# All Questions

137,805
questions

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### 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
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24
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### 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?

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### 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 $B$:
...

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52
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### 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 ...

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### 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 ...

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22
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### 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
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56
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### 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

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44
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### 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 ...

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64
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### 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
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135
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### 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'...

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22
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### 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
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1
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70
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### 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
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2
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111
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### 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 \...

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1
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28
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### 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
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1
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60
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### 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:
...