# All Questions

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### Find a shortest way between nodes in graph [on hold]

I have a next structure : Each node in graph may have more than 2 links. I want to find a shortest way with node 1 and 13. ...
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### Reference request: monochromatic paths in edge-colored complete graphs

Given $k,c \in \mathbb{N}$, let $P(k,c)$ be the minimum $n$ such that no matter how we color the edges of the complete graph $K_n$ with $c$ colors, there is always a monochromatic path of length $k$. ...
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### Push-forward of sum of two maps

Let $X=R^n$ and $Y=R^m$ are two Euclidean spaces with $m<n$. Let $\varphi$ and $\phi$ are two (smooth) maps from $X$ to $Y$ and $\mu$ is a probability measure on $X$. Is there any relationship ...
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### Are sections of $\tau M$ differential operators on the exterior algebra?

Let $M$ be a smooth manifold and $\tau M$ its second-order tangent bundle. A second-order vector field $A\in \Gamma(\tau M)$ can locally be expressed as a finite sum of operators ...
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### What math do I need to know in order to understand basic trigonometry? [on hold]

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few ...
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### Log-convexity preserved by sum? [migrated]

I'm currently reading Boyd's book on Convex Optimization (free book which can be found here : http://stanford.edu/~boyd/cvxbook/) , and there is one proof I do not understand : p. 105, the book says ...
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### The Stratonovich formulation of the Double Mean Reverting Model

I am writing my Bachelor's Thesis on the fast Ninomiya-Victoir calibration of the Double Mean Reverting model and have a question to its Stratonovich formulation. I am new to mathoverflow and a novice ...
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### How to use the derived functor to write down a lot of natural morphisms or isomorphisms? [on hold]

In the Kashiwara’s book：Sheaves on manifolds, the derived functor is defined in the abstract form, you can see some discussing at here: Derived functor Kashiwara’s book gives a lot of natural ...
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### Is every frame monomorphism regular?

Is every monomorphism in $\mathbf{Frm}$, the category of frames, regular?
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### Parallelizable nearly-Kahler manifolds

In this question, we have discussed how the following bundle: $E_{d} = TS^{d}\oplus \Lambda^2 T^{\ast}S^{d}$ is always trivial, where $S^{d}$ is the $d$-dimensional standard sphere. Now, let us take ...
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### does a lattice have a minimal item [on hold]

A lattice (L, ≤) is a partially ordered set, where each two elements of the set have a least upper bound and a greatest lower bound. Let's consider the situation where L is finite. I think that ...
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### Is there a more general obstruction to the existence of moduli spaces than the existence of automorphisms?

We are taught that, in general: A type of objects that has nontrivial automorphisms cannot have a fine moduli space. The proof generally goes along the lines of: Take an object $X$ with a ...
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### Is the exterior power of a primitive matrix still primitive?

the question is already in the title. Here some more details. I have a primitive matrix $M$ (primitive means $\exists k\geq 0$ such that $M^k > 0$). I take exterior powers $\wedge^n M$ and I would ...
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### A variant of Goldbach Conjecture

I'm asking if this variant of weak Goldbach's Conjecture is already known. Let $N$ be an odd number. Does there exists prime numbers $p_1$, $p_2$ and $p_3$ such that $p_1+p_2-p_3=N$? Ideally, can we ...
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### Identify ring of polynomials symmetric under forgetting variables

I came across the following ring $A$, which appears as a Chow ring. I am wondering if it has been studied before; in particular, I am looking for a reference where this object might have been ...
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### How does a level set look like when the minimum point of a function degenerate?

I apologize in advance if this question is well-known. I would like to know an explicit example of a compact, connected manifold $M$ and a smooth function $f: M \to\mathbb{R}$ which satisfy the ...
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### Area enclosed by Brownian motion (without winding number)

The question Average Value of Area Closed by Brownian Motion turned out to be about the Lévy area process, which measures "signed area with multiplicity" enclosed by Brownian motion (e.g. each ...
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### Is there a Degenerate Dependency Local Lemma?

The Lovasz Local Lemma has several generalizations, with names usually starting with L, such as Lopsided or Lefthanded. Here I ask whether another possible generalization (for which I could not yet ...
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### Examples of surface automorphisms with no periodic points

Consider a smooth projective complex surface $S$ with an automorphism $g:S\to S$. A point $p$ is periodic if it has finite orbit under iterates of $g$. What are some examples of surface ...
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### Comparision of two $C^{*}$ algebras associated to a non vanishing vector field on a compact manifold

Let $X$ be a non vanishing vector field on a compact manifold $M$ so we have a one dimensional foliation $F$ of $M$ with orbits of $X$. This foliation defines a $C^{*}$ algebra $C^{*}(F)$. On the ...
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### Number of ways you can form pairs with a group of people when certain people cannot be paired with each other [migrated]

Let's say you have a group of eight people and you want to form them into pairs for group projects. There are 8!/(4!*2!) ways to do it. (8! Is the total ...
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### Binary algebra, is it possible to partition the elements in GF(2^12) into 65 subgroups closed under addition?

The set of all binary vectors with 12 components forms a field with 2^12 elements containing 000000000000 and another 65*63 elements. Is it possible to partition these elements into 65 subgroups of 63 ...