# All Questions

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### Power-Method convergence proof for not-diagonalizble Matrix

I would like to find proof of Power-Method convergence for non-diagonalizble Matrix. I have seen the only Version on Wikipedia and do not manage to find the original proof. Maybe someone knows, where ...
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### Variational Lower Bound with latent SDE

In this paper https://arxiv.org/pdf/2007.06075.pdf, the authors give a formula in equations 13 and 14, for the ELBO for a specific VAE (latent variable governed by an SDE) that I have difficulty ...
• 101
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### Symmetric monoidal categories and modules over the unit

Consider a symmetric monoidal category $(C, \otimes, I)$, where $I$ is the unit. Then there is a restricted Yoneda functor $$C \rightarrow Hom(I,I)-mod$$ taking an object $X$ of $C$ to $Hom(I, X)$, ...
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### A inequation about convex functions

if f is a convex function, prove: $$\frac{1}{3}\int_0^1 f(x)dx-\frac{1}{2}\int_0^1 xf(x)dx \geq \frac{1}{12}$$
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### $\int_0^1 \frac{1}{u+f(x)} dx= a \exp(b u)$, solve $f(x)$

$\int_0^1 \frac{1}{u+f(x)} dx= a \exp(b u)$, solve $f(x)$. I want the integral at left is equal to the form of $a \exp(b u)$. Here $a$ and $b$ are just some parameters or constants, they both can be 1 ...
• 31
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### A question about ideals $(6,7+\sqrt{-5})=(1+\sqrt{-5})$.

$(6,7+\sqrt{-5})=(1+\sqrt{-5})$. Is it correct? These are ideals of the ring $\mathbb Z[\sqrt {-5}]$. Can I write this equivalence becasue $1+\sqrt{-5}=7+\sqrt {-5}-6$ and so $(1+\sqrt{-5})$ is a ...
1 vote
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### How can one prove that if $f$ linear, then $f$ is continuous [duplicate]

Let $(V,\|.\|)$ be a normed vector space, $f:V\to \mathbb{R}$ be linear and $\ker(f)$ closed. Then $f$ is continuous. How does one prove this? My idea was to distinguish between two cases. Because ...
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### What is the gauge theory field-configuration moduli space?

Suppose we want to consider a (global, but not necessarily purely topological) gauge QFT for a principal $G$-bundle $P \xrightarrow{\pi} M$, with just one (bosonic) gauge field and no others. Without ...
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1 vote
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### A Simple Example of a Function on $[0, 1]$

I am looking for a concrete example of a continuous function $f$ on the unit interval $[0, 1]$ such that $0\leq f(x) <1$ for each $x\in [0, 1]$, but $\int_0^1 f(x) dx = 1$. Any help is greatly ...
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### Definition of static spherically symmetric spacetime as fiber bundle

I am working on a physical paper about solutions of Einstein field equations in case of static spacetimes with perfect fluid spheres and wanted to use a new definition of the spherical symmetry there. ...
1 vote
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### Minimize norm of difference, mapped into several spaces

I'm looking for a non-computational solution, in other words for an explicit formula, for the following problem. Let $Y$ be a vector space and $X$ a subspace of $Y$. Given $y\in Y$, and $n$ morphisms ...
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1 vote
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### Calculating how many automorphisms a graph has

I am trying to figure out how many automorphisms graphs have but I believe I am going wrong when calculating for this graph. The answer I am getting is 48 but that seems too high for this graph: EDIT: ...
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### Vector space: How to prove $(a+b)(x+y) =ax+ay+bx+by$

How to prove $(a+b)(x+y) =ax+ay+bx+by$, where $x,y \in V$ and $a,b \in F$, where $V$ is a vector space and $F$ is the field?
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### Reading about the null set and Lebesgue measure - asking for reading recommendation

I hope its allowed to ask a more "general" question here I just started learning multivariable integral, and we just learned about the null set and Lebesgue measure ( in our defention we use ...
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1 vote
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### Series representation of GCD(x, y)

While playing around with WolframAlpha, I discovered that apparently the GCD of any integers x, y is equal to the following sum: $$x + y - xy + 2\sum_{k = 1}^{x-1} \lfloor \frac{ky}{x}\rfloor$$ I've ...
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### Random truncation with poisson process

Suppose, a Poisson process is observed in fixed time intervals, e.g. we record the output of a Geiger counter during a time interval $\Delta t$ started randomly. The decay rate is much larger than ...
1 vote
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### Prove uniform convergence of bounded sequence

Supose we have a sequence of real continuous functions on an interval $[0,b] \in \mathbb{R}$ $(f_n)_{n=0}^{\infty}$ (hence uniformly continuous). Moreover the sequence has the following properties: ...
This MO question https://mathoverflow.net/questions/249541/formal-power-series-is-taylor-expansion-of-rational-function-iff-hankel-determin states that if $k$ is a field and $k[[T]]$ is the power ...