# All Questions

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### K-theory of complete intersection

Let $X$ be a smooth complete intersection in $\mathbb{P}^n$. I am searching for literature on the K-theory for $X$? I guess the K-theory is known...
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### Is $f(z) =\zeta(1-iz)$ of Polya class?

Is $f(z) =\zeta(1-iz)$ of Polya class? The Pólya class is a set of entire functions satisfying the requirement that if E(z) is in the class, then E(z) has no zero (root) in the upper half-plane. ...
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### Spherical to Cylindrical coordinate conversion with different radius [on hold]

It is easy to find Spherical to Cylindrical coordinate conversion formula. My question is what if the point at the Sphere extends, what is the point of contact at the Cylinder? Example: I have ...
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### A class of Lie groups with $f^{abc} \neq -f^{acb}$ (not fully anti-symmetrized) or $f^{abc} \neq f^{bca}$ (not-cyclic)

With the motivation to understand the Lie group structure constraint on a non-Abelian Chern-Simons theory, could some experts give a class of Lie groups with structure constants cannot fully ...
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### Equivalence relations on powerset of R^2

Let A and B be two subsets of R^2. I define the relation T(A,B) to hold between A and B iff there exists a translation f on R^2 such that the image set of A under f is B. It is easy to prove that T is ...
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### Could you help me to solve the question about othonormal? [on hold]

suppose{$e_1,e_2,...$}is an orthonormal basis for $H$ and for each $n$ there is a vector $Ae_n$ in $H$ such that $\sum\|A\|<\infty$ .show that A has an unique extension to a bounded opearator on ...
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### How to bound the curvature tensor?

If a manifold is Kahler, and its Ricci curvature is bounded two side. How to bound the curvature tensor in L2 sense by a topology invariant which only depend on the first and second chern class?
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### Formalizations of category theory in proof assistants

What are the existing formalizations of category theory in proof assistants? The ones I know about are: https://bitbucket.org/JasonGross/catdb, which became ...
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### Mordell-Weil and finiteness of rational points

Let $E$ be a CM elliptic curve defined over a quadratic imaginary field $K$ with maximal order, that is, $\mathrm{End}_K(E)\cong \mathcal{O}_K$. Suppose the class number of $K$ is equal to $1$. Let ...
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### Classes for which the Spectrum determines a Convex Shape

Given a planar domain $\Omega \subset \Bbb{R}^2$ bounded and open we can associate to it the spectrum of the Laplace operator with Dirichlet boundary condition. It is known that there are planar ...
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### The fibre product of two quotient stacks

My question is to know whether the fibre product of $[X/G]$ by $[Y/H]$ over a base scheme is $S$ is $[X \otimes_S Y/G \times H]$? And if yes, do you have any reference for it? Thank you.
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### Do varieties with ample canonical bundle have finite automorphism group in small characteristic?

Suppose $X$ is a smooth projective variety over a field $k$, with ample canonical bundle. If $\operatorname{char}(k)=0$ or $\operatorname{char}(k)>\dim(X)$ and $X$ lifts to $W_2(k)$ (thanks ...
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### Accidental, unplanned breakthroughs in Mathematics [on hold]

In math/physics, or generally in science, there are many moments where the success and the triumph come from the accidental, unplanned attempts. Moreover, there are some cases that originally having ...
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### Some questions about an “infinite-dimensional” regular simplex [on hold]

Let H be the Hilbert space of square-summable sequences of real numbers. Let S be the set of all points of H having exactly one coordinate equal to 1 and all other coordinates equal to 0. Let C(S) be ...
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### intersection points and lines, part two

Two years ago I asked a question about finding couples of integers (p,l) such that one may draw l lines on the euclidean plane, creating exactly p intersection points, and I got very interesting ...
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### What is the geometric meaning of content or intersection flatness?

The polynomial extension $R \rightarrow R[X]$ ($X$ an indeterminate) has many nice properties beyond faithful flatness. The one I'm most interested in at the moment is the following. Say that a flat ...
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### When is a collection of exponentials dense in $L^2(K), |K|<\infty$

Suppose we have a relatively dense collection of points $\Lambda \subset \mathbb{R}^d$ and $K \subset \mathbb{R}^d$ where $K$ is compact and measurable. When will the linear span of the collection of ...
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### Eigen value distribution of autocorrelated Wishart matrix

Suppose the matrix W is constructed as $W=XX^T$ where $X_i(t) = \phi_i X_i(t-1) + a_i(t)$, and $a_i(t)$ ~ $N(0,1)$. I am interested in knowing the eigen value distribution of W. My google search on ...
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### $x^x = y$, given $y$ solve for $x$ analytically [migrated]

This question has been bugging me since high school where I was told "not to be concerned with such matters", but years later I still haven't found a satisfying answer. The question is really simple: ...
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### Repeated draws from multinomial distribution

(This is a cross-post from Math StackExchange http://math.stackexchange.com/questions/609641/multinomial-distribution-sum-of-squared-probabilities) Let $\vec X = (X_1, \dots, X_k)$ be a draw from a ...
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### Homotopy groups of filtered homotopy limits

Let $X$ be the homotopy limit of a filtered system of simplicial sets $X_i$. When are the morphisms $\pi_j(X)\to \varprojlim \pi_j(X_i)$ surjective for all $j\ge 0$? This seems to be no problem when ...
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### Nowhere Fréchet differentiable homemorphism of $R^{n}$ [on hold]

Does there exist a homeomorphism of $R^{n}$, $n\geq 2$, which is Fréchet differentiable at no point? This question is somehow related to the following post: A real analytic curve which is nowhere ...
hi i see in forum the following problem \int_0^{\infty } \frac{\cos (x) I_0\left(\sqrt{2} \sqrt{x}\right)}{2 \sqrt{e}} \, dx=-\frac{\sin \left(\frac{1}{2}\right)}{4 \sqrt{e}}-\frac{\sin (1) \cos ...
I am reading "Ample divisors on fine moduli spaces on the Projective plane" by Stromme. In the proof of Proposition 2.4, he seems to claim that if $E$ is a torsion free sheaf of projective dimension ...