All Questions
137,805
questions
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-...
-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?
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 $B$:
...
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 ...
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 ...
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.
-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
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 ...
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 .
$$\pi(x) = \operatorname{R}(x) - \sum_{\rho}\operatorname{R}(x^{\rho}) - \frac1{\ln x} + \frac1\pi \arctan \frac\...
8
votes
1
answer
135
views
Are there arbitrarily large families of lines in $\Bbb R^3$ with average angle $\ge \pi/3$?
Question: Can I have an arbitrarily large finite family of lines $\ell_1,...,\ell_n\subset\Bbb R^3$ so that the average angle between two (distinct) lines is $\ge \pi/3$?
If my integral calculus hasn'...
1
vote
0
answers
22
views
How to extend this sum involving generalized harmonic numbers?
It is well-known since Euler that the Generalized harmonic numbers, defined for $n\in\mathbb N$ by $$H_n^{(r)}=\sum_{k=1}^n\frac1{k^r},$$ can be naturally extended for non integer $n$ in terms of ...
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"?
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 \...
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 ...
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:
...