# All Questions

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### Asymptotic decay for the inhomogeneous Schrödinger equation

Let $H$ be an Schrödinger operator $(-\Delta+V(x))$ with a radially symmetric and smooth potential and $H$ is e.s.a. on $C^\infty_0(\mathbb{R}^n)$, furthermore let $\lambda$ be an element of the ...
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### Generalization of the alternating sign test for convergence of a series?

I'm struggling with a series of the form $$\sum_n |a_n|\, s_n$$ where $s_n$ is the sign of a simple function of $n$. The $|a_n|$ monotonically decrease and are relatively simple functions of ...
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### Hilbert triples

I apologize if this is a trivial matter for the analysts out there, but I looked this up in a number of books (e.g., H. Brezis, J. Wloka) and could not find a satisfying discussion, one that would ...
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### Is there a relationship between the standard conjectures and Langlands program?

I would like to know are there connections between Standard conjectures on algebraic cycles and Langlands program (in the light of Motives, I assume)? What implications would a development of the ...
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### A perturbation question for the intersection of C*-subalgebras

This feels like something I may have asked before (in which case, apologies) and it also might be some kind of "standard counterexample in a book on C* algebras". Let M be a unital C*-algebra and let ...
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### Old Math books, will research and sell most [on hold]

I saw an earlier thread on selling old math books. My dad was a professor at Manhattan College for many years, he passed away a couple of years ago and has tons of old math books. I promised him I ...
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### Fast computation of a Groebner basis - What is Possible

I need to compute a Groebner basis of 18 polynomials in 19 variables the terms of which have degree at most 3. My aim is to exploit a symmetry in a PDE problem and I am not an expert in algebra or ...
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### graphical estimate of convergence rates [looking for textbook reference] [on hold]

I asked this question already in mathematics, but got no sufficient answer. I am writing a paper for engineers. There, under other things, I compare convergence rates of sequences $x_n \to x^*$, ...
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### Lower central series in a free pro-p group

Let $F$ be a nonabelian finitely generated free pro-$p$ group, $H \leq_c F$ of infinite index. Denote by $\{F_n\}_{n \in \mathbb{N}}$ the lower central series of $F$, and set $r_n = [F : F_nH]$. Is ...
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### Intersection of closed geodesics in hyperbolic surface

This question may be easy but I could not come up with a proof. Let $F$ be a hyperbolic surface of finite type (with finitely many boundary and finitely many puncture). Let $\gamma$ be a closed ...
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### The set of matrices with same spectral radius

I am working on an optimization problem over the set of positive matrices (that is, matrices where all entries are positive numbers) that have the same spectral radius. My main problem is how to ...
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### Trees with a maximal convex hull: are the only optimal solutions Steiner trees?

For given $n\geqslant 3$, I'm looking for a connected set composed of $n$ equal segments in the plane such that the convex hull of it has maximal area $A(n)$. To simplify notation, we'll take ...
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### Bounding Random Quadratic Gauss sums

I'm interested in seeing whether the following is true. Assume $u$ is uniform on $[0,1]$ and $|\epsilon_k|=1$ for all $k=1,2,\ldots,n$. We have \begin{align*} ...
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### Period doubling bifurcations [on hold]

In the bifurcation diagram, is it true that if the function $f_r(x)$ at $x^*$ (where $x^*$ is a fixed point where a bifurcation occurs) can be locally written as a smooth function then ...
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### Linear extensions and directed, rooted spanning trees

Let $P$ be a poset with a unique bottom element $\perp$ and view its Hasse diagram $H$ as an oriented graph. Can the principle of exclusion-inclusion be used to calculate the number of linear ...
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### Singularities in mixed characteristic

Let $R$ be a regular local ring in mixed characteristic. Moreover, I assume that $R$ is the local ring of a point on a smooth $\mathbb Z_p$-scheme and that $R/pR$ is regular. ($\mathbb Z_p$ is the ...
I know that if $A$ is a simple abelian variety over a number field $k$ with all endomorphisms defined over $K$ then $\mbox{End}(A_K)\otimes \mathbb{Q}$ is a division algebra with a positive ...
Say I have a cluster algebra with principal coefficients and initial cluster $x_1,\ldots,x_n$. I don't want to invert the coefficient variables $y_1,\ldots,y_n$. The Laurent Phenomenon says that ...