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The present volume contains the proceedings of the workshop on "Minimax Theory and Applications" that was held during the week 30 September - 6 October 1996 at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Cul ture in Erice (Italy) . The main theme of the workshop was minimax theory in its most classical meaning. That is to say, given a real-valued function f on a product space X x Y, one tries to find conditions that ensure the validity of the equality sup inf f(x, y) = inf sup f(x, y). yEY xEX xEX yEY This is not an appropriate place to enter into the technical details of the proofs of minimax theorems, or into the history of the contribu tions to the solution of this basic problem in the last 7 decades. But we do want to stress its intrinsic interest and point out that, in spite of its extremely simple formulation, it conceals a great wealth of ideas. This is clearly shown by the large variety of methods and tools that have been used to study it. The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this volume will offer a rather complete account of the state of the art of the subject."
'I think I'm a human being before anything else. I don't care what other people say. I don't care what people write in books. I need to think for myself.' Henrik Ibsen's A Doll's House premiered in 1879 in Copenhagen, the second in a series of realist plays by Ibsen, and immediately provoked controversy with its apparently feminist message and exposure of the hypocrisy of Victorian middle-class marriage. In Ibsen's play, Nora Helmer has secretly (and deceptively) borrowed a large sum of money to pay for her husband, Torvald, to recover from illness on a sabbatical in Italy. Torvald's perception of Nora is of a silly, naive spendthrift, so it is only when the truth begins to emerge, and Torvald appreciates the initiative behind his wife, that unmendable cracks appear in their marriage. This compelling new version of Ibsen's masterpiece by playwright Simon Stephens premiered at the Young Vic Theatre, London, on 29 June 2012. It was updated with minor changes in 2013.
The present volume contains the proceedings of the workshop on "Minimax Theory and Applications" that was held during the week 30 September - 6 October 1996 at the "G. Stampacchia" International School of Mathematics of the "E. Majorana" Centre for Scientific Cul ture in Erice (Italy) . The main theme of the workshop was minimax theory in its most classical meaning. That is to say, given a real-valued function f on a product space X x Y, one tries to find conditions that ensure the validity of the equality sup inf f(x, y) = inf sup f(x, y). yEY xEX xEX yEY This is not an appropriate place to enter into the technical details of the proofs of minimax theorems, or into the history of the contribu tions to the solution of this basic problem in the last 7 decades. But we do want to stress its intrinsic interest and point out that, in spite of its extremely simple formulation, it conceals a great wealth of ideas. This is clearly shown by the large variety of methods and tools that have been used to study it. The applications of minimax theory are also extremely interesting. In fact, the need for the ability to "switch quantifiers" arises in a seemingly boundless range of different situations. So, the good quality of a minimax theorem can also be judged by its applicability. We hope that this volume will offer a rather complete account of the state of the art of the subject."
In this new edition of LNM 1693 the essential idea is to reduce questions on monotone multifunctions to questions on convex functions. However, rather than using a ?big convexification? of the graph of the multifunction and the ?minimax technique?for proving the existence of linear functionals satisfying certain conditions, the Fitzpatrick function is used. The journey begins with a generalization of the Hahn-Banach theorem uniting classical functional analysis, minimax theory, Lagrange multiplier theory and convex analysis and culminates in a survey of current results on monotone multifunctions on a Banach space. The first two chapters are aimed at students interested in the development of the basic theorems of functional analysis, which leads painlessly to the theory of minimax theorems, convex Lagrange multiplier theory and convex analysis. The remaining five chapters are useful for those who wish to learn about the current research on monotone multifunctions on (possibly non reflexive) Banach space.
There have been five central crises in America's post World War II
encounter with the Middle East, and the Obama administration now
faces a sixth. Iran's progress toward a nuclear weapons capability,
and the prospect of Israel launching air strikes to stop it, are
ingredients for a conflict that could ruin any residual hopes for
fostering peace in the region.
"A persuasive and utterly frightening picture of the current state
of America's war on terror."--Michiko Kakutani, The New York
Times
From two of the world’s foremost experts on the new terrorism comes the definitive book on the rise of al-Qaeda and America’s efforts to combat the most innovative and dangerous terrorist group ever. Daniel Benjamin and Steven Simon trace the growth of radical Islam from its medieval origins and, drawing on their years of counter-terrorism work at the National Security Council, provide essential insights into the thinking of Usama bin Laden and his followers. With unique authority, they analyze why America was unable to defend itself against this revolutionary threat on September 11, 2001, why bin Laden’s apocalyptic creed is gaining ground in the Islamic world, and what the United States must do to stop the new terror.
Chris Neilson (Robin Williams) is robbed of his blissful life with his wife Annie (Annabella Sciorra) when he dies in a car crash. His ghost is allowed to keep in touch with Annie by residing in one of her paintings, but both parties remain frustrated by the mortal divide between them. When Annie kills herself, however, she is not allowed to join her husband, as all suicides go to hell. Chris determines to rescue his loved one from eternal damnation, enlisting the help of the Tracker (Max von Sydow) and Albert (Cuba Gooding Jr) to do so.
Would you like to discover a new world of movies that expands your
mind, warms your hearts and stirs your soul? If so, this book is
sure to become a valuable resource for you. Here you will find a
treasure trove of films that inspire you and celebrate every aspect
of the human spirit." Spiritual Cinema" asks the big questions
about life and living: "Who are we? Why are we here?" "Where are we
bound? "and "What can we become when we live at our highest level
of potential? "
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