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Let $(M,omega)$ be a symplectic manifold and $gamma in C^infty(I,M)$ a path in $M$. For $X,Y in Gamma_gamma(TM)$ I would like to compute the derivative...
1Mathematics Asked by TheGeekGreek on 2 years ago
I have found that the curve $z(x)$ on the complex plane with$$z=frac{ax+b}{x^2+1}$$at real $x$ spanning from $-infty$ to $+infty$ looks very...
2Mathematics Asked by Alexey Sokolik on 2 years ago
Can you find a function $beta(x)$ where if $a+b=n^m$ then $beta(frac{a}{b})$ is irrational but if $a+b$ isn't equal to $n^m$ then it is rational (...
1Mathematics Asked on 2 years ago
Prove that $xge dfrac{n(n-1)(n-3)}8$, where $x$ is the number of $4$-cycles in a graph on $n$ vertices with at least $displaystylefrac12,binom{n}{2}$ edges.If there are no...
2Mathematics Asked by shakir on 2 years ago
Given tetrahedron $ABCD$, let $r$ be the radius of the sphere inscribed tetrahedron. Prove that $$r<dfrac{ABcdot CD}{2,AB+2,CD}$$This is difficult question, my friends and I could not find...
2Mathematics Asked by mja on 2 years ago
Consider a measure space $(S, Sigma, mu)$ and the normed vector space $mathcal{L}^2(mu)$. Then for any measurable function $f: S to mathbb{R}$ with $f in mathcal{L}^2(mu)$ the norm is...
3Mathematics Asked by bcf on 2 years ago
Given a smooth real function $f$, we can approximate it as a sum of polynomials as$$f(x+h)=f(x)+h f'(x) + frac{h^2}{2!} f''(x)+ dotsb = sum_{k=0}^n frac{h^k}{k!} f^{(k)}(x) + h^n...
7Mathematics Asked on 2 years ago
Example 1Rational tangle dance mentioned here with operations:T(tangle)R(rotate)For example, sequence of operations $TTRTT$ is considered as $T^2 cdot R cdot T^2$ but not $2T...
1Mathematics Asked by user1787812 on 2 years ago
Let $U sim Unif(S^{d-1}).$ I was wondering if it's true that, and if yes, how could we prove that: $U = frac{Z}{|Z|}$ where $Z sim mathcal{N}(0, I_d),...
1Mathematics Asked on 2 years ago
I have measured the parameters for a hyperbola and an ellipse, let us call them$$begin{cases} a^2x^2 + b^2y^2 = 1 \ c^2x^2 + d^2y^2 = 1 end{cases}...
1Mathematics Asked by a20 on 2 years ago
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