Let us say that a non averaging sequence in a group G is a sequence x1,…,xn such that x2i≠xjxk for any indices i,j,k such that two at least are distinct. My question is: given n, what is the smallest group having a non-averaging sequence of length n? Has this question been already tackled in the … Read more
Closed. This question needs details or clarity. It is not currently accepting answers. Want to improve this question? Add details and clarify the problem by editing this post. Closed 6 years ago. Improve this question Consider the following double sum: Q(n)=1n2n∑i=1n∑j=1[∂ijlnf(x)]2 where ∂ij is the partial second order derivative (bounded for all indices), the function … Read more
In 2004 Kevin Ford established sharp asymptotics on Erdős’ problem on the number of different products a⋅b, a,b∈{1,…,n}. (http://arxiv.org/abs/math/0401223, see also discussion here: Number of elements in the set {1,⋯,n}⋅{1,⋯,n}) My naive question is whether there are much less different numbers of the form lcm(a,b), where a,b∈{1,…,n}. Answer AttributionSource : Link , Question Author : … Read more
I will be grateful for any reference for the following statements/claims. 1) Let’s consider the case of $p=2$ and the classic Adams spectral sequence with the $E_2$-term given by $\mathrm{Ext}_{A}(\mathbb{F}_2,\mathbb{F}_2)$. If $\alpha$ and $\beta$ are two permanent cycles in the Adams spectral sequence, converging to elements $f\in{_2\pi_i^s}$ and $g\in{_2\pi_j^s}$, then is it true that $\alpha\beta$ … Read more
I’ll start off a little vauge: Let E be a noncommutative ring which is finitely generated over its noetherian center Z. Denote by modE the category of finitely generated left E-modules and similarly for modZ. We have a functor F:modZ→modE which takes M to E⊗ZM, hence an induced map on (Quillen) K1-groups K1(F):K1(modZ)→K1(modE). I’m interested … Read more
This question is related to this one (https://math.stackexchange.com/questions/1383511/normal-curvature-of-geodesic-spheres) I’ve asked at math.stackexchange. Let (M,g) be a compact Riemannian manifold with no conjugate points and (˜M,˜g) its universal covering. Let ˆg the Sasaki metric on TM−{0} and dˆg its associated distance function. Fix ˜p∈˜M and R=1. Let ˜H:=˜M−¯B1(p). For x∈˜H, consider the geodesic sphere centered at … Read more
Let $\ell$ be an integer parameter. I want to ask the existence of the following design: There is a universal constant $\beta < 1$ such that for all sufficiently large $\ell$, the following holds: The universe size $d = O(\ell)$. There are $\ell^2$ sets in the design, $S_1, \dots, S_{\ell^2} \subseteq [d]$. $(\forall i \in … Read more
I am trying to get familiar with hyperfunctions, and I do have some familiarity with the classical theory of distributions. I am wondering whether hyperfunctions have any advantages over distributions. Are there any applications of the former which cannot be obtained using the latter? Any important examples? I was told one general property of hyperfunctions … Read more
I’ve asked this question on math.stackexchange some time ago (https://math.stackexchange.com/questions/1380176/how-to-compute-colimits-of-enriched-categories) and I received no complete answers, so I’m posting it here. Let $\mathscr{V}$ be a monoidal category. Let $\mathbf{Cat}_{\mathscr{V}}$ be the category of (small) categories enriched over $\mathscr{V}$. I would like to know how to compute (co)limits in $\mathbf{Cat}_{\mathscr{V}}$. This leads to some questions. 1)When … Read more
Let A and B be dg-categories over a field, viewed as A∞-categories. The A∞-category (actually, dg-category) of strictly unital A∞-functors A→B will be denoted by Fun∞(A,B). It is described explicitly (in the non-unital case) for example in P. Seidel’s book (“Fukaya category and Picard-Lefschetz theory”). Let Δ1 be the 1-simplex category, namely, the linear category … Read more
