0
votes
0answers
17 views

Rounding to decimal places by using simple formula and basic math operations [on hold]

Is there way to round number to decimal places using just simple math operations in one formula? No converting to text allowed. No considerations (like "if point is..then") allowed. No ...
0
votes
1answer
20 views

Local root numbers of the Hecke character associated with some specific CM elliptic curves, should they be some roots of unity?

TL;DR. Some local root numbers of the Hecke character associated with our specific CM elliptic curve by $\mathbf{Q}(i)$ seem to have value in $\mu_4$. But apparently our computation via Rohrlich's ...
2
votes
1answer
45 views

Is a symmetric, parallel (0,2)-tensor a metric?

I'm interested in affinely connected spaces, on which a metric is not necessarily defined, i.e. $(\mathcal{M},\Gamma)$. Since (as a physicist) my goal is to consider a generalized model of gravity, I ...
0
votes
1answer
18 views

Meaning of “Herbrand-Goedel recursive” in Kleene's “On Notation for Ordinal Numbers”

In Kleene's "On Notation for Ordinal Numbers", Journal of Symbolic Logic, Volume 2, Number 4, December 1938, he says that a function of natural numbers is taken to be effective if it is Herbrand-...
0
votes
1answer
31 views

Pushing forward a complex structure by submersion

I have a surjective smooth map with surjective differential between two balls $\phi:B^{2n}\rightarrow B^{2k}$. Fix an integrable almost complex structure $J$ on $B^{2n}$. Assume that $\mathrm{Ker}\:d\...
1
vote
0answers
38 views

How to show mapping cones are homotopy cofibers

In a dg-category $\mathcal{C}$, the $n$-translation of an object $C$ is an object $C[n]$ representing the functor $$ {\rm Hom}(-,C)[n]. $$ The cone of a closed morphism $f\colon C \to D$ of degree ...
0
votes
0answers
35 views

Prove or disprove the non colinearity of three points

Prove or disprove: Let $ABCD$ be a quadrilateral in Pasch Geometry for which the following holds $AB\cap CD=\{E\}$, $AC\cap BD=\{F\}$ and $AD\cap BC=\{G\}$. Then the points $E,F,G$ are not collinear. ...
0
votes
0answers
24 views

Heegaard diagrams for surgery on “nice links”

The following observation appears to be implicit in this paper but I am having trouble seeing it. Let $H \cup_\Sigma H'$ be the Heegaard splitting of $S^3$ of genus $g$. Let $L$ be a $g$ component ...
0
votes
0answers
27 views

Existence of universal covering group

Let $G$ be a connected simple Lie group, and $K$ its maximal compact subgroup. Denote by $\tilde{G}$ the universal covering group of $G$, and the covering map $p:\tilde{G}\rightarrow G$ gives a ...
2
votes
0answers
49 views

How to construct the espace etale (space of sections) for an arbitrary category?

I want to consider the sheaf of an arbitrary category (not only of sets, groups, modules and so on) on a topological space, using the language of etale space. In all references I am reading (...
8
votes
2answers
481 views

A Putnam problem with a twist

This question is motivated by one of the problem set from this year's Putnam Examination. That is, Problem. Let $S_1, S_2, \dots, S_{2^n-1}$ be the nonempty subsets of $\{1,2,\dots,n\}$ in some ...
0
votes
0answers
17 views

Reference for Minkowski functional when 0 is not in the interior

The Minkowski functional on a normed linear space $E$ is usually defined for convex (or sometimes even non convex) subsets $C$ of $E$ such that $0 \in \operatorname{int}(C)$. Is there any standard ...
0
votes
0answers
16 views

Approximating Uniform/Arbitrary distribution with Gaussian mixture model?

so Silverman in his 1986 book mentioned about approximating distributions with Gaussian mixture models but he didn't go much further into the topic...I'm just wondering, say I'm given a N-dimensional ...
4
votes
0answers
95 views

Is there some computational evidence of the $pq$ analog of Serre's conjecture?

The $pq$ analog of Serre's conjecture (see "Mod pq Galois representations and Serre's Conjecture"- Khare, Kiming) states that if $\bar{\rho}_1:G_{\mathbb{Q}}\rightarrow \text{GL}_2(\mathbb{F}_p)$ is a ...
4
votes
2answers
162 views

Elliptic regularity on compact manifold without boundary

Let $(M,g)$ be a Riemannian compact manifold without boundary, and $\Delta$ is the Laplace-Beltrami operator on $M$. Is there any result on the elliptic regularity like this: For any $u\in H^1(M)$, ...

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