Abel On Analysis

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.

#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.

Award-winning Nisga'a poet Jordan Abel's third collection, Injun, is a long poem about racism and the representation of indigenous peoples. Composed of text found in western novels published between 1840 and 1950 - the heyday of pulp publishing and a period of unfettered colonialism in North America - Injun then uses erasure, pastiche, and a focused poetics to create a visually striking response to the western genre. After compiling the online text of 91 of these now public-domain novels into one gargantuan document, Abel used his word processor's "Find" function to search for the word "injun." The 509 results were used as a study in context: How was this word deployed? What surrounded it? What was left over once that word was removed? Abel then cut up the sentences into clusters of three to five words and rearranged them into the long poem that is Injun. The book contains the poem as well as peripheral material that will help the reader to replicate, intuitively, some of the conceptual processes that went into composing the poem. Though it has been phased out of use in our "post-racial" society, the word "injun" is peppered throughout pulp western novels. Injun retraces, defaces, and effaces the use of this word as a colonial and racial marker. While the subject matter of the source text is clearly problematic, the textual explorations in Injun help to destabilize the colonial image of the "Indian" in the source novels, the western genre as a whole, and the Western canon.

The Abel Symposium 2005 was organized as a tribute to the work of Kiyosi Ito on the occasion of his 90th birthday. Distinguished researchers from all over presented the newest developments within the exciting and fast growing field of stochastic analysis. This volume combines both papers from the invited speakers and contributions by the presenting lecturers. In addition, it includes the Memoirs that Kiyoshi Ito wrote for this occasion.

From Griffin Poetry Prize winner Jordan Abel comes a groundbreaking, deeply personal, and devastating autobiographical meditation that attempts to address the complicated legacies of Canada's residential school system and contemporary Indigenous existence. As a Nisga'a writer, Jordan Abel often finds himself in a position where he is asked to explain his relationship to Nisga'a language, Nisga'a community, and Nisga'a cultural knowledge. However, as an intergenerational survivor of residential school--both of his grandparents attended the same residential school--his relationship to his own Indigenous identity is complicated to say the least. NISHGA explores those complications and is invested in understanding how the colonial violence originating at the Coqualeetza Indian Residential School impacted his grandparents' generation, then his father's generation, and ultimately his own. The project is rooted in a desire to illuminate the realities of intergenerational survivors of residential school, but sheds light on Indigenous experiences that may not seem to be immediately (or inherently) Indigenous. Drawing on autobiography and a series of interconnected documents (including pieces of memoir, transcriptions of talks, and photography), NISHGA is a book about confronting difficult truths and it is about how both Indigenous and non-Indigenous peoples engage with a history of colonial violence that is quite often rendered invisible.

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.

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.