Elements of Kktheory

A quantum computer is a computer based on a computational model which uses quantum mechanics, which is a subfield of physics to study phenomena at the micro level. There has been a growing interest on quantum computing in the 1990's and some quantum computers at the experimental level were recently implemented. Quantum computers enable super-speed computation and can solve some important problems whose solutions were regarded impossible or intractable with traditional computers.

This book grew out of a 2-semester graduate course in laser physics and quantum optics. It requires a solid understanding of elementary electro­ magnetism as well as at least one, but preferably two, semesters of quantum mechanics. Its present form resulted from many years of teaching and research at the University of Arizona, the Max-Planck-Institut fiir Quanten­ optik, and the University of Munich. The contents have evolved signifi­ cantly over the years, due to the fact that quantum optics is a rapidly chang­ ing field. Because the amount of material that can be covered in two semes­ ters is finite, a number of topics had to be left out or shortened when new material was added. Important omissions include the manipulation of atomic trajectories by light, superradiance, and descriptions of experiments. Rather than treating any given topic in great depth, this book aims to give a broad coverage of the basic elements that we consider necessary to carry out research in quantum optics. We have attempted to present a vari­ ety of theoretical tools, so that after completion of the course students should be able to understand specialized research literature and to produce original research of their own. In doing so, we have always sacrificed rigor to physical insight and have used the concept of "simplest nontrivial exam­ ple" to illustrate techniques or results that can be generalized to more com­ plicated situations.

Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

This book attempts to present the concepts which underlie the various optimization procedures which are commonly used. It is written primarily for those scientists such as economists, operations researchers, and en­ gineers whose main tools of analysis involve optimization techniques and who possess a (not very sharp) knowledge of one or one-and-a-half year's calculus through partial differentiation and Taylor's theorem and some acquaintance with elementary vector and matrix terminology. Such a scientist is frequently confronted with expressions such as Lagrange multi­ pliers, first-and second-order conditions, linear programming and activity analysis, duality, the Kuhn-Tucker conditions, and, more recently, dy­ namic programming and optimal control. He or she uses or needs to use these optimization techniques, and would like to feel more comfortable with them through better understanding of their underlying mathematical concepts, but has no immediate use for a formal theorem-proof treatment which quickly abstracts to a general case of n variables and uses a style and terminology that are discouraging to people who are not mathematics majors.

Deals with photonics in free space and special media such as anisotropic crystals.
* Covers all important topics from Fourier optics, such as the properties of lenses, optical image processing, and holography to the Gaussian beam, light propagation in anisotropic media, external field effects, polarization of light and its major applications.

Intégration is the sixth and last of the Books that form the core of the Bourbaki series; it draws abundantly on the preceding five Books, especially General Topology and Topological Vector Spaces, making it a culmination of the core six. The power of the tool thus fashioned is strikingly displayed in Chapter II of the author's Théories Spectrales, an exposition, in a mere 38 pages, of abstract harmonic analysis and the structure of locally compact abelian groups.

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