Series: Contemporary Mathematicians
2009, Approx. 250 p., Hardcover
ISBN: 978-3-7643-8857-7
Due: April 2009
About this book
This book presents translations of selected works of the famous Russian mathematician A.I. Shirshov (1921-1981). He was a pioneer in several directions of associative, Lie, Jordan, and alternative algebras, as well as groups and projective planes. His name is associated with notions and results on Grobner-Shirshov bases, the Composition-Diamond Lemma, the Shirshov-Witt Theorem, the Lazard-Shirshov elimination process, Shirshov’s Height Theorem, Lyndon-Shirshov words, Hall-Shirshov bases, Shirshov’s theorem on the Kurosh problem for alternative algebras, Shirshov’s theorem on Jordan algebras with two generators. Shirshov’s ideas were used by his student Efim Zelmanov for the solution of the Restricted Burnside Problem. Several famous algebraists provide a detailed comment on the impact of Shirshov’s work on current algebra.
Specialists and graduate students in algebra and computer algebra
Series: Publications of the Scuola Normale Superiore
Subseries: Theses (Scuola Normale Superiore) , Vol. 9
2009, Approx. 150 p., Softcover
ISBN: 978-88-7642-338-3
Due: November 2008
This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author. After recalling the preliminary and necessary notions of complex analysis, the survey focuses on extension of holomorphic functions (filling both compact and non-compact holes), on the reflection principle, on extension results via cohomology vanishing, and on the boundary problem. The last two subjects include detailed results by the author on non-compact extension: the cohomology of semi q-coronae and the unbounded boundary problem.
PhD students and researchers in the field of complex and CR geometry
1. Introduction.- 2. Classical extension theorems in one and several complex variables.- 3. Extension of CR-functions up to a Levi-flat boundary and of holomorphic maps.- 4. Cohomology vanishing and extension problems for semi q-coronae.- 5. Cohomology of semi 1-coronae and extension of analytic subsets.- 6. The boundary problem.- 7. Non-compact boundaries of complex analytic varieties.- 8. Semi-local extension of maximally complex submanifolds.
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Series: Sources and Studies in the History of Mathematics and Physical Sciences
2008, XXIV, 780 p. 35 illus., Hardcover
ISBN: 978-0-387-77939-3
This book presents a selection of 434 carefully annotated letters from and to the Dutch physicist and Nobel Prize winner Hendrik Antoon Lorentz (1853-1928), covering the period from 1883 until a few months before his death in February 1928. Most of these letters are of a scientific nature, with the exception of letters between Lorentz and Albert Einstein, Max Planck, Woldemar Voigt, and Wilhelm Wien during World War I, since these letters shed important light on the disruption of scientific relations during the war and on the political views of these correspondents as well as of Lorentz.
The letters are being reproduced in their original language (German, French and English), and a few Dutch drafts are accompanied by English translations.
A concise biography of Lorentz is also included, as well as a full bibliography of his writings.
Physicists, historians of science
Preface.- Letters.- General bibliography.- Lorentz bibliography.- Index.
Various types of probabilistic proof systems have played a central role in the development of computer science in the last couple of decades. These proof systems deviate from the traditional concept of a proof by introducing randomization and interaction into the verification process. Probabilistic proof systems carry an error probability (which is explicitly bounded and can be decreased by repetitions), but they offer various advantages over deterministic proof systems.
This primer concentrates on three types of probabilistic proof systems: interactive proofs, zero-knowledge proofs, and probabilistically checkable proofs (PCP). Surveying the basic results regarding these proof systems, the primer stresses the essential role of randomness in each of them.
Contents:
Preface
Conventions and Organization
Interactive Proof Systems
Zero-Knowledge Proof Systems
Probabilistically Checkable Proof Systems
Bibliographic Notes
Bibliography
Readership: Postgraduates, researchers and professors of computer science.
104pp Pub. date: Aug 2008
ISBN 978-1-60198-152-3(pbk)