# All Questions

**0**

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**0**answers

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

**1**answer

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

**1**answer

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

**1**answer

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

**1**answer

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**

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**0**answers

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**

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**0**answers

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**

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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**

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**0**answers

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**

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**0**answers

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

**2**answers

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**

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**0**answers

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**

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**0**answers

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

**0**answers

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

**2**answers

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 $u\in H^1(M)$, ...