All Questions

Filter by
Sorted by
Tagged with
1 vote
0 answers
6 views

On the Bogoliubov-de Gennes equation (BdG equation)

I'm interested in the BdG (Bogoliubov-de Gennes) Eq. BdG Eq. is a evolution equation of coupled operator $(\gamma(t), \alpha(t))$, see Eq. (1.11) in [1] for details. $\gamma(t)$ in BdG Eq. is a one-...
user avatar
  • 11
-3 votes
0 answers
24 views

Percentage problem [closed]

There is a poll where 27% of people voted yes, 73% voted no. After you vote the new poll suggests 31% voted yes, 69% voted no. Is there a way to know the number of people who voted in the first poll?
user avatar
0 votes
0 answers
9 views

Behavior of correlations in Gaussian sampled matrices

Suppose I take $B$ samples of $x\sim \text{Normal}(0,\Sigma)$ and stack them as rows of matrix $X$. Expectation of the following two quantities seem to follow a simple law as a function of $B$: ...
user avatar
1 vote
0 answers
52 views

Simple motivation to study arithmetic geometry

Is there a simple-to-understand diophantine equation (in the sense that it's easy to explain to a child) that has a positive integer solution, but to prove that such a solution exists and to find it ...
user avatar
  • 213
1 vote
0 answers
15 views

Isometry induced on the Grassmannian of planes to the tangent space

Let $(M,g)$ be a Riemannian manifold and assume that $G$ acts isometrically and effectively on $M$. We can then split $TM = \mathcal V\oplus \mathcal H$ globally, though it not does not need to ...
user avatar
1 vote
0 answers
22 views

Intersecton form of complete smooth Toric surface

Given a complete smooth Toric surface (over $\mathbb C$), is its intersection form well-known? Or is there an algorithm to calculate it? Thanks in advance.
user avatar
  • 311
-5 votes
0 answers
56 views

Is this some math rule. If so, who discrebed it? [closed]

calculator Divided by two is the same as multiplied by five. It also applies if we multiply two and five to the second third, etc... Thank you all
user avatar
0 votes
0 answers
44 views

About Euclidean distances

$\newcommand\R{\mathbb R}$Let $0<d_1<\cdots<d_k<\infty$ and let $m_1,\dots,m_k$ be any integers $\ge1$. Let $n:=m_1+\dots+m_k-1$. Let $d$ denote the Euclidean distance in $\R^n$. Do then ...
user avatar
0 votes
0 answers
64 views

Explicit formula of Zeta function with special type of weight:

First of all , I myself is not so sure what I'm asking here but please bear with me . $$\pi(x) = \operatorname{R}(x) - \sum_{\rho}\operatorname{R}(x^{\rho}) - \frac1{\ln x} + \frac1\pi \arctan \frac\...
user avatar
  • 458
8 votes
1 answer
135 views

Are there arbitrarily large families of lines in $\Bbb R^3$ with average angle $\ge \pi/3$?

Question: Can I have an arbitrarily large finite family of lines $\ell_1,...,\ell_n\subset\Bbb R^3$ so that the average angle between two (distinct) lines is $\ge \pi/3$? If my integral calculus hasn'...
user avatar
  • 10.1k
1 vote
0 answers
22 views

How to extend this sum involving generalized harmonic numbers?

It is well-known since Euler that the Generalized harmonic numbers, defined for $n\in\mathbb N$ by $$H_n^{(r)}=\sum_{k=1}^n\frac1{k^r},$$ can be naturally extended for non integer $n$ in terms of ...
user avatar
  • 12.7k
0 votes
1 answer
70 views

What does mean by "$\omega +1$ is convergent sequence"? [closed]

Let $X=\omega +1$ be convergent sequence. Then what does mean by "$X$ is convergent sequence"?
user avatar
  • 317
9 votes
2 answers
111 views

How exotic can an infinite biproduct in an additive category be?

Let $C$ be a category with a zero object $0$, small products, and small coproducts. Let $(A_i)_{i \in I}$ be a (possibly infinite) list of objects. There is a canonical map $\amalg_{i \in I} A_i \to \...
user avatar
  • 50.5k
1 vote
1 answer
28 views

Tangent cone of a proper CAT(0) is a proper CAT(0) space

Let $(X,d)$ be a proper CAT$(0)$ space. Let $x\in X$ and let $T_x X$ be the tangent cone of $X$ at $x$ equipped with its usual distance denoted $d_x$. It is a known fact that $(T_x X, d_x)$ is a ...
user avatar
  • 71
3 votes
1 answer
60 views

A faulty proof that a Whitehead Double of a knot is smoothly slice

We denote the untwisted Whitehead double of a knot $K$ to be $Wh(K)$. As an example, here is the oriented Whitehead double of the figure eight knot: Let us look in the neighborhood of the clasp: ...
user avatar

15 30 50 per page
1
2 3 4 5
9187