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Related lectures (12)
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Fourier Inversion Formula
Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.
Lattices: Properties and Theta Functions
Explores lattices in Rd, Gram matrices, theta functions, and modular properties.
Ewald Summation: Electrostatic Coulomb Energy
Explores Ewald summation for electrostatic Coulomb energy in periodic systems, emphasizing the importance of Gaussian screening charges.
Fourier Inversion Formula and Plancherel Identity
Covers the Fourier inversion formula and the Plancherel identity, emphasizing their importance in mathematical analysis.
Ewald Summation: Long-Range Interaction and Self-Interaction Correction
Explains Ewald summation, self-interaction correction, and short-range interaction calculations.
Ewald Summation: Long-range Interactions and Self-interaction Correction
Explores Ewald summation for long-range interactions and self-interaction correction in Fourier space and real space.
Summation Formulas of Arithmetic Functions
Covers the Euler-Maclaurin summation formula and the method of convolution for evaluating arithmetic functions.
Trigonometric Polynomials: Fourier Inversion and Plancherel Formulas
Explores trigonometric polynomials, emphasizing Fourier inversion and Plancherel formulas.
Pentagonal Number Theorem and Jacobi Identity
Covers the pentagonal number theorem, Jacobi identity, and modularity of eta and theta functions.
Reciprocal lattice: Shape effects
Explains how sample geometry affects the size and shape of reciprocal lattice nodes in multiple beam scattering.
Non-Parametric Estimation: Kernel Density Estimators
Explores non-parametric estimation using kernel density estimators to estimate distribution functions and parameters, emphasizing bandwidth selection for optimal accuracy.
Electrostatics and Green's Functions: Mathematical Methods
Discusses electrostatics, Green's functions, and the application of complex analysis in deriving potentials.
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