With the vacancy of the flowers, and the ambient smell of quietus; Death is always swaying to the curve of the execution of life. With the daunting groove of mankind during World War II; Death sits there in all of its emptiness and counts the myriad of seconds as it waits for the velvet narcotics to kick in. It lays there in its pool of indecisive love and tries to indulge in every little detail and story that falls halfway between ecstasy and a boy named Henri Tomasz.
Singularity theory is a far-reaching extension of maxima and minima investigations of differentiable functions, with implications for many different areas of mathematics, engineering (catastrophe theory and the theory of bifurcations), and science. The three parts of this first volume of a two-volume set deal with the stability problem for smooth mappings, critical points of smooth functions, and caustics and wave front singularities. The second volume describes the topological and algebro-geometrical aspects of the theory: monodromy, intersection forms, oscillatory integrals, asymptotics, and mixed Hodge structures of singularities. The first volume has been adapted for the needs of non-mathematicians, presupposing a limited mathematical background and beginning at an elementary level. With this foundation, the book's sophisticated development permits readers to explore more applications than previous books on singularities.
... there is nothing so enthralling, so grandiose, nothing that stuns or captivates the human soul quite so much as a first course in a science. After the first five or six lectures one already holds the brightest hopes, already sees oneself as a seeker after truth. I too have wholeheartedly pursued science passionately, as one would a beloved woman. I was a slave, and sought no other sun in my life. Day and night I crammed myself, bending my back, ruining myself over my books; I wept when I beheld others exploiting science fot personal gain. But I was not long enthralled. The truth is every science has a beginning, but never an end - they go on for ever like periodic fractions. Zoology, for example, has discovered thirty-five thousand forms of life ... A. P. Chekhov. "On the road" In this book a start is made to the "zoology" of the singularities of differentiable maps. This theory is a young branch of analysis which currently occupies a central place in mathematics; it is the crossroads of paths leading from very abstract corners of mathematics (such as algebraic and differential geometry and topology, Lie groups and algebras, complex manifolds, commutative algebra and the like) to the most applied areas (such as differential equations and dynamical systems, optimal control, the theory of bifurcations and catastrophes, short-wave and saddle-point asymptotics and geometrical and wave optics).
This is a compact guide to the principles and main applications of Singularity Theory by one of the world’s top research groups. It includes a number of new results as well as a carefully prepared and extensive bibliography that makes it easy to find the necessary details. It’s ideal for any mathematician or physicist interested in modern mathematical analysis.
Professor Arnold is a prolific and versatile mathematician who has done striking work in differential equations and geometrical aspects of analysis. In this volume are collected seven of his survey articles from Russian Mathematical Surveys on singularity theory, the area to which he has made most contribution. These surveys contain Arnold's own analysis and synthesis of a decade's work. All those interested in singularity theory will find this an invaluable compilation. Professor C. T. C. Wall has written an introduction outlining the significance and content of the articles.
Wings of the White Crane is unquestionably the most unusual and sensational of all the books by or about Tibetan Buddhists yet to appear in English. Westerners previously baffled by the Tibetan mind will have no difficulty in finding sympathy with the sixth Dalai Lama, a spiritual pope to the Tibetan Buddhists of his time, who poured o0ut his very human heart into these simple, eloquent, often erotic songs of lovers lost and found, and of his inner conflicts as a monk. Most older Tibetans know all these fifty- three poems by memory sunce all humans everywhere know what the strife of love can bring .
Bifurcation theory and catastrophe theory are two well-known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, previously published as Volume 5 of the Encyclopaedia, have given a masterly exposition of these two theories, with penetrating insight.
SUMMATION OF A POPULAR WAR Author V. I. Brown wrote this memoir from authority. He grew up with the war, participated as a member of the military and then observed its aftermath. He provides a penetrating, chronological examination of the wars policies, politics, judicial decisions, public opinion and reflection in the popular culture. As he examines such complex topics as anti-war sentiment, dissent within the military and the galvanizing of the clergy against the war, Brown offers an in-depth glimpse into the turmoil and emotions spawned by the war that gripped the nation for over a decade. Herein one will find a more complete chronological examination of the Vietnam Conflict than has previously been available. All of the factors which compelled the U. S. to intervene in a foreign civil war are spelled out in vivid detail from the wars inception to its termination. Also examined is the climate within the national and international communities which led up to the conflict. This book details how the war was an exercise in deception, in futility, in the power of ego and also a lesson in how the U.S. contradicted its own ideals. Further, the author affirms what others including CBS News and The New York Times contended during and after the conflict: that the government almost continually promulgated deceptive information in order to justify continued pursuit of the war. In the end the reader will comprehend that it was all for nothing, and indeed that the former enemy earned what a U. S. President wanted for Vietnam. Herein one will further observe the wars impact on the lives of the many players in the comdie, both major and minor, who were elevated to the stage of one of the great events of history. The degree to which the war reverberates in U. S. society is also examined in detail. As of this writing, the war is still in the national consciousness.
As a result of the generally low quality of child care in the United States, quality rating and improvement systems (QRISs) are proliferating in the child-care arena. This study examines the QRIS developed by Qualistar Early Learning, a nonprofit organization based in Colorado, evaluating how reliable the system's components are, whether the QRIS process helped providers to improve, and whether and how much children benefit from such improvement.
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