# All Questions

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### The Sato-Tate conjecture for hypersurfaces?

The Sato-Tate conjecture for elliptic curves $E$ predicts the distribution of the eigenvalues of Frobenius at $p$ on the Tate module of $E$ as $p$ varies in terms of the distribution of the ...
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### About an equivalent to Tutte's 5-flow Conjecture

A while back I remember reading that F. Jaeger proved that Tutte's $5$-flow conjecture is equivalent to a statement about the co-planarity of a certain set of points in some euclidean space. But I ...
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### Can the natural boundary be part of the unit circle?

It is well-known that the function $f(z)=\sum_{n=0}^\infty z^{n!}$ is analytic in the open unit disk and it can not be extended analytically to any proper open superset of the unit disk, i.e., the ...
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### Cominuscule property of nilpotent orbits

Let $G$ be a complex reductive Lie group, $G/P$ a flag manifold, and $\Phi: T^* G/P \to {\mathfrak g}^*$ the moment map. So $\Phi(T^* G/P)$ is the closure of a nilpotent orbit. Lots of classes of ...
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I noticed that in the proof of Stokes' theorem on manifolds, the condition that the form $\omega$ is compactly supported ensures that the sum is finite so that we can change the order of sum and ...
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### How to figure out all possible combinations of 3,3,3 and 3 between 0 and 100 [on hold]

... *,/,+,-,decimal point,!,power funtion,() eg. You can make 7 by doing 3/3 +3+3 or 24 by (3*3!)+3+3
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### Sequence that contains palindromic numbers [on hold]

When studying the theory of palindromic numbers, there were particular sequences that generated infinitely many palindromic numbers. I faced an introductory problem which asked to prove that the ...
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### where is there a survey of field dependent gauge symmetries/parameters? [on hold]

Where can I find a survey/review of field dependent gauge symmetries/parameters? symmetries meaning for a group action, gauge parameters mean, e.g. Lie alg elements. infiniteimal In math lab, how do ...
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### Bad subforcings of nice forcing notions

Let $\mathbb{P}$ and $\mathbb{Q}$ be two forcing notions. Recall that we say $\mathbb{Q}$ is a subforcing of $\mathbb{P}$ if there exists a regular embedding $\mathbb{Q} \to \text{r.o.}(\mathbb{P}).$ ...
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### Which directed graphs have a normal adjacency matrix?

I am working on a problem in matrix analysis and I am looking for certain types of normal matrices. I suspect that these "special" normal matrices arise as adjacency matrices of certain graphs. My ...
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### Universal C^*-algebra with generators and relations

We say that the $C^*$-algebra $A$ generated by $a_1,...,a_n$ is universal subject to relations $R_1,...,R_m$ if for every $C^*$-algebra $B$ with elements $b_1,...,b_n$ satisfying relations ...
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### Counting Chains with Bounded Types [closed]

You have pearl of 3 types. Type 1 pearl can be of color from 1 to X. Type 2 pearl can be of color from X+1 to X+Y Type 3 pearl can be of color from X+Y+1 to X+Y+Z. You have unlimited supply of ...
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### What is a Homotopy between $L_\infty$-algebra morphisms II

I would like to continue on question I asking, what is a homotopy between Lie infinity algebras, since I'm not satisfied in two directions: 1.) The naive approach to define a homotopy would be ...
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### Can the Vertices of cubic graph be partitioned into and induced cycle and a forest?

Let $G$ be a $2$-connected $3$-regular graph. Can $V(G)$ be partitioned into $V_1$ and $V_2$ where $G[V_1]$(the induced subgraph on $V_1$) is a cycle of $G$ and $G[V_2]$ is a forest (Acyclic ...
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### Is the set of edge of a cubic graph the union of a cycle and and an Acyclic graph?

Let $G$ be a $2$-connected $3$-regular graph. Is it true that $E(G) = E_1 \cup E_2$ where $G[E_1]$(the induced subgraph on $E_1$) is a cycle of $G$ and $G[E_2]$ is a forest (Acyclic subgraph) of $G$? ...
In basic algebraic topology, we know the following well-known chain homotopy theorem: Let $X$ be a topological space and $I=[0,1]$ be the unit interval. Let $S_*(X)$ and $S_*(X\times I)$ be the ...
I'm working on a problem which depends on solving explicitly the partial differential equation below. Consider a positive function $u=u(x,t)$ satisfying the equation \$u_{tt} = \frac{x^2}{t^2} ...