Beginning with the work of Grothendiek, the theory of motives is, very loosely speaking, an attempt at a "unified theory" of number theory and algebraic geometry. This years Fields Medals reflect the interest in motives, as one of the authors in this book (Voevodsky) was awarded for his research in this area. In a gist, this book tries to see how much of (standard) algebraic topology can be carried over to the study of algebraic varieties and schemes. By defining a new topology on algebraic cycles, the "qfh topology", Voevodsky showed that the techniques of sheaf theory can be used to study them from the standpoint of algebraic topology. This topology is finer than the etale topology and allows one to use sheaf cohomology to study algebraic cycles. The reader will be expected to have a substantial background in the theory of schemes, higher K-theory, algebraic topology, and sheaf theory. Reading this book will give one a deep appreciation of how difficult it is to do algebraic topology in algebraic geometry, requiring formidable technical machinery.

The use of K-theory in topology and algebra goes back half a century, beginning with the K-theory of CW-complexes and the construction of Atiyah and Hirzebruch of spectral sequences relating singular cohomology to topological K-theory. The K-theory of algebraic varieties is a little more subtle, and involves looking at the isomorphism classes of algebraic vector bundles on the variety. These form an abelian group with the group operation being defined via the existence of an exact sequence between the isomorphism classes.

As a warm-up to the scheme-theoretic setting, the K-theory of an arbitrary ring proceeds by analogy with the simplicial setting, the latter of which involves the classifying space of homotopy maps of the complex and the notion of stable equivalence. But for a general ring, the unit interval used in the definition of homotopy is replaced by the affine line. The work of Karoubi and Villamayor, and Quillen defined precisely higher algebraic K-theory for rings, the former using this simplicial motivation, the latter using what is called a "Q-construction". The definitions coincide for regular schemes but not for singular ones.

Motivic cohomology, which is an algebraic analog of singular cohomology, arose in the setting of the Chow ring of algebraic cycles modulo rational equivalence. A homology theory of the free abelian group of algebraic cycles of a variety, with the replacement of the unit interval with the affine line, was developed. The products existing in cohomology arise from the consideration of the intersection of subvarieties, leading to the familiar Chow ring. The Chow ring is functorial under pull-backs, and can be related to the zeroth K-group via the use of the Chern class and the Riemann-Roch theorem. The higher K-groups of Quillen give the desired long exact sequence of K-groups.

Bloch then defined motivic cohomology via the construction of higher Chow groups, again by analogy to the simplicial theory, and with a careful definition of intersection product, so as to insure the algebraic cycles intersect the faces in the correct codimension. It was then shown that the higher Chow groups are related to the the higher K-groups for a variety which is smooth over a field.

One of the authors (Frielander) and Dwyer, using the etale cohomology of Grothendieck, gave a mod-n topological K-theory, called etale K-theory, which led to the work of Suslin and Voevodsky on the motivic homology of algebraic cycles, which is the main focus of this book.

After a brief introduction to motivic cohomology in chapter 1 and an historical introduction, the second chapter deals with relative cycles on schemes and Chow sheaves. Relative cycles are defined for schemes of finite type over a Noetherian (base) scheme and are well-behaved for morphisms of of the base scheme. The authors concentrate most of their attention not to general schemes but to varieties over a field. The cdh-topology is introduced here as one which allows the construction of long exact sequences for sheaves of relative cycles.

Chapter 3 overviews the cohomological theory of presheaves and defines the notion of a transfer map. For smooth schemes over a field, these maps are used to define a "pretheory" over the field, and homotopy invariance of pretheories can then be defined. Examples of pretheories include etale cohomology, algebraic K-theory, and algebraic de Rham cohomology. The Mayer-Vietoris exact sequence for the Suslin homology is proven, giving another analogue of ordinary algebraic topology.

In chapter 4 the authors consider the generalization of the duality property of homology and cohomology in algebraic topology using bivariant cycle cohomology. The bivariant cycle cohomology groups are defined for schemes of finite type over a field in terms of the higher Chow groups. They have the origin in the generalization of the simplicial theory to the algebraic geometry setting. Homotopy invariance, suspension maps, and the Gysin sequence find their place here also. The authors detail to what extent the higher Chow groups can be considered to be a motivic cohomology theory. Motivic homology, motivic cohomology, and Borel-Moore motivic cohomology are shown to be related to the bivariant cycle cohomology and their algebraic topological properties discussed briefly.

Chapter 5 studies algebraic cycle cohomology theories categorically via the construction of triangulated categories of motives. This is the key step in allowing the techniques of (ordinary) sheaf cohomology to be applied to the category of motives. The discussion is done in the context of smooth schemes, but it would be interesting if the authors would have given some concrete examples, possibly with elliptic curves, showing how these constructions come into play for elementary algebraic varieties.

The book ends with a discussion of the higher Chow groups and how they relate to etale cohomology. A relatively concrete presentation, the author proves the equality between the higher Chow groups and etale cohomology with compact supports for quasiprojective schemes over algebraically closed fields of characteristic zero.

