# Questions tagged [regularization]

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### Laplace transform

\begin{cases}\mathbb{D}_t^\beta u(x, y, t)=-a(x)\left(u_x(x, y, t)+u_y(x, y, t)\right)+\ell(x, y, t, u(x, y, t)), & x>0, y>0, t>0 \\ u(x, y, 0)=0, & x>0, y>0 \\ ...
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### Normalizing a parameter in a regression

I am thinking about the possibility of making a parameter in my regression, let's say the $\lambda$ in a ridge regression, somehow, inside a range : $\lambda \in [0,1]$. Do you have any ideas how I ...
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### Evaluating $\sum_{n=0}^\infty n^k n!$ in p-adics, and its connection to the summation of divergent series

Often, in the discussion of the regularization of the geometric series it is mentioned that $\sum_{n=0}^\infty p^n$ converges in the p-adics, and indeed, that it converges to $\frac{1}{1-p}$. I had ...
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### Interesting questions for inverse parabolic problems

I'm looking for some interesting questions and maybe open problems in inverse problems theory, especially in the framework of parabolic PDEs (basically the heat equation). As key words here we can ...
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### When will the upper regularization of a bounded function not defined?

Suppose $E$ is a compact metric space. A function $f :E \rightarrow \mathbb{R}$ is upper semicontinous if for all $c \in \mathbb{R}$, $f^{-1}(-\infty, c)$ is open in $E.$ For any real-valued ...
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