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I am currently looking into Halley's Method. However, I wanted to see if there were better methods to solve the problem I am looking to solve. Fast means a low...
Asked on 12/29/2021
0 answerLet G be a group and A an abelian subgroup of G. I want to prove that for each irreducible representation $p$ we have that $dim(p)leq [G:A]$.I...
Asked on 12/29/2021 by Myanklana
1 answerThe Leibniz integral rule states $${displaystyle {frac {d}{dx}}left(int _{a}^{b}f(x,t),dtright)=int _{a}^{b}{frac {partial }{partial x}}f(x,t),dt}$$ when the integral bounds are not a function of $x$, i.e. the variable...
Asked on 12/29/2021
3 answerLet $X$ and $Y$ be two random variables with values in $[0,1]$, such that $$E[X] = E[Y]$$ and $$ E[X+(1-X) ln(1-X)] = E[Y+(1-Y) ln(1-Y)] .$$...
Asked on 12/29/2021 by Adrien Deliège
1 answerWe have tha matrix begin{equation*}A:=begin{pmatrix}1 & 5 & 8 & 2 \ 2 & 4 & 6 & 0 \ 3 & 3 & 8 & 2 \...
Asked on 12/29/2021
1 answerSuppose that $f, g$ are non negative continuous functions in $[a, b]$, and $K, L$ positives constants such that$$f(x) leq K + L int_a^x...
Asked on 12/29/2021
2 answerUse Cauchy formula to solve $$int _0^{2pi} frac{dt}{a cos t+ b sin t +c} $$ Given $sqrt{(a^2+b^2)}=1<c$.I tried a variable substitution, but nothing elegant. Can anyone solve...
Asked on 12/29/2021
3 answerThis is a question that appeared in the $2018$ Southeast Asian Mathematical Olympiad:In a triangle with sides $a,b,c$ opposite angles $alpha,beta,gamma$, it is known that $$a^2+b^2=2019c^2$$...
Asked on 12/27/2021
3 answerIt is given in the book by Malcolm Cameron, titled: Mathematics the Truth; that the circle $x^2+y^2=5$ has an infinite number of points with at least one coordinate irrational,...
Asked on 12/27/2021
1 answerAll the natural numbers from $1$ to $100$ are written adjacent to each other in a single row. Now, this is considered as a single number, $N$...
Asked on 12/27/2021 by Shane Watson
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