# All Questions

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### Ellipticity of an operator in Gunther's proof of the isometric embedding

In Deane Yang's notes about Gunther's proof of the celebrated isometric embedding theorem, at the end it is stated that $v$ inherits the regularity of $h$ because the operator $I-Q_0(v,\cdot)$ is ...
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### If there exists a sequence $(\phi_n)$ of step functions such that $\phi_n \longrightarrow f$ almost everywhere on $[a,b]$, can we prove that $f\in L$?

I know, if $f\in L$ (the set of all Lebesgue integrable functions), then there exists a sequence $(\phi_n)$ of step functions such that $\phi_n \longrightarrow f$ almost everywhere on $[a,b]$ and ...
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### Minimum vertex cover of vertex disjoint odd holes and antiholes

I am interested in knowing whether the minimum vertex cover of a graph that can be written as the union of vertex-disjoint odd holes and odd antiholes can be found exactly, in polynomial time. I could ...
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### Algebraic Multiplicity and Geometric Multiplicity

Problem Let $V$ be a finite dimensional vector space over $\mathbb{C}$ and suppose the linear transformation $T:V\rightarrow V$ has eigenvalue $\lambda_0$ with algebraic multiplicity $n_0=3$. (a) ...
### What is the probability to pass through $1\le m\le n$ vertices of an $n$-sided polygon after $t$ seconds?
Suppose a flea is on a vertex of an $n$-sided polygon. It stays still for exactly one second, and then jumps instantly to an adiacent vertex. Let us assume it has no memory of its previous jumps and ...