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Let $X$ be a smooth projective $n$-fold and $L$ be a line bundle on $X$. We have Riemann-Roch formula, when $n=1$,$chi(L)=chi(mathcal{O}_X)+mathrm{deg}(L)$, when $n=2$,...
Asked on 12/06/2021
0 answerI have tried to do it myself and then looked for any hint here, but I can't reach the solution. Is it possible that it simplifies to a sine function...
Asked on 12/06/2021 by marooz
1 answerWhy does $$frac{n!n^x}{(x+1)_n}=left(frac{n}{n+1}right)^xprod_{j=1}^{n}left(1+frac{x}{j}right)^{-1}left(1+frac{1}{j}right)^x$$ where the subscript n is the rising factorial in the left denominator my attempt:the index n in the product indicates the indicates the term ...
Asked on 12/06/2021
1 answerI am trying to understand the radix-2 square root shown in Chapter 6 of Digital Arithmetic(Miloš D.ErcegovacTomásLang). I am missing something in the computation of F[j]. I am attaching the...
Asked on 12/06/2021 by ammrra
0 answerLet $mathbb{K}$ be a field with $1_{mathbb{K}}+1_{mathbb{K}}neq 0_{mathbb{K}}$. Let $V$ be a $mathbb{K}$-vector space and let $phi:Vrightarrow V$ be a inear map with $phi^2=text{id}_V$....
Asked on 12/06/2021
1 answer$$lim_{xto 0} frac{(e^x-1)+(e^{-x}-1)}{xtan x}$$$$=lim_{xto 0} frac{1}{tan x } left(frac{e^x-1}{x} -frac{e^{-x}-1}{-x}right)$$ $$=0$$Which is invalid. What am I doing wrong?...
Asked on 12/06/2021
4 answerLet $mathbb{K}$ be a field and for each $displaystyle{f=sum_{i=0}^ma_it^iin mathbb{K}[t]}$ let $displaystyle{f'=sum_{i=1}^mia_it^{i-1}in mathbb{K}[t]}$ be the formal derivative of $f$. Let begin{equation*}phi : mathbb{K}[t]rightarrow mathbb{K}[t], ...
Asked on 12/06/2021
1 answerThe paper "The Distribution of the Maxima of a Random Curve" derives a certain probability as the following integral (p. 413):$$int_{y_0}^{y_0+Delta y}dxiint_{0}^{M_2Delta x}detaint_{-M_2}^{eta/Delta x}dzeta P(xi,eta,zeta)tag{a}...
Asked on 12/06/2021 by Code mx
1 answerLet $k$ an algebraically closed field.I want to prove the following:Every $2$-dimensional $k$-algebra with only one prime ideal is isomorphic to $k[x]/(x^2)$.Not every $3$-dimensional...
Asked on 12/06/2021 by LeviathanTheEsper
2 answerQuestion:If $x^2+y^2=1$, prove that $-{sqrt2}leq x+y leqsqrt2$My approach:$$frac{x^2+y^2}{2}geqsqrt{x^2y^2}$$$$ frac12geq xy$$$$frac{-1}{sqrt2}leqsqrt{xy}leq frac{1}{sqrt2} $$Now how do I proceed from here?...
Asked on 12/06/2021 by General Kenobi
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