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This monograph covers the existing results regarding Green’s functions for differential equations with involutions (DEI).The first part of the book is devoted to the study of the most useful aspects of involutions from an analytical point of view and the associated algebras of differential operators. The work combines the state of the art regarding the existence and uniqueness results for DEI and new theorems describing how to obtain Green’s functions, proving that the theory can be extended to operators (not necessarily involutions) of a similar nature, such as the Hilbert transform or projections, due to their analogous algebraic properties. Obtaining a Green’s function for these operators leads to new results on the qualitative properties of the solutions, in particular maximum and antimaximum principles.
Suitable for advanced undergraduates and graduate students, this was the first English-language text to offer detailed coverage of boundedness, stability, and asymptotic behavior of linear and nonlinear differential equations. It remains a classic guide, featuring material from original research papers, including the author's own studies. The linear equation with constant and almost-constant coefficients receives in-depth attention that includes aspects of matrix theory. No previous acquaintance with the theory is necessary, since author Richard Bellman derives the results in matrix theory from the beginning. In regard to the stability of nonlinear systems, results of the linear theory are u...
Yawning is a stereotyped phylogenetically ancient phenomenon that occurs in almost all vertebrates. As an emotional behavior and an expressive movement, yawning has many consequences; nevertheless, it has so far been poorly addressed in medical research and practice. Bringing together the latest research from many fields, this volume integrates current insights within embryology, ethology, neurophysiology, psychology, fMRI and pathology. The phylogenetic and ontogenetic aspects of yawning offer an interesting perspective on human development, and its occurrence in neurological diseases - an area explored by only a few investigators - may provide useful clinical information. This book will make valuable and fascinating reading to neurologists, sleep specialists, psychologists, ethologists and pharmacologists, as well as to anybody interested in uncovering the mystery of yawning.
Learn how fashion developed in Britain from the early 1970s, when designer fashion scarcely existed, to the present day, when London ranks alongside Paris, New York and Milan as a global fashion capital.
In its 114th year, Billboard remains the world's premier weekly music publication and a diverse digital, events, brand, content and data licensing platform. Billboard publishes the most trusted charts and offers unrivaled reporting about the latest music, video, gaming, media, digital and mobile entertainment issues and trends.
Sobolev spaces are a fundamental tool in the modern study of partial differential equations. In this book, Leoni takes a novel approach to the theory by looking at Sobolev spaces as the natural development of monotone, absolutely continuous, and BV functions of one variable. In this way, the majority of the text can be read without the prerequisite of a course in functional analysis. The first part of this text is devoted to studying functions of one variable. Several of the topics treated occur in courses on real analysis or measure theory. Here, the perspective emphasizes their applications to Sobolev functions, giving a very different flavor to the treatment. This elementary start to the ...