# All Questions

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### Complex Kronecker foliation

Let $\theta \in \mathbb{C}$ be a fixed complex number. The submersion $f:\mathbb{C}^{2}\to \mathbb{C}\; \text{with}\; f(x,y)=y-\theta x$ defines a complex foliation on $\mathbb{C}^{2}$. Consider the ...
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### Solving limit problems versus the difference quotient

I am working my way through a Calculus 1-level online course, and there is something about limits and the difference quotient that is bothering me. To define the limit used in the difference ...
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### Cosets of the fixer of an action of a monoid on a finite set

Let $M$ be a monoid that acts transitively from the right on a finite set $X$. Assume furthermore that the action of $M$ on $X$ induces for every $m \in M$ a bijection on $X \to X, x \mapsto x.m$. Let ...
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### Self-similarity for simple algebraic structures

I'm doing this thread because I have some ideas about how to define self-similarity in algebra, but I don't know if this is known at all. Any critics, comments and references are more than welcomed. ...
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### Is there some Riemannian manifold's version of Whitney theorem?

Given any Riemannian or Semi-Riemannian manifold $(M,g)$, does there exist a Eucildean space $(E,g^\prime)$ of enough high dimension with metric $g^\prime=diag\{-1,-1,...,+1,+1,...\}$ with any n ...
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### centeredness in forcing iterations

Suppose $A$ is a complete subalgebra of a complete boolean algebra $B$, and $B$ is $\kappa$-centered. Let $G \subset A$ be a generic ultrafilter. Is $B/G$ $\kappa$-centered in $V[G]$? Naively, we ...
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### Treating The Differential of Independent Variables in Integral [on hold]

I need some comments from real infinitessimal calculus and real analysis point of view like limit-theorems etc. regarding the following Consider that B is constant ($\frac{dB}{dt}=0$) There is a ...
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### How to choose subject of pure math for PhD? [on hold]

I'm seeking about PhD in Maths. I'm really confused about choosing the area of research. I enjoyed studying and teaching Algebra & Topology, But I don't know how to start writing a research on ...
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### Decomposition of non-singular matrix [on hold]

Is there any way to show that a non-singular matrix A can be partitioned as follows: \begin{eqnarray*} A&=&\left[ \begin{array}{cc} \underset{\left( k\times k_{1}\right) ...
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### Faltings height in short exact sequences

Let $K$ be a number field and $0 \rightarrow A \rightarrow B \rightarrow C \rightarrow 0$ a short exact sequence of abelian varieties over $K$. Let $h(A)$ denote the logarithmic Faltings height ...
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### Example of an operator whose domain is infinite dimensional but range is not closed [on hold]

Give me an example of an operator $T:D->R$, such that $D$ is an infinite dimensional Hilbert space and $R$ is not closed/dense.
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### Transversality of stable and unstable manifolds for geodesic flows associated to different metrics on the same manifold

Let $M$ be a closed smooth manifold carrying two negatively curved Riemannian metrics $g$ and $h$. Take a point $p \in M$ and vector $v \in T^{1}M$. Let $\gamma_{v,g}$ and $\gamma_{v,h}$ be the unique ...
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### Is a “central” extension of $\mathbb{Z}/m\mathbb{Z}$ by $\mathrm{GL}_n$ necessarily split?

Let $m \ge 1$ be an integer, let $k$ be a field of characteristic $0$, and let $$1 \rightarrow \mathrm{GL}_n \rightarrow E \rightarrow \mathbb{Z}/m\mathbb{Z} \rightarrow 1$$ be an extension of ...
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### Is $\{(\frac{3}{2})^{n}\}_{\mathbb{N}}$ is equidistributed in [0,1] (related open question) [on hold]

Is $\{(\frac{3}{2})^{n}\}_{\mathbb{N}}$ is dense in [0,1] (open question). A more general question is: Is $\{(\frac{3}{2})^{n}\}_{\mathbb{N}}$ is equidistributed in [0,1]?If so, Then density ...
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### best MAX-SAT solver for ising spin glass [on hold]

What is the best MAX-SAT solver problems for Ising spin glass? I tried Scip-Max-sat and open-wbo. While open-wbo cannot solve the instance with only 27 variable Scip-max-Sat fail to solve the one with ...
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### The real numbers object in Sh(Top)

If $X$ is a sober topological space, the real numbers object in the topos $\mathrm{Sh}(X)$ is the sheaf of continuous real-valued functions on $X$. This is proven very explicitly in Theorem VI.8.2 of ...
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### properties of formal delta functions

The formal delta function is $\,\,\displaystyle\delta(x):=\sum_{n\in\mathbb Z}x^n.$ If we agree that expressions $(x+y)^n$ for $n\in\mathbb Z$ are always expanded in non-negative powers of the second ...
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### Definition of Givental $J$-function of cotangent bundle of flag variety

I would like to know the definition of Givental $J$-function of cotangent bundle of flag variety. To state my question more precisely, let us briefly recall the definition of the Givental $J$-function ...
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### Eigenfunction of ergodic skew product fixed by commutator?

Background: Let $(Y, \mathcal{B},\mu,T)$ be an ergodic probability system and let $G$ be a compact metrizable group with compact subgroup $H$. Given a measurable map $\rho:Y \to G$. We may define the ...
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### Mutant pairs distinguished by [2,1]-colored HOMFLY polynomials

Morton and Cromwell showed that the famous mutant pair, Kinoshita-Terasaka and Conway knots, can be distinguished by HOMFLY polynomials colored by [2,1] Young diagram. Are there any other mutant pairs ...
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### Special fiber of $X(p)$ in characteritic $p$
Let $p \geq 5$ be a prime. Let $Y(p)$ be the fine moduli space representing elliptic curves + basis of the $p$-torsion over $\mathbb{Q}_p$ and let $Y_1(p)$ be the fine moduli space representing ...