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blog.georgeshakan.com | ||
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pfzhang.wordpress.com
Consider a smooth one-parameter family $latex {f_t}$ of diffeomorphisms on a manifold $latex M$. It is a flow if $latex f_0(x)=x$ and $latex f_{t}\circ f_{s}(x) = f_{s+t}(x)$ for every $latex x\in M$, , $latex t ,s \in \mathbb{R}$. Set $latex X(x)=\lim\limits_{h\to 0} \frac{1}{h}(f_h(x) - x)$. This generates a vector field $latex X: M \to TM$.... |
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fabricebaudoin.blog
Exercise 1.Solve Exercise 44 in Chapter 1 of the book. Exercise 2.Solve Exercise 3 in Chapter 1 of the book. Exercise 3.Solve Exercise 39 in Chapter 1 of the book. Exercise 4.The heat kernel on $latex \mathbb{S}^1$ is given by $latex p(t,y) =\frac{1}{2\pi}\sum_{m \in \mathbb{Z}} e^{-m^2 t} e^{im y} =\frac{1}{\sqrt{4\pi t}} \sum_{k \in \mathbb{Z}} e^{-\frac{(y... |
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algorithmsoup.wordpress.com
The ``probabilistic method'' is the art of applying probabilistic thinking to non-probabilistic problems. Applications of the probabilistic method often feel like magic. Here is my favorite example: Theorem (Erdös, 1965). Call a set $latex {X}&fg=000000$ sum-free if for all $latex {a, b \in X}&fg=000000$, we have $latex {a + b \not\in X}&fg=000000$. For any finite... |
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manjubhat.wordpress.com
Mark Russinovich's blog |
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