The Question (with details and generality removed) With proper capitalization, how many grammatical English sentences could "buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo buffalo" possibly represent? Motivation The Eng...

If $f$ be a meromorphic function on the complex plane and $(1-|z|)|f(z)|$ $\longrightarrow$ $0$ as $|z|$ $\longrightarrow$ 1 then show that $f$ does not have any pole on the unit circle. This looks very simple but I somehow have not able to prove it rigorously. Thanks for any help.

Consider the Fourier transform defined as $$ \mathcal{F}[f](p) = \int_{-\infty}^{+\infty}f(x)e^{-j2\pi xp}dx $$ Assume that $$ f(x) = \left\{ \begin{array}{ll} 1 & |x| < \frac{1}{2} \\ 0 & \text{otherwise} \end{array} \right. $$ under such hypothesis we now that $$ \mathcal{F}[f](p) = \hat{...

From my limited understanding, complex differential geometry studies the differential geometry of complex manifolds, and complex algebraic geometry studies algebraic geometry where the underlying field is the field of complex numbers. I have come across the term complex analytic geometry in a num...

I've seen in some books and notes that in order to define the tangent vector $v:C^\infty(p)\to\mathbb R$, the author defines $C^\infty(p)$ as the set of real valued functions $f:M\to\mathbb R$ such that does there exist an open set $U\subseteq M$ containing $p$ and $f|_U$ is smooth and then defin...