Week 5 (due May[removed]Consider a classical particle on a manifold X with an action Z
pi dq i − αi dq i − H(p, q)dt . S=

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• Hamiltonian mechanics
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HRIS USER PROFILE ENTRY FORM AGENCY NAME: ___________________________________________________________________________________________________ FIMS NUMBER: _____________________________________________ AUTHORIZATION NUMBE

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Week 2 (due April[removed]Consider a surface S in R3 given by the equation z = f (x, y). The standard flat metric on R3 induces a curved metric on this surface. It also gives rise to a second fundamental form. (a) Express

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Week 4 (due April[removed]The Todd genus is the Chern genus corresponding to the analytic function f (z) = z/(ez − 1). Express the Todd genus in terms of Chern classes up to and including terms of cohomological degree 6

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• Mathematics
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Draft Version, April, 2013 Preprint typeset using LATEX style emulateapj v[removed]ULTRA-FAINT ULTRAVIOLET GALAXIES AT Z ∼ 2 BEHIND THE LENSING CLUSTER ABELL 1689: THE LUMINOSITY FUNCTION, DUST EXTINCTION AND STAR FORM

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Week 9 (due March[removed]Compute the Chern-Simons 5-form and 7-form. 2. Consider a gauge theory on a Riemannian 3-manifold M with gauge group U (N ) and an action Z Z

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MARTINREA INTERNATIONAL INC. ANNUAL INFORMATION FORM For the fiscal year ended December 31, 2012

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2014 I-090 Form WI-Z, Wisconsin income tax - short form

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2013 I-090 Form WI-Z, Wisconsin income tax - short form (fillable)

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Simplest form of the Central Limit Theorem: Let X1 , X2 , · · · be a sequence of iid random variables with mean 0 and variance 1 on a probability space (Ω, F, P). Then ! Z y −t 2 /2 X 1 + · · · + Xn e

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