41. Mirror Symmetry Workshop given such a manifold B without singularities, one obtains easily from it two manifolds one symplectic and one complex. These form a mirror pair. http://www.math.lsa.umich.edu/~crenzo/mg/gross.html

Affine manifolds and Mirror Symmetry Workshop April 25 - 27, 2008 University of Michigan Ann Arbor, Michigan Outside Participants Ann Arbor University of Michigan Mathematics Department Airport shuttle number: (reserve 24h in advance) Organizers Renzo Cavalieri Hannah Markwig For website problems, contact webmaster This year the goal of the workshop is to try and get a grasp of the circle of ideas contained in recent work of Mark Gross and Bernd Siebert: Affine manifolds, log structures, and mirror symmetry (survey) The SYZ conjectures: from torus fibrations to degenerations (survey) From real affine geometry to complex geometry The Gross-Siebert mirror symmetry program, inspired by the Strominger-Yau-Zaslow conjecture, builds on the idea that the fundamental objects controllingmirror symmetry are integral affine manifolds: real manifolds with transition maps being integral affine transformations. In toy situations, given such a manifold B without singularities, one obtains easily from it two manifolds: one symplectic and one complex. These form a mirror pair. However, this leads to few interesting examples, and B must be allowed to have singularities where the affine structure is not defined in order to get interesting examples of mirror symmetry, such as for hypersurfaces in toric varieties.

42. Gas Handling Equipment: Gas Cylinder Enclosures, Source Manifolds, And Panels Gas Handling Equipment. •, Gas Purification Systems. •, SEMIGAS® Special Delivery Equipment. •, Gas Cylinder Enclosures, Source manifolds, and Panels http://www.mathesontrigas.com/gas-cylinder-enclosures-source-manifolds-and-panel

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43. AN INTRODUCTION TO DIFFERENTIAL MANIFOLDS Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups http://www.worldscibooks.com/mathematics/p285.html

Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... Join Our Mailing List AN INTRODUCTION TO DIFFERENTIAL MANIFOLDS by (University of Cambridge, UK) This invaluable book, based on the many years of teaching experience of both authors, introduces the reader to the basic ideas in differential topology. Among the topics covered are smooth manifolds and maps, the structure of the tangent bundle and its associates, the calculation of real cohomology groups using differential forms (de Rham theory), and applications such as the Poincaré–Hopf theorem relating the Euler number of a manifold and the index of a vector field. Each chapter contains exercises of varying difficulty for which solutions are provided. Special features include examples drawn from geometric manifolds in dimension 3 and Brieskorn varieties in dimensions 5 and 7, as well as detailed calculations for the cohomology groups of spheres and tori. Contents: Differential Manifolds and Differentiable Maps The Derivatives of Differentiable Maps Fibre Bundles Differential Forms and Integration The Exterior Derivative De Rham Cohomology Degrees, Indices and Related Topics

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45. Vacuum Manifolds SigmaAldrich Online Catalog Product List Vacuum manifolds. http://www.sigmaaldrich.com/catalog/search/TablePage/12873366

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46. Regularized Principal Manifolds Your browser may not have a PDF reader available. Google recommends visiting our text version of this document. http://www.springerlink.com/index/88tufxjbfmbyvrd7.pdf

47. Wiley::Multivariable Mathematics: Linear Algebra, Multivariable Calculus, And Ma Multivariable Mathematics Linear Algebra, Multivariable Calculus, and manifolds. Theodore Shifrin. ISBN 9780-471-52638-4. Hardcover. 504 pages http://www.wiley.com/WileyCDA/WileyTitle/productCd-047152638X.html

United States Change Location Home Subjects About Wiley ... Mathematics Special Topics Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds Related Subjects Number Theory Numerical Methods Mathematics Optimization Queuing Theory ... Statistics Experimental Design . Exclusive offers, news and more. Related Titles Mathematics Special Topics Introduction to Topology and Geometry by Saul Stahl Topology and Its Applications by William F. Basener The Numerical Solution of Ordinary and Partial Differential Equations, 2nd Edition by Granville Sewell Beyond Born-Oppenheimer: Electronic Nonadiabatic Coupling Terms and Conical Intersections by Michael Baer The Mathematics of Infinity: A Guide to Great Ideas by Theodore G. Faticoni Introduction to Real Analysis by John DePree, Charles Swartz TI-83 Plus Graphing Calculator For Dummies by C. C. Edwards Click to Close Larger Image Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds Theodore Shifrin ISBN: 978-0-471-52638-4 Hardcover 504 pages January 2004 US $125.95

48. Welcome To IEEE Xplore 2.0 Random Projections Of Signal Manifolds In many cases, however, we may have a more specific lowdimensional model for signals in which the signal class forms a nonlinear manifold in RN. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1661432

49. 250A Differentiable Manifolds 250A is roughly vector calculus on manifolds. An example of a manifold is a surface in space when you ignore the rigid structure of space. http://math.ucsd.edu/~lindblad/250a/250a.html

