QUALIFYING EXAMINATION Harvard University Department of Mathematics Tuesday August 30, 2011 (DayLet f be a differentiable function on R whose Fourier transform is bounded

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Soft-DTW: a Differentiable Loss Function for Time-Series

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Derivatives of self-intersection local times Jay Rosen∗ Abstract We show that the renormalized self-intersection local time γt (x) for the Brownian motion and symmetric stable process in R1 is differentiable in the sp

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• Mathematical analysis
• Generalized functions
• Digital signal processing
• Dirac delta function
• Fourier analysis
• Measure theory
• Continuous function
• Distribution

arXiv:0801.4345v2 [math.DG] 26 FebLimit leaves of a CMC lamination are stable William H. Meeks III∗ Joaqu´ın P´erez

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• Mathematical analysis
• Curvature
• Mathematics
• Riemannian geometry
• Geometry
• 3-manifold
• Geometric topology
• Differential geometry of surfaces
• Holonomy
• Limit of a function
• Riemannian manifold
• Differentiable manifold

CHARACTERIZATION OF FUNCTIONS REPRESENTING TOPOGRAPHIC SURFACES Gert W. WOLF Department of Geography, University of Klagenfurt Universitaetsstrasse 65, A-9010 Klagenfurt, Austria

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• Mathematical analysis
• Calculus
• Mathematics
• Multivariable calculus
• Smooth functions
• Singularity theory
• Differential calculus
• Critical point
• Hessian matrix
• Morse theory
• Derivative
• Differentiable function

TANGENT PLANES AND LINEAR APPROXIMATIONS MATH 195, SECTION 59 (VIPUL NAIK) Corresponding material in the book: SectionNote: We are, for now, omitting the topic of differentials, which is the second half of this se

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• Mathematics
• Mathematical analysis
• Calculus
• Differential geometry
• Differential calculus
• Differential topology
• Multivariable calculus
• Surfaces
• Tangent
• Derivative
• Normal
• Differentiable function

REVIEW SHEET FOR MIDTERM 2: ADVANCED MATH 152, SECTION 55 (VIPUL NAIK) This is the part of the review sheet that we will concentrate on during the review session. 1. Left-overs from differentiation basics 1.1. Derivative

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• Mathematical analysis
• Mathematics
• Analysis
• Differential calculus
• Functions and mappings
• Analytic geometry
• Multivariable calculus
• Inflection point
• Derivative
• Critical point
• Differentiable function
• Sine

CLASS QUIZ: NOVEMBER 23: MEMORY LANE MATH 152, SECTION 55 (VIPUL NAIK) Your name (print clearly in capital letters): (1) For which of the following specifications is there no continuous function satisfying the specificat

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• Multivariable calculus
• Differential calculus
• Mathematical analysis
• Smooth functions
• Calculus
• Continuous function
• Differentiable function
• Vertical tangent
• Derivative
• Vector bundle

CLASS QUIZ: NOVEMBER 2: INTEGRATION MATH 152, SECTION 55 (VIPUL NAIK) Your name (print clearly in capital letters): (1) Suppose f and g are both functions on R with the property that f 00 and g 00 are both everywhere the

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• Differential calculus
• Functions and mappings
• Integral calculus
• Antiderivative
• Derivative
• Continuous function
• Semi-differentiability
• Limit of a function
• Integral
• Differentiable function
• Left and right derivative
• Fundamental theorem of calculus

Gradient Descent Objective Function Some differentiable function f : Rn → R. Gradient Descent Start with some x0, i = 0 and learning rate λ repeat

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