I have to admit I only read the Russian original, so I was pretty puzzled and pleased to discover that author Vladimir Orlov acted as a translator of his own work. When I grew up in the early 80s' Soviet Russia, _Danilov: The Violist_ was a must read for all intellectual young Russian people, a true cult book. Combining bitter realism with humorous fantasy in quite an entertaining way, the story focuses on a gifted musician (Danilov) struggling with both his creative inhibitions and the bureaucratic ones, those of the strictly controlled Soviet artistic world. Danilov's gradual discovery of his own talent is something any creative person can relate to, be they American, Russian or Japanese -- even if you neglect the fact that Danilov is, in fact... half demon. Not a traditional ugly evil-doer one foot in Hell, but just the unlucky result of a (quite common, if you believe Orlov :-)) love affair between a human and a demon. As such, he belongs neither on Earth nor in the Next (sort of parallel) World and has to deal with both -- defending himself, his art and the relationships he develops against both worlds' cynical bureaucratic systems. On the safe Earth, Danilov's creativity and honesty are tested -- away from it, in a magical universe that just for fun copycats human development and culture, his very existence is doubted and endangered. In all his tribulations, Danilov has to choose between honesty and career, hate and understanding, love and betrayal. While the novel can't boast any of the universal philosophical revelations of Mikhail Bulgakov's Master and Margarita -- its obvious predecessor in style and subject matter -- _Danilov: The Violist_ is funny, easy to read and makes the reader think. To a non-Russian reader the book has an added plus of giving a very realistic and detailed picture of the everyday life in the 60s-80s Soviet Union, full of humor and understanding. In three words -- funny, honest, and cleverly written.

The term 'dictatorship of the proletariat' is so obscured by its history of reversed meaning amid the semantic misfortunes it has suffered at the hands of all parties since its first limited usage by Marx and Engels, as to be a case study in semantic catastrophe. Hal Draper valiantly traces the way in which the early usages, in the generation of 1848, not at first counterposed to the term 'democracy, later become fatally misleading and are finally appropriated in the Leninist and final Stalinist versions. This actual history is so tricky that I would not contribute further to short clarifications perpetuating confusion by summarizing the book here, and one can only recommend reading the details, since short summaries and official corrections and clarifications trying to get the matter straight are themselves part of the confusion. Suffice it to say that Marx's occasional references were quite innocent of the later interpretations of the phrase. This book should be required reading for anyone attempting to plot against the government.

What a feast of imagination! My daughter (7) really enjoyed that book. Now she is in the middle of her own discovery of New York but her eyes were opened even wider by the book. Such a delight to have Joseph Brodsky addressing young children. I'm ashamed to call Radunsky's work illustrations. The book was created by what journalists call "fresh pair of eyes," even two pairs! Thanks for the book.

This book is so far the most complete reference of the transform "discrete cosine transform". We can see the author's time and effort by only looking at the reference section (more then 200+ references). This book outlines different algorithms for computing 1D, 2D DCT, IDCT, some includings FORTRAN codes. Without this book, collecting all the existing journals about DCT will probably takes several months. This book is good for novices about DCT, as well as good for experts.

Book provides a comprehensive overview of the structure and properties of electret materials used in engineering, medicine, and biotechnology. Starting with a discussion of traditional applications such as acoustic transducers and filters, it then moves on to more novel uses. Their use as anticorrosion and polymer coating technique is examined as well as their role in the lubrication of friction joints. Biological and medical applications are also covered before the final chapter looks into economic and ecological aspects of these materials.

I consider that this book is one of the most interesting book about friction of polymeric materials. The book contains new research results and analysis and review of published ones in this scientific area.

I have been stunned by how beautiful these two books by Bagirov are. I have become used to the cranked out works you see nowadays. These works, although fairly recent (1994 and 1995) hearken back to days of Polugayevsky, when books were written as labors of love, with tremedous care and depth. These books on the English are very special, and should be sought and bought. They go into tremedous depth, but also have constant explanatory textual comments.

I have been a professional jazz musician for as long as I remember. But it wasn't untill the concert in 1964 just before Eric Dol;phy died that I became serious in my approach to practice. The concert took place in Wuppertal in Germany with Charles Mingus. Johnny Coles was on Trumpet, Jacky Byard on piano. The others I forget. Danny Richmond on drums. The audience was so jammed into the town hall that everybody was standing for the entire performance. It was such a moving experience that there was almost no applause. This must have been very disturbing to the musicians. At one point Erics Bass Clarinet fell off its stand and he spent no little time examining it to make sure it was ok. The concert was an experience that I will never forget because it quite literaly changed my life. This was because of one tune that Dolphy and Mingus played as an encore , also as a duet on flute and arco bass. This was "what love" So wonderful was this presentation that people where openly crying with emotion. It is perhaps difficult to explain the impact of musicians who can bring about such feelings in an audience. and it is indeed a rare thing to experience within any artistic performance. To listen to artists on record does not do the true greats justice. Suffice to say that for me I became a serious jazz musician from that day forward. People. myself included where still choked up even after leaving the town hall and walking out into the afternoon sunshine. Little did we know how prophetic our tears were because less than one month later Eric Dolphy died in Berlin. I can only owe this wonderful human being, Eric Dolphy a reason and a shape for all of my life. from that day untill whenever. Grahame Rhodes Jazz Musician Sat 13 march 1999

I haven't gotten to "The Long Road Ahead" yet, but the first novella, "Escape Hatch" was so moving and engrossing that I finished it (after an intense morning with it glued to my fingers) changed. What struck me most about the work is how it refuses to pass judgement on its characters-- no one is good or evil, but everyone is lost, everyone is stuck in a world they don't want to be in. And the passages with the retarded son were especially touching. Read this story.