All Questions

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-...

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?

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 $B$: ...

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 ...

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 ...

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.

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

$\newcommand\R{\mathbb R}$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 ...

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\...

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'...

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 ...

Let $X=\omega +1$ be convergent sequence. Then what does mean by "$X$ is convergent sequence"?

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 \...

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 ...

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: ...