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www.jeremykun.com
| | vcansimplify.wordpress.com

Recently I have been reading up on frequency domain image processing. I am still just beginning to understand how it works. Over the last few weeks I have been trying to understand the ** Fourier Transform **. Although the gist of Fourier Series is easy to understand from its formula, that of the Fourier Transform...
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| | lucatrevisan.wordpress.com

In which we show how to find the eigenvalues and eigenvectors of Cayley graphs of Abelian groups, we find tight examples for various results that we proved in earlier lectures, and, along the way, we develop the general theory of harmonic analysis which includes the Fourier transform of periodic functions of a real variable, the...
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| | djalil.chafai.net

This post is mainly devoted to a probabilistic proof of a famous theorem due to Schoenberg on radial positive definite functions. Let us begin with a general notion: we say that \( {K:\mathbb{R}^d\times\mathbb{R}^d\rightarrow\mathbb{R}} \) is a positive definite kernel when \[ \forall n\geq1, \forall x_1,\ldots,x_n\in\mathbb{R}^d, \forall c\in\mathbb{C}^n, \quad\sum_{i=1}^n\sum_{j=1}^nc_iK(x_i,x_j)\bar{c}_j\geq0. \] When \( {K} \) is symmetric, i.e. \( {K(x,y)=K(y,x)} \) for...
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| | statsandr.com

This article illustrates how to draw a world map of the countries you have visited in R. This world map can also be used to highlight some specific countries
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