Math 250A: Differentiable Manifolds - Fall 04 - Hans Lindblad 250A is roughly vector calculus on manifolds. An example of a manifold is a surface in space when you ignore the rigid structure of space. Many things in geometry and physics, such as Einstein's equations of general relativity, are best stated independent of a particular coordinate system. A manifold together with invariantly defined differential operators is the natural setting for many nonlinear equations of physics. Applications include general relativity, fluid mechanics, electromagnetism, Hamiltonian mechanics, dynamical systems and control theory. The core topics in the course are: Differentiability. Inverse and implicit function theorem. Submanifolds of Euclidean space. Topological and smooth manifolds. Tangent space and bundle. Vector bundles. Vector fields, existence for ODE, Lie bracket and derivative, Frobenius theorem. Tensors and differential forms. Tensor bundles and cotangent bundle. Integration, partition of unity, orientation, Poincare lemma, Stokes formula, De Rham Additional topics that we might cover: Applications to Hamiltonian Mechanics and Electromagnetism Connections and covariant derivatives. Parallel transport.

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51. JSTOR Transversality In $G$-Manifolds This paper is devoted to an extension of transversality theory to Gmanifolds. The theorems we prove were motivated by earlier work on equivariant dynamical http://links.jstor.org/sici?sici=0002-9947(197708)231:2<429:TI>2.0.CO;2-Q&origin

52. Invariant Manifolds And Applications I will explain some recent work on the construction of finite dimensional invariant manifolds in the phase space of the NavierStokes equation on ${\bf http://math.bu.edu/people/josic/willmington/index.html

Invariant Manifolds and Their Applications A special session in Fourth International Conference on Dynamical Systems and Differential Equations Wilmington, NC, USA, May 24-27, 2002 Organizers: Kresimir Josic , Boston University List of Confirmed Invited Speakers: Lora Billings Montclair State University R.E. Lee DeVille , Rensselaer Polytechnic Institute Brian Hunt , University of Maryland, College Park Kresimir Josic , Boston University Igor Kukavica , University of Southern California Weishi Liu , University of Kansas Horacio Rotstein , Boston University Gene Wayne , Boston University Chongchun Zeng , University of Virginia Titles and Abstracts: C. Eugene Wayne: Invariant Manifolds and the Navier-Stokes Equation Lora Billings: Noise induced chaos We identify a global mechanism to induce chaos by stochastic perturbations. Two systems in which we find this are the class B laser and the SEIR population dynamics model. The bifurcation to chaos requires two co-existing saddle periodic orbits in a multistable system, which we call a bi-instability. The noise induces a heteroclinic connection between the invariant manifolds of the saddle periodic orbits, therefore inducing a chaotic attractor. To refine the possibility of control, we have also analyzed the stochastic transport between basins. This is joint work with Ira Schwartz and Erik Bollt. Brian Hunt: Bubbling Bifurcations For a one-parameter family of dynamical systems with a persistent invariant submanifold, I will characterize how a chaotic attractor in the invariant manifold loses asymptotic stability transverse to the manifold as the parameter is varied. After this bifurcation, the attractor generically remains weakly stable, having a basin of attraction that is "riddled" it has positive Lebesgue measure but is not open. Small perturbations of the system can then lead to intermittent behavior called "bubbling" trajectories spend most of their time near the (formerly) invariant manifold but occasionally burst far away. I will describe different types of bifurcations that can lead to bubbling and the resulting size and frequency of bursts near the bifurcation. The results are relevant to the synchronization of coupled chaotic systems, where bursting represents temporary loss of synchronization.

53. A Self-organizing Principle For Learning Nonlinear Manifolds -- Agrafiotis And X Unlike previous approaches, our method can reveal the underlying geometry of the manifold without intensive nearestneighbor or shortest-path computations http://www.pnas.org/cgi/content/full/99/25/15869

Published online on November 20, 2002, 10.1073/pnas.242424399 December 10, 2002 This Article Abstract Full Text (PDF) Supporting Text ... Citation Map Services Email this article to a colleague Similar articles in this journal Similar articles in ISI Web of Science Similar articles in PubMed ... Download to citation manager Citing Articles Citing Articles via HighWire Citing Articles via CrossRef Citing Articles via ISI Web of Science (24) Citing Articles via Google Scholar Google Scholar Articles by Agrafiotis, D. K. Articles by Xu, H. Search for Related Content PubMed PubMed Citation Articles by Agrafiotis, D. K. Articles by Xu, H. Social Bookmarking What's this? Previous Article Table of Contents Next Article Computer Sciences A self-organizing principle for learning nonlinear manifolds Dimitris K. Agrafiotis , and Huafeng Xu 3-Dimensional Pharmaceuticals, Inc., 665 Stockton Drive, Exton, PA 19341 Edited by Michael Levitt, Stanford University School of Medicine, Stanford, CA, and approved October 9, 2002 (received for review July 17, 2002) Abstract Top Abstract Methods Results and Discussion References Modern science confronts us with massive amounts of data: expression profiles of thousands of human genes, multimedia documents, subjective

