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This volume collects papers based on plenary and invited talks given at the 50th Barrett Memorial Lectures on Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models that was organized by the University of Tennessee, Knoxville and held virtually in May 2021. The three-day meeting brought together experts from the computational, scientific, engineering, and mathematical communities who work with nonlocal models. These proceedings collect contributions and give a survey of the state of the art in computational practices, mathematical analysis, applications of nonlocal models, and explorations of new application domains. The volume benefits from the mixture of contributions by computational scientists, mathematicians, and application specialists. The content is suitable for graduate students as well as specialists working with nonlocal models and covers topics on fractional PDEs, regularity theory for kinetic equations, approximation theory for fractional diffusion, analysis of nonlocal diffusion model as a bridge between local and fractional PDEs, and more.
Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year was a tutorial on Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular Biology, held September 15--21 at the IMA. This volume is dedicated to the memory of Nicholas R. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. It contains a personal remembrance of Nick Cozzarelli, plus 15 papers contributed by workshop speakers. The papers give an overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes.
Why does my child seem to worry so much? Being the parent of a smart child is great—until your son or daughter starts asking whether global warming is real, if you are going to die, and what will happen if they don't get into college. Kids who are advanced intellectually often let their imaginations ruin wild and experience fears beyond their years. So what can you do to help? In Why Smart Kids Worry, Allison Edwards guides you through the mental and emotional process of where your child's fears come from and why they are so hard to move past. Edwards focuses on how to parent a child who is both smart and anxious and brings her years of experience as a therapist to give you the answers to questions such as: •How do smart kids think differently? •Should I let my child watch the nightly news on TV? •How do I answer questions about terrorists, hurricanes, and other scary subjects? Edwards's fifteen specially designed tools for helping smart kids manage their fears will help you and your child work together to help him or her to become more relaxed and worry-free.
"This Olovely' book promotes the simple message that we are all different and that is lovely. A beautiful celebration of diversity!"--Julie Downing, award-winning author-illustrator ("Mozart Tonight"). Full color.or.
New York Times bestselling author and host of the podcast Nurture vs Nurture Dr. Wendy Mogel shows parents how to navigate the challenging teenage years. When a child becomes a teenager, her sense of entitlement and independence grows, the pressure to compete skyrockets, and communication becomes fraught with obstacles. Dr. Wendy Mogel emphasizes empathy, and offers guidance over micromanaging teens’ lives and overreacting to missteps. She reveals that emotional outbursts, rudeness, rule-breaking, staying up late, and other worrisome teen behaviors are in fact normal and necessary steps in psychological growth and character development. With her signature wit and warmth, Mogel gives parents the tools to meet these behaviors with thoughtful care, offering reassuring advice on: · why influence is more effective than control · teenage narcissism · living graciously with rudeness · the surprising value of ordinary work · why risk is essential preparation for the post–high school years · when to step in and when to step back The Blessing of a B Minus is an important and inspiring book that fortifies parents through the teenage years.
Studies of complexity, singularity, and anomaly using nonlocal continuum models are steadily gaining popularity. This monograph provides an introduction to basic analytical, computational, and modeling issues and to some of the latest developments in these areas. Nonlocal Modeling, Analysis, and Computation includes motivational examples of nonlocal models, basic building blocks of nonlocal vector calculus, elements of theory for well-posedness and nonlocal spaces, connections to and coupling with local models, convergence and compatibility of numerical approximations, and various applications, such as nonlocal dynamics of anomalous diffusion and nonlocal peridynamic models of elasticity and fracture mechanics. A particular focus is on nonlocal systems with a finite range of interaction to illustrate their connection to local partial differential equations and fractional PDEs. These models are designed to represent nonlocal interactions explicitly and to remain valid for complex systems involving possible singular solutions and they have the potential to be alternatives for as well as bridges to existing models. The author discusses ongoing studies of nonlocal models to encourage the discovery of new mathematical theory for nonlocal continuum models and offer new perspectives on traditional models, analytical techniques, and algorithms.
New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.