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djalil.chafai.net | ||
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fabricebaudoin.blog
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| | | | | Let $latex x\in C^{1-var} ([0,T], \mathbb{R}^d)$ and let $latex V : \mathbb{R}^e \to \mathbb{R}^{e\times d} $ be a Lipschitz continuous map. In order to analyse the solution of the differential equation, $latex y(t)=y_0+\int_0^t V(y(s)) dx(s),$ and make the geometry enter into the scene, it is convenient to see $latex V$ as a collection of vector... | |
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mattbaker.blog
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| | | | | In my last blog post, I discussed a simple proof of the fact that pi is irrational. That pi is in fact transcendental was first proved in 1882 by Ferdinand von Lindemann, who showed that if $latex \alpha$ is a nonzero complex number and $latex e^\alpha$ is algebraic, then $latex \alpha$ must be transcendental. Since... | |
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fabricebaudoin.blog
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| | | | | In this section, we consider a diffusion operator $latex L=\sum_{i,j=1}^n \sigma_{ij} (x) \frac{\partial^2}{ \partial x_i \partial x_j} +\sum_{i=1}^n b_i (x)\frac{\partial}{\partial x_i}, $ where $latex b_i$ and $latex \sigma_{ij}$ are continuous functions on $latex \mathbb{R}^n$ and for every $latex x \in \mathbb{R}^n$, the matrix $latex (\sigma_{ij}(x))_{1\le i,j\le n}$ is a symmetric and non negative matrix. Our... | |
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ivyfanchiang.ca
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| | | [AI summary] The author provides a comprehensive mathematical derivation of the normal distribution using multi-variable calculus and the Herschel-Maxwell theorem. | ||
