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Two Strand Twist Picture
 Hopper by Mark Strand, As Adam Gopnik has said about this book, "Mark Strand looks more deeply into Hopper's pictures than anyone has before." In the page or two that accompanies each of the 32 paintings -- including "Nighthawks, " "Gas 1940, " "People in the Sun, " "Automat" -- Strand leads us into an astonishingly complex and aesthetically satisfying way of seeing that particular work and the whole of Hopper's oeuvre. Approaching a painting visually, or formally, he subtly draws us to a place where what the painting has to say us is free of the usual sociological or psychological terms in which Hopper is discussed. In Strand's own words he shows that "Hopper's paintings locate the viewer in a virtual space where the influence and availability of feeling predominate." "Hopper" is a gift to anyone who is interested in the painter, or in fact in any painter -- it expands the way we look at a work of art.
 Twisted L-Functions and Monodromy by Nicholas M. Katz, X For hundreds of years, the study of elliptic curves has played a central role in mathematics. The past century in particular has seen huge progress in this study, from Mordell's theorem in 1922 to the work of Wiles and Taylor-Wiles in 1994. Nonetheless, there remain many fundamental questions where we do not even know what sort of answers to expect. This book explores two of them: What is the average rank of elliptic curves, and how does the rank vary in various kinds of families of elliptic curves? Nicholas Katz answers these questions for families of ''big'' twists of elliptic curves in the function field case (with a growing constant field). The monodromy-theoretic methods he develops turn out to apply, still in the function field case, equally well to families of big twists of objects of all sorts, not just to elliptic curves. The leisurely, lucid introduction gives the reader a clear picture of what is known and what is unknown at present, and situates the problems solved in this book within the broader context of the overall study of elliptic curves. The book's technical core makes use of, and explains, various advanced topics ranging from recent results in finite group theory to the machinery of l-adic cohomology and monodromy. "Twisted L-Functions and Monodromy is essential reading for anyone interested in number theory and algebraic geometry.
Picture-in-picture - Picture in Picture (PiP) allows you to watch more than one TV program(channel) at the same time on television sets or other devices. With PiP feature of TV, one program will be displayed on the entire TV screen, and another program or programs will be displayed in individual smaller squares on the screen. Interaction picture - In quantum mechanics, the Interaction picture (or Dirac picture) is an intermediate between the Schrödinger picture and the Heisenberg picture. Whereas in the other two pictures either the state vector or the operators carry time dependence, in the interaction picture both carry part of the time dependence of observables. Strand, Cape Town - Strand (usually refered to as The Strand- in Afrikaans as Strand or Die Strand), is a seaside resort town situated on the eastern edge of False Bay between Maccasser and Gordons Bay, about 50 km southeast of Cape Town, in the Western Cape Province of South Africa. It is now regarded as part of the greater city of Cape Town itself and is 10 km away from the inland town of Somerset West. Sandymount Strand - Sandymount Strand is a large strand on the east coast of Ireland, adjacent to the village/suburb of Sandymount in Dublin, Republic of Ireland. The strand forms the south side of Dublin Bay.
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