54. Custom Stainless Steel Manifolds From The Manifold Center The Manifold Center specializes in all types of manifolds and machined parts including custom stainless steel manifolds, custom brass manifolds, http://www.manifoldcenter.com/

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56. Analysis, Manifolds And Physics - Elsevier Differential manifolds, finite dimensional case IV. Integration on manifolds V. Riemannian manifolds, kahlerian manifolds Vbis. Connections on a principal http://www.elsevier.com/wps/product/cws_home/600404

Home Site map Elsevier websites Alerts ... Analysis, Manifolds and Physics Book information Product description Author information and services Ordering information Bibliographic information Conditions of sale Volume information Part I Part II Set Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view ANALYSIS, MANIFOLDS AND PHYSICS http://books.elsevier.com/elsevier/?isbn=0444860177 By Y. Choquet-Bruhat C. DeWitt-Morette Contents Contents. I. Review of fundamental notions of analysis II. Differential calculus on banach spaces III. Differential manifolds, finite dimensional case IV. Integration on manifolds V. Riemannian manifolds, kahlerian manifolds Vbis. Connections on a principal fibre bundle VI. Distributions VII. Differentiable manifolds, infinite dimensional case Problems and exercises References Symbols Index Volumes Part I Part II Set Part I Hardbound, ISBN: 0-444-86017-7, 650 pages, publication date: JAN-1982 Imprint: NORTH-HOLLAND Price: Order form USD 71.95 GBP 41 EUR 62 Part II Hardbound, ISBN: 0-444-87071-7, 462 pages, publication date: NOV-1996

57. Manifold - Wikipedia, The Free Encyclopedia A manifold is an abstract mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may http://en.wikipedia.org/wiki/Manifold

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58. Smooth Manifold -- From Wolfram MathWorld (infinitely differentiable) manifold, also called a differentiable manifold. A smooth manifold is a topological manifold together with its functional http://mathworld.wolfram.com/SmoothManifold.html

Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Budney Smooth Manifold Another word for a (infinitely differentiable) manifold , also called a differentiable manifold. A smooth manifold is a topological manifold together with its "functional structure" (Bredon 1995) and so differs from a topological manifold because the notion of differentiability exists on it. Every smooth manifold is a topological manifold , but not necessarily vice versa. (The first nonsmooth topological manifold occurs in four dimensions.) Milnor (1956) showed that a seven-dimensional hypersphere can be made into a smooth manifold in 28 ways. SEE ALSO: Exotic R4 Exotic Sphere Hypersphere Manifold ... Topological Manifold REFERENCES: Bredon, G. E. New York: Springer-Verlag, p. 69, 1995. Milnor, J. "On Manifolds Homeomorphic to the 7-Sphere." Ann. Math. CITE THIS AS: Weisstein, Eric W. "Smooth Manifold." From MathWorld A Wolfram Web Resource. http://mathworld.wolfram.com/SmoothManifold.html Contact the MathWorld Team Wolfram Research, Inc.

59. Afra Has Moved! As of July 2006, my webpage has moved with me to Dartmouth College. You should be automatically redirected to this page in 5 seconds. http://graphics.stanford.edu/~afra/

As of July 2006, my webpage has moved with me to Dartmouth College. You should be automatically redirected to this page in 5 seconds.

60. Crocheted Chaos Dec 16, 2004 Their crocheted model, called the ‘Lorenz manifold’, is a very helpful If you would like to crochet your own Lorenz manifold in time for http://www.physorg.com/news2395.html

PhysOrg Account: Sign In Sign Up Home Nanotechnology ... General Science Published: 05:04 EST, December 16, 2004 Toolbox Rating: 5 Bookmark Save as PDF Print Email Blog It Digg It del.icio.us Slashdot It! Stumble It! Crocheted chaos The famous Lorenz equations that describe the nature of chaotic systems – such as the weather – have been turned into a beautiful real-life object, by crocheting computer-generated instructions. It is not often that a serious mathematics journal contains a crochet pattern, but the current issue of the Mathematical Intelligencer has instructions on how to crochet your very own model of chaos. It looks like a large Christmas decoration. Dr Hinke Osinga and Professor Bernd Krauskopf, both in Bristol University's Department of Engineering Mathematics, have turned the famous Lorenz equations that describe the nature of chaotic systems – such as the weather or a turbulent river – into a beautiful real-life object, by crocheting computer-generated instructions. Dr Osinga explained: “Imagine a leaf floating in a turbulent river and consider how it passes either to the left or to the right around a rock somewhere downstream. Those special leaves that end up clinging to the rock must have followed a very unique path in the water. Each stitch in the crochet pattern represents a single point (a leaf) that ends up at the rock.” Together all the points (stitches) define a complicated surface, according to the Lorenz equations. Osinga and Krauskopf have developed a method to describe such surfaces using a computer. After months of staring at animations on a screen, they suddenly realised that in fact their computations had naturally generated crochet instructions.

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