Block decompositions

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  • The Fourier transform and its extensions have historically been the prime vehi- cle for signal analysis and representation. Since the early 1970s, block transforms with real basis functions, particularly the discrete cosine transform (DCT), have been studied extensively for transform coding applications. The availability of simple fast transform algorithms and good signal coding performance made the DCT the standard signal decomposition technique, particularly for image and video. The international standard image-video coding algorithms, i.e., CCITT...

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  • This is a book I wished I had found when, many years ago, I first learned the subject of ring theory. All those years have flown by, but I still did not find that book. So finally I decided to write it myself. All the books I have written so far were developed from my lectures; this one is no exception. After writing A First Course in Noncommutative Rings (Springer-Verlag GTM 131, hereafter referred to as “FC ”), I taught ring theory in Berkeley again in the fall of 1993, using FC as text. Since the main theory is already fully developed in FC, I asked my...

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  • Combinatorics is generally concerned with counting arrangements within a finite set. One of the basic problems is to determine the number of possible configurations of a given kind. Even when the rules specifying the configuration are relatively simple, the questions of existence and enumeration often present great difficulties. Besides counting, combinatorics is also concerned with questions involving symmetries, regularity properties, and morphisms of these arrangements. The theory of block designs is an important area where these facts are very apparent.

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