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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  for details. $\gamma(t)$ in BdG Eq. is a one-...
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?
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
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
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
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.
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
44 views

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

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"?