# All Questions

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### What's the formal name of this matiematical modeling problem

There is a right angle corner with the width of 1 in the both directions. I wonder the shape that can pass this corner with the largest area. I know that this is a famous problem, but what's the ...
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### Equivalence of Lie subalgebras, within a (irreducible) representation

Lie subalgebras inside Lie algebras have been classified up to equivalence, and linear equivalence (by Dynkin et al). How does one classify embeddings of a Lie algebra h inside a Lie algebra g, where ...
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### Is every algebraic $K3$ surface a quartic surface?

Algebraic $K3$ surface means the $K3$ surface admits an ample line bundle. So the question is equivalent to asking whether every algebraic $K3$ surface can be embedded in $\mathbb{P}^3$.
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### A short problem with minimal projections and biprojections

Let $(N \subset M)$ be a finite index irreducible subfactor, $P=P(N \subset M)$ its planar algebra. Notation: For $a,b \in P_{2,+}$ positive operators, then $\langle a,b \rangle$ is the biprojection ...
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### Decay of solutions to Schrodinger equation with local minimum in potential

Consider the one-dimensional Schrodinger operator on the real line $\mathbb{R}$ given by $$L = - \partial_x^2 + V$$ where $V$ is a potential with the following properties: $V$ is non-negative, ...
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### Why does this fundamental group do not have elements of finite order?

Let $X$ be a subset of $\mathbb R^3$ with its induced topology and let $a\in X$ be a point. Then the fundamental group $\pi_1(X,a)$ seems not to have elements of finite order (except the identity of ...
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### How large can a set of nearly equidistant points be?

Suppose that $D$ is a set of points in $\mathbb{R}^{k}$ such that all pairwise distances between them belong to $[1,1+\epsilon]$. It seems that such a set cannot be very large and that its ...
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### Representability of deformation functors via SGA

I'm trying to understand Böckle's proof of Theorem 2.1.1 in his notes on deformation theory. Let's start with some motivation. Let $\Gamma$ be a profinite group (I'm thinking of an absolute Galois ...
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### Is $[0,1]^\kappa$ an affine complete lattice?

A $k$-ary function $f$ on a bounded distributive lattice $L$ is called compatible if for any congruence relation $\theta$ on $L$ and $(a_i, b_i)\in \theta$ for $i=1,\ldots,k$ we always have ...
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### Ehresmann fibration theorem for manifolds with boundary

All manifolds in consideration may have nonempty boundary and may be disconnected. Let me fix a definition first. A map between smooth manifolds $M\rightarrow N$ is a fiber bundle, iff it's locally ...
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### Existence of a projection operator onto subspace of Hilbert space

Let $V \subset H$ be Hilbert spaces with a continuous and dense imbedding. Let $\{w_j\}_j \subset V$ be a basis of $V$ and of $H$ (so finite linear combinitions are dense) which is not orthogonal. ...
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### Embedding of classical into intuitionistic linear logic

Following on from this recent question, there is another construction that is well-known, but I don’t know a good primary source for: the Kolmogorov-style double-negation embedding of classical into ...
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### If $(X_n+Y_n)$ has bounded variance, is the same true for $(X_n)$ and $(Y_n)$? [on hold]

let $(X_n)$ and $(Y_n)$ be two sequences of random variables defined on the same probability space such that the variance of all components $X_n$, $Y_n$ is finite and the sequence of variances of ...
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### When does the integral of a Dolbeault-exact form vanish?

What conditions (if any) can be imposed on a Kahler manifold $M$ so that we get a Dolbeault analogue of Stokes' theorem on a closed manifold, i.e. $\int_M \partial ( ... ) =0$ The trivial solution ...
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### Normal basis with cyclotomic units

Let p be an odd prime integer and let $\zeta$ be a primitive p-th root of unity. Let $\alpha$ be a non-trivial cyclotomic unit of $\mathbb Q(\zeta)$, i.e. an element of the form ...
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### Shortest paths in Alexandrov spaces

Let $X$ be an Alexandrov space with curvature bounded from below (if necessary, $X$ might be assumed to be finite dimensional or even compact). Question 1. Is it true that every point of $X$ has a ...
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### conjugate operation on vector bundle

Is the conjugate operation on $\overset{\sim}{K}(\mathbb{C}\mathbb{P}^n)$ known? If so, can I get the full formula at least in terms of the basis $\eta^i$? Here $\overset{\sim}{K}(X)$ denotes the ...
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### Consistency strength of $\aleph_2$-Souslin hypothesis

Question 1. What is known about the consistency strength of $\aleph_2$-Souslin hypothesis? Question 2. What is known about the consistency strength of having both $\aleph_2$-Souslin hypotheis and ...
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### Global error estimates for numerical solutions of ODEs in Matlab or Mathematica [on hold]

I need to find the first zero (smallest positive root) of the solution of the initial value problem $ry''+y'+f(r)y=0, \ \ y(0)=y'(0)=1$ for certain $f \in C^{\infty}(R)$. One can easily use ...
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### Local time for reflected random walk [on hold]

Say I have a process starting from 0, and last for 100 steps, each step either moves up or down by one unit, within the boundary -10 and 10. My understanding is that expected hitting time would be ...
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### Need a calculator to evaluate function at irregular input values [on hold]

I'm trying to evaluate the magnitude of an appreciably complex transfer function using a variety of input frequencies. Because I'm lazy, I really don't want to have to scroll around in the function ...
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### Solving $Ax=e_k$ for standard basis vector $e_k$, sparse $A$

Given a sparse matrix $A \in \mathbb{R}^{n \times m}$, are there any efficient methods for determining whether there exists an $x \in \mathbb{R}^m$ such that $Ax=e_k$, the $k^{th}$ standard basis ...
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### Avoiding Fibonacci-like sequences

Suppose we are trying to avoid 3-term arithmetic progressions. There are two relevant sequences in the OEIS pertaining to this: A003278: The sequence whose $n^{\text{th}}$ term is the smallest number ...
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### On OPNs and SOPNs

(I hope that this question is appropriate for this site. If it is not, please feel free to point it out and I will then cross-post to MSE.) OPNs are odd perfect numbers. SOPNs are spoof odd perfect ...
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### Universal coefficient theorem for group homology and cohomology

I've been looking for any kind of universal coefficient theorem for group homology and cohomology, including dual universal coefficient theorems. However, the only things I can find are ones where the ...