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My Red Shirt and Me The red shirt incident begins with a rather ordinary red shirt. Not a brightly colored red shirt, not a dramatic cherry or firehouse red, more like a faded burgundy. But, for several days, my very iden tity was bound up in its redness. It was me, and I wore it with the pride a matador takes in his splendid cape, a hero in his medals of bravery, or a nun in her religious habit. I'll never forget the bound less joy I felt wearing that simple, pullover, short-sleeved red shirt in the hospital--or the rush of relief that I experienced when, at last, I decided to surrender it. However, we are getting ahead of our story, which starts a short time earlier with a most unfortunate accident. A light flurry of wet snow had begun to fall as the university limousine turned the corner on its way from the Bronx campus of New York University to the downtown campus. Although eight of us were packed into the car and had resigned ourselves to the usual boring faculty meeting awaiting us, somehow a spontaneous air of joviality was created.
The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.
This book addresses both probabilists working on diffusion processes and analysts interested in linear parabolic partial differential equations with singular coefficients. The central question discussed is whether a given diffusion operator, i.e., a second order linear differential operator without zeroth order term, which is a priori defined on test functions over some (finite or infinite dimensional) state space only, uniquely determines a strongly continuous semigroup on a corresponding weighted Lp space. Particular emphasis is placed on phenomena causing non-uniqueness, as well as on the relation between different notions of uniqueness appearing in analytic and probabilistic contexts.
YIS has been thought as an annual series of volumes collecting contributes aimed at developing the integration of idiographic and nomothetic approaches in psychological and more in general social science. At the beginning, 3 years ago, we got an agreement with an Italian publisher (FGP - Firera Publishing Group) interested in the scientific project and therefore willing to help the start up of this scientific enterprise. After publishing the first volume (YIS 2008- yet published in 2009 - the Volume is freely available on the FPG's website) we have had many positive feedbacks and signals of interests, as well as several submissions, from many parts of the world . This has provided an acceleration of the following issues - Above all, this led us to realize that it was time to give an editorial collocation to YIS that can be more consistent with the interest it has raised and that can ulteriorly raise. FPG does not put constraint on this perspective, being aware and agreed of the necessity of a worldwide context for the YIS's development. Moreover, there are no constraints in the possibility of going on in using the label "YIS," starting from Volume 4 The Series addresses a quite large potential public - students and researchers interested to theoretical and methodological development of psychology and, more in general, social science. Persons engaged with qualitative, dynamic informed models of analysis will find YIS a precious tool as well as a context enabling to develop a worlwide network of practices and cultures of research. The first three volumes' TOC witness how large and constantly increasing is the interest around the scientific project.
This monograph aims to fill a void by making available a source book which first systematically describes all the available uniqueness and nonuniqueness criteria for ordinary differential equations, and compares and contrasts the merits of these criteria, and second, discusses open problems and offers some directions towards possible solutions.
“Life’s journey taught me how staying inspired strengthens purposefulness, enthusiasm empowers a creative mindset for realizing possibilities, and yielding to destiny’s calling awakens the giant within. Along the way, I learned that Communication is a powerful alignment tool. Attitude decides a person’s perspective. Knowledge holds the primary resource that generates personal power when united with a vibrant vision. And Expertise confirms an individual’s dominant talent sculpted into giftedness and evidenced by moments of brilliance. This book holds unique insights for pursuing your vision while realizing your ambitions, desires, and “meant to be” calling so that you, too, can prosper beyond expectations amid the COVID-19 era.”
This book addresses the issue of uniqueness of a solution to a problem – a very important topic in science and technology, particularly in the field of partial differential equations, where uniqueness guarantees that certain partial differential equations are sufficient to model a given phenomenon. This book is intended to be a short introduction to uniqueness questions for initial value problems. One often weakens the notion of a solution to include non-differentiable solutions. Such a solution is called a weak solution. It is easier to find a weak solution, but it is more difficult to establish its uniqueness. This book examines three very fundamental equations: ordinary differential equations, scalar conservation laws, and Hamilton-Jacobi equations. Starting from the standard Gronwall inequality, this book discusses less regular ordinary differential equations. It includes an introduction of advanced topics like the theory of maximal monotone operators as well as what is called DiPerna-Lions theory, which is still an active research area. For conservation laws, the uniqueness of entropy solution, a special (discontinuous) weak solution is explained. For Hamilton-Jacobi equations, several uniqueness results are established for a viscosity solution, a kind of a non-differentiable weak solution. The uniqueness of discontinuous viscosity solution is also discussed. A detailed proof is given for each uniqueness statement. The reader is expected to learn various fundamental ideas and techniques in mathematical analysis for partial differential equations by establishing uniqueness. No prerequisite other than simple calculus and linear algebra is necessary. For the reader’s convenience, a list of basic terminology is given at the end of this book.
This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish mathematician, early in the 1920's, research in the field has developed rapidly over the past three decades with a great deal of fruitful results. This book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results. In addition, useful skills and simple proofs are introduced. This book is suitable for higher level and graduate students who have a basic grounding in complex analysis, but will also appeal to researchers in mathematics.
A self-contained introduction to the mathematical theory of black holes.
Now that the Law of Attraction is becoming well known and practiced globally, it appears that humanity is expanding to a new belief system that unlike before, is based in our heart, our passion, our feeling and love. During times of changes of any kind the question of "Who am I?" is brought to our awareness. One way or another, eventually inventory of our life is required to better understand different parts of it or altogether. This book offers you a way to explore your true self through stories and exercises. Author's hope is that it awakens different aspects of your true self and leads you to recognize and experience the power of your uniqueness as well as embrace it. All of us deserve to be in touch with our true self and this is what leads us to live the life of our dreams. The main intention for this book is to encourage you to be true to yourself, accept and love yourself! May it help you on your journey!