Majorization definition: $x $ is majorized by $y$ iff $x$ is in the convex hull of all the points formed by permuting the components of $y$.
Question: $(5,5,0) $ is majorized by $(10,0,0)$ according to the alternate definition of majorization given at wikipedia.
My confusion is: the convex hul...
For the record, the tag gmat-exam has been manually removed as per what is suggested in this answer (since the community seems to have reached an unanimous agreement).
Proposal: Remove gre-exam, gmat-exam.
These are meta tags with very bare-bones tag wikis. Furthermore, there aren’t any other tags for important math exams, i.e. the IMO or USAMO, so why should we make an exception for these two?
Using differentiation under integral sign, prove that $\int_{0}^{\infty} e^{-(x^2+\frac {a^2}{x^2})b^2} dx=\frac {\sqrt {\pi}}{2b} \cdot e^{-2ab^2}$.
My Attempt:
Let,
$$F(a)= \int_{0}^{\infty} e^{-(x^2+\frac {a^2}{x^2})b^2} dx$$
Differentiating both sides with respect to $a$
$$\frac {dF(a)}{da}=...
Majorization definition: $x $ is majorized by $y$ iff $x$ is in the convex hull of all the points formed by permuting the components of $y$.
Question: $(5,5,0) $ is majorized by $(10,0,0)$ according to the alternate definition of majorization given at wikipedia.
My confusion is: the convex hul...
Proposal: Remove gre-exam, gmat-exam.
These are meta tags with very bare-bones tag wikis. Furthermore, there aren’t any other tags for important math exams, i.e. the IMO or USAMO, so why should we make an exception for these two?
