Selim Ghazouani
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 Dec11 revised When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product? added 8 characters in body Dec11 comment When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product? For example any conjugate of a rotation preserve a scalar product, but does not belong to $O_2(\mathbb{R})$. Dec11 comment When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product? Not really. I'm looking for conjugates of the orthogonal group since the scalar product is not necesserally the canonical euclidean product in the canonical basis. Dec11 reviewed Approve When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product? Dec11 asked When does an element of $\mathrm{Sl}_n(\mathbb{R})$ preserve a scalar product? Dec4 comment Automorphism of the free group I'm not sure I get what you want to say. If you read carefully Farb and Margalit(p.87, I guess there is only one edition), the mapping class group of the once punctured torus is isomorphic to the central extension of $GL(2,\mathbb{Z})$. Maybe you make the distinction whether the torus is thought with or without boundary. Nevertheless, I would be glad to have further explaination on this proof. Dec3 comment Automorphism of the free group Could you detail a bit I'm not sure I understand your proof. Dec3 revised Automorphism of the free group added 1 characters in body Dec3 revised Automorphism of the free group added 142 characters in body Dec3 asked Automorphism of the free group Nov25 answered Let $x,y$ in a group G with odd order. Let $x^2=y^2$. Show that $x=y$. Nov25 accepted Defining a group morphism using generators Nov25 comment Defining a group morphism using generators Yes I have edited. Then $\varphi)$ is trivial on $\mathcal{R}$. $\mathcal{R}$ is a word in $a$ and $b$. It is clear $\varphi$ must be trivial on $\mathcal{R}$. But does such a $\varphi$ exist ? Nov25 revised Defining a group morphism using generators edited body Nov25 asked Defining a group morphism using generators Nov23 comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. Anyway your proof had to be false because you proved that $f'$ is continuous, what we clearly know to be false ! What would be great is to construct explicitly such function ... Is there here food for another $MSE$ question ? Nov23 comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. Sorry I may I have been a bit hard on your proof. There are 2 mistakes: 1) in the assumption that left and right limits exists of the derivative exists 2) the values of $d$ are not unspecified, they clearly depends on the values of $\frac{f(x) - f(c)}{x-c}$ so you cannot conclude $\lim_{c+} f' = A$. Is it clearer ? Nov23 comment Prove that if a function $f$ has a jump at an interior point of the interval $[a,b]$ then it cannot be the derivative of any function. This proof is false. The relevant result is the Darboux theorem which is a bit deeper. Nov23 comment Calculate $\int_{\partial D}\left ( 1+z+z^{2} \right ) (e^{\dfrac{1}{z}} +e^{\dfrac{1}{z-1}}+e^{\dfrac{1}{z-2}} ) dz$ Have you ever heard of the Residues theorem ? Nov22 comment A complex problem. @Mat He Mat Cian : let $\theta$ be in $[0,2\pi]$ and $\epsilon > 0$ . Since $A$ is dense there exist $j_n$ and $k_n$ two sequences such that $k_n r + j_n$ goes to $\frac{\theta}{2\pi}$. Since the exponential is a continous mapping $e^{2i\pi(k_n r + j_n)} = e^{2i\pi k_n r}$ converges to $e^{i\theta}$.