# All Questions

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### Behaviors of zeros of analytic functions on upper complex plane at its boundary

If $f$ is analytic in $\{z\in \mathbb{C}, \Im z>0\}$, and continuous in $\{z\in \mathbb{C}, \Im z\ge 0\}$. I'm curious about the structure of the set $$E=\{z\in \mathbb{R},~~ f(z)=0\}$$ Is ...
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### Common covariance matrix for linear bayes classifier

I am a bit confused on the calculation of shared covariance matrix. As far as I understood, the shared covariance matrix is one of the assumptions that we make to eliminate(or reduce) negative results ...
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### Closure of subset of $\ell^\infty$

I am doing some assignment and I am trying to understand the nature of the closure of $A\subset \ell^\infty$ as I am having trouble exactly getting an image of how the elements in it is. Our set A ...
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### What happens when the normal to surface is zero?

In Differential Geom we're always given that surfaces should be regular, meaning the partial derivatives at every point are linearly independent, or the normal is non-zero. I get that the tangent ...
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### what's the difference between Eisenstat trick and an implicit preconditioner?

Assume ${A}$ is Hermitian positive definite and $\hat A$=$D^{-1/2}$$A$$D^{-1/2}$ is to obtain a symmetric variant. and $M$=($L_{A}$+$D$)$D^{-1}$($D$+$U_{A}$) where $D$ is a suitable diagonal matrix ...
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### Compactness of the $K \subset C[0,1]$

Let's consider the following function space $$K = \{ x \in C[0, 1] | \int_{0}^{t}{|x(s)| dt} \leq t^{4}, \forall t \in \mathbb{R} \}$$ I would like to establish, whether this space is compact or ...
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### How to resolve a set of equations when everything is cross related

First off mathematics isn't my field, so if I've made any rookie mistakes please forgive me! (also I'm not sure what tags to use) I have a set of equations that boil down to this; s = Integral(V.dt) ...
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### derivative of an multiple integral

i have a problem in derivative of multiple integrals. for example i don't know how can I do it for the below question. would you please help me to solve it? thanks
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### For which $n\in\mathbb{N}$ exists $f:S^{2n}\to \mathbb{C}P^n$ such that $f$ induces an isomorphism $H^{2n}(\mathbb{C}P^n)\to H^{2n}(S^{2n})$

My question is: For which $n\in\mathbb{N}$ exists a map $f:S^{2n}\to \mathbb{C}P^n$ such that $f$ induces an isomorphism $H^{2n}(\mathbb{C}P^n)\to H^{2n}(S^{2n})$ on singular cohomology with ...
I consider some surfaces $P_t = \partial\{v<t\}$ moving under inverse mean curvature flow. I need to show that their eccentricity $\Theta(P_t)$ is decreasing. Note that the function $v$ is ...