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Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudohol...
The 2008 U.S. presidential campaign offered a unique opportunity to evaluate the usefulness and applicability of social media technology in the American political environment. This study's assessment of the role that social media played during the 2008 U.S. presidential campaign confirms some widely held tenets of conventional wisdom about social media, but it also indicates that the role of social media as the new sine qua non of American politics is far from certain.
The most lauded playwright in American history, Eugene O'Neill (1888-1953) won four Pulitzer Prizes and a Nobel Prize for a body of work that includes The Iceman Cometh, Mourning Becomes Electra, Desire Under the Elms, and Long Day's Journey into Night. His life, the direct source for so much of his art, was one of personal tumult from the very beginning. The son of a famous actor and a quiet, morphine-addicted mother, O'Neill had experienced alcoholism, a collapse of his health, and bouts of mania while still a young man. Based on years of extensive research and access to previously untapped sources, Sheaffer's authoritative biography examines how the pain of O'Neill's childhood fed his desire to write dramas and affected his artistically successful and emotionally disastrous life.
This volume is based on PDE courses given by the authors at the Courant Institute and at the University of Notre Dame, Indiana. Presented are basic methods for obtaining various a priori estimates for second-order equations of elliptic type with particular emphasis on maximal principles, Harnack inequalities, and their applications. The equations considered in the book are linear; however, the presented methods also apply to nonlinear problems.
Nature tries to minimize the surface area of a soap film through the action of surface tension. The process can be understood mathematically by using differential geometry, complex analysis, and the calculus of variations. This book employs ingredients from each of these subjects to tell the mathematical story of soap films. The text is fully self-contained, bringing together a mixture of types of mathematics along with a bit of the physics that underlies the subject. The development is primarily from first principles, requiring no advanced background material from either mathematics or physics. Through the Maple applications, the reader is given tools for creating the shapes that are being ...
Discover a beacon of hope and healing in "The Conquest of Cancer" by H. W. S. Wright, a groundbreaking exploration of humanity's ongoing battle against one of the most formidable diseases of our time. Join H. W. S. Wright as he delves into the frontiers of medical science and human resilience, offering readers a comprehensive look at the history, progress, and future prospects of cancer research and treatment. With his insightful analysis and compassionate storytelling, Wright sheds light on the complexities of cancer and the tireless efforts of scientists, doctors, and patients to overcome this devastating illness. As you journey through the pages of "The Conquest of Cancer," you'll encount...
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