non-parametric formulations, multiple testing, classification, factor models, clustering, and preselection. Highlighting cutting-edge research and casting light on future research directions, the contributions will benefit graduate students and researchers in computational biology, statistics and the machine learning community.




The Legacy of Niels Henrik Abel


Book Description

A unique series of fascinating research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century.