Vector bundles

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  • The protocol wars are over and TCP/IP won. TCP/IP is now universally recognized as the pre-eminent communications protocol for linking together diverse computer systems. The importance of interoperable data communications and global computer networks is no longer debated. But that was not always the case. When I wrote the first edition of this book, IPX was far and away the leading PC communications protocol. Microsoft did not bundle communications protocols in their operating system.

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  • The purpose of this paper is to carry out the abelianization program proposed by Atiyah [1] and Hitchin [9] for the geometric quantization of SU(2) Wess-Zumino-Witten model. Let C be a Riemann surface of genus g. Let Mg be the moduli space of semi-stable rank 2 holomorphic vector bundles on C with trivial determinant. For a positive integer k, let Γ(Mg , Lk ) be the space of holomorphic sections of the k-th tensor product of the determinant line bundle L on Mg . An element of Γ(Mg , Lk ) is called a rank 2 theta function...

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  • Given a holomorphic vector bundle E over a compact K¨hler manifold X, a one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f : Σ → X with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle H 0 (Σ, f ∗ E) H 1 (Σ, f ∗ E). Using the formalism of quantized quadratic Hamiltonians [25], we express the descendant potential for the twisted theory in terms of that for X. ...

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  • This paper should be regarded as a sequel to [7]. There it was shown that the geometric Langlands conjecture for GLn follows from a certain vanishing conjecture. The goal of the present paper is to prove this vanishing conjecture. Let X be a smooth projective curve over a ground field k. Let E be an m-dimensional local system on X, and let Bunm be the moduli stack of rank m vector bundles on X.

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  • We assume that the manifold with boundary, X, has a SpinC -structure with spinor bundle S Along the boundary, this structure agrees with the /. structure defined by an infinite order, integrable, almost complex structure and the metric is K¨hler. In this case the SpinC -Dirac operator . agrees with a ¯ ¯ ∂ + ∂ ∗ along the boundary. The induced CR-structure on bX is integrable and either strictly pseudoconvex or strictly pseudoconcave.

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  • Israel Moiseevich Gelfand is one of the greatest mathematicians of the 20th century. His insights and ideas have helped to develop new areas in mathematics and to reshape many classical ones. The influence of Gelfand can be found everywhere in mathematics and mathematical physics from functional analysis to geometry, algebra, and number theory. His seminar (one of the most influential in the history of mathematics) helped to create a very diverse and productive Gelfand school; indeed, many outstanding mathematicians proudly call themselves Gelfand disciples....

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  • Over the years, CorelDRAW has developed into a full-featured, professional suite of graphics applications for users of all skill levels to create illustrations, design professional layouts, and work seamlessly between pixel-based and vector graphics, with powerful editing tools in a completely integrated, easy-to-use bundle. The team at Corel continues to strive to provide products that both delight and inspire users around the world with the release of CorelDRAW Graphics Suite X4 and this new Official Guide....

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  • Getting Started with Open Office .org 3 part 43. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 3. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 4. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 1. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 2. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 5. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 6. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 7. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 8. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 9. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 10. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 11. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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  • Getting Started with Open Office .org 3 part 12. This Manual Book is for anyone who wants to get up to speed quickly with the latest OpenOffice.org version 3.0. “GETTING STARTED WITH OpenOffice.org 3.0″ introduces all software programs of the OpenOffice bundle: Writer (word processing), Calc (spreadsheets), Impress (presentations), Draw (vector drawings), Math (equation editor) and Base (database). This book was written by volunteers from the OpenOffice.org community working through OOoAuthors.org and is distributed under the CreativeCommon Attribution Licence 3.0....

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