Normal Families
Normal Families

Author: Joel L. Schiff

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 241

ISBN-13: 1461209072

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A book on the subject of normal families more than sixty years after the publication of Montel's treatise Ler;ons sur les familles normales de fonc tions analytiques et leurs applications is certainly long overdue. But, in a sense, it is almost premature, as so much contemporary work is still being produced. To misquote Dickens, this is the best of times, this is the worst of times. The intervening years have seen developments on a broad front, many of which are taken up in this volume. A unified treatment of the classical theory is also presented, with some attempt made to preserve its classical flavour. Since its inception early this century the notion of a normal family has played a central role in the development of complex function theory. In fact, it is a concept lying at the very heart of the subject, weaving a line of thought through Picard's theorems, Schottky's theorem, and the Riemann mapping theorem, to many modern results on meromorphic functions via the Bloch principle. It is this latter that has provided considerable impetus over the years to the study of normal families, and continues to serve as a guiding hand to future work. Basically, it asserts that a family of analytic (meromorphic) functions defined by a particular property, P, is likely to be a normal family if an entire (meromorphic in

Normal Families and Normal Functions
Normal Families and Normal Functions

Author: Peter V. Dovbush

Publisher: CRC Press

Published: 2024-02-27

Total Pages: 269

ISBN-13: 1003849857

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This book centers on normal families of holomorphic and meromorphic functions and also normal functions. The authors treat one complex variable, several complex variables, and infinitely many complex variables (i.e., Hilbert space). The theory of normal families is more than 100 years old. It has played a seminal role in the function theory of complex variables. It was used in the first rigorous proof of the Riemann mapping theorem. It is used to study automorphism groups of domains, geometric analysis, and partial differential equations. The theory of normal families led to the idea, in 1957, of normal functions as developed by Lehto and Virtanen. This is the natural class of functions for treating the Lindelof principle. The latter is a key idea in the boundary behavior of holomorphic functions. This book treats normal families, normal functions, the Lindelof principle, and other related ideas. Both the analytic and the geometric approaches to the subject area are offered. The authors include many incisive examples. The book could be used as the text for a graduate research seminar. It would also be useful reading for established researchers and for budding complex analysts.

Nevanlinna Theory, Normal Families, and Algebraic Differential Equations
Nevanlinna Theory, Normal Families, and Algebraic Differential Equations

Author: Norbert Steinmetz

Publisher: Springer

Published: 2017-07-24

Total Pages: 249

ISBN-13: 3319598007

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This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.

A Nearly Normal Family
A Nearly Normal Family

Author: M. T. Edvardsson

Publisher: Celadon Books

Published: 2019-06-25

Total Pages: 361

ISBN-13: 1250204429

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Now a Netflix Limited Series "...A compulsively readable tour de force." —The Wall Street Journal New York Times Book Review recommends M.T. Edvardsson’s A Nearly Normal Family and lauds it as a “page-turner” that forces the reader to confront “the compromises we make with ourselves to be the people we believe our beloveds expect.” (NYTimes Book Review Summer Reading Issue) M.T. Edvardsson’s A Nearly Normal Family is a gripping legal thriller that forces the reader to consider: How far would you go to protect the ones you love? In this twisted narrative of love and murder, a horrific crime makes a seemingly normal family question everything they thought they knew about their life—and one another. Eighteen-year-old Stella Sandell stands accused of the brutal murder of a man almost fifteen years her senior. She is an ordinary teenager from an upstanding local family. What reason could she have to know a shady businessman, let alone to kill him? Stella’s father, a pastor, and mother, a criminal defense attorney, find their moral compasses tested as they defend their daughter, while struggling to understand why she is a suspect. Told in an unusual three-part structure, A Nearly Normal Family asks the questions: How well do you know your own children? How far would you go to protect them?

Normal Family Processes, Fourth Edition
Normal Family Processes, Fourth Edition

Author: Froma Walsh

Publisher: Guilford Publications

Published: 2015-10-02

Total Pages: 609

ISBN-13: 1462525482

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Widely adopted, this valued course text and practitioner guide has expanded the understanding of family normality and healthy functioning in our increasingly diverse society. The editor and contributors are at the forefront of research and clinical training. They describe the challenges facing contemporary families and ways in which clinicians can promote resilience. With consideration of sociocultural and developmental influences, chapters identify key family processes that nurture and sustain strong bonds in couples; dual-earner, divorced, single-parent, remarried, adoptive, and kinship care families; gay and lesbian families; culturally diverse families; and those coping with adversity, such as trauma,ÿ poverty, and chronic illness.ÿNew to This Edition*Reflects important research advances and the changing contexts of family life.*Additional chapter topics: kinship care, family rituals, evidence-based assessment, and neurobiology.*All chapters have been fully updated.

Normal Family
Normal Family

Author: Chrysta Bilton

Publisher: Hachette UK

Published: 2022-07-12

Total Pages: 317

ISBN-13: 0316536520

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This riveting, nuanced memoir about unforgettable individuals thrown together by chance and DNA tells a story of nature, nurture, and coming to terms with one's true inheritance. What is a “normal family,” and how do you go about making one? Chrysta Bilton’s magnetic, larger-than-life mother, Debra, yearned to have a child, but as a single gay woman in 1980s California, she had few options. Until one day, while getting her hair done in a Beverly Hills salon, she met a man and instantly knew he was the one she’d been looking for. Beautiful, athletic, artistic, and from a well-to-do family, Jeffrey Harrison appeared to be Debra’s ideal sperm donor. A verbal agreement, a couple of thousand in cash, and a few squirts of a turkey baster later, and Chrysta was conceived. Over the years, Jeffrey would make regular appearances at the family home, which grew to include Chrysta’s baby sister. But how much did Debra really know about the man she’d chosen to father her daughters? And as a single mother torn between ferocious independence and abject dependence—on other women, alcohol, drugs, and the adrenaline of get-rich-quick schemes—what secrets of her own was she keeping? It wasn’t until Chrysta was a young adult that she discovered just how much her parents had hidden from their daughters—and each other—including a shocking revelation with far-reaching consequences not only for Debra, Chrysta, and her sister, but for dozens and possibly hundreds of unsuspecting families across the country. After a lifetime of longing for a “normal family,” can Chrysta face the reality of her own, in all its complexity? Bringing us into the fold of a deeply dysfunctional yet fiercely loving clan that is anything but “normal,” this emotional roller coaster of a memoir will make you cry, laugh, and rethink the meaning of family. Named a 'Best Book of the Summer' by LA Times, People, USA Today, Vanity Fair, The Hollywood Reporter, Amazon, Apple, Cup of Jo, Kirkus, Parade, & Today

Normal
Normal

Author: Magdalena M. Newman

Publisher: HMH Books For Young Readers

Published: 2020

Total Pages: 338

ISBN-13: 1328631834

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"Praised by RJ Palacio as "wondrous"--this moving memoir follows a teenage boy with TC syndrome and his exceptional family from diagnosis at birth to now. "This touching memoir is a must-read for anyone who wants to know more about the real world experiences of a child with craniofacial differences and his extraordinary family. It's also more than that. It's a story about the love between a mother and a son, a child and his family, and the breadth of friends, helpers, and doctors that step in when the unexpected happens. It's a story that will make young readers reevaluate the word "normal" -- not only as it applies to others, but to themselves. Any book that can do that is pretty wondrous, as far as I'm concerned." --R. J. Palacio, author of Wonder"--

Parenting Matters
Parenting Matters

Author: National Academies of Sciences, Engineering, and Medicine

Publisher: National Academies Press

Published: 2016-11-21

Total Pages: 525

ISBN-13: 0309388570

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Decades of research have demonstrated that the parent-child dyad and the environment of the familyâ€"which includes all primary caregiversâ€"are at the foundation of children's well- being and healthy development. From birth, children are learning and rely on parents and the other caregivers in their lives to protect and care for them. The impact of parents may never be greater than during the earliest years of life, when a child's brain is rapidly developing and when nearly all of her or his experiences are created and shaped by parents and the family environment. Parents help children build and refine their knowledge and skills, charting a trajectory for their health and well-being during childhood and beyond. The experience of parenting also impacts parents themselves. For instance, parenting can enrich and give focus to parents' lives; generate stress or calm; and create any number of emotions, including feelings of happiness, sadness, fulfillment, and anger. Parenting of young children today takes place in the context of significant ongoing developments. These include: a rapidly growing body of science on early childhood, increases in funding for programs and services for families, changing demographics of the U.S. population, and greater diversity of family structure. Additionally, parenting is increasingly being shaped by technology and increased access to information about parenting. Parenting Matters identifies parenting knowledge, attitudes, and practices associated with positive developmental outcomes in children ages 0-8; universal/preventive and targeted strategies used in a variety of settings that have been effective with parents of young children and that support the identified knowledge, attitudes, and practices; and barriers to and facilitators for parents' use of practices that lead to healthy child outcomes as well as their participation in effective programs and services. This report makes recommendations directed at an array of stakeholders, for promoting the wide-scale adoption of effective programs and services for parents and on areas that warrant further research to inform policy and practice. It is meant to serve as a roadmap for the future of parenting policy, research, and practice in the United States.