2,682 reputation
1629
bio website
location Besançon, France
age 34
visits member for 1 year, 6 months
seen Apr 3 at 18:32

Hello!

I am a statistician at INSEE, the French national statistical institute.

Mathematics is mainly a hobby for me, and I strive not to forget too much from university (MS in applied mathematics at Lyon 1). MSE helps enormously in giving ideas to learn more.

I also like computing and numerical analysis.


Feb
18
comment Solve linear equation system $A'Ax=A'Bz$
Singular value decomposition, see also here
Feb
18
comment How much is ${\aleph_0}^{\aleph _ 0}$?
An idea to prove they are both equipotent to $[0,1]$: for the LHS one, use binary digits decomposition, for the RHS, use decomposition in continued fractions. There are some tricks not to forget, but it should work.
Jan
28
comment Let $f : [0;1] \to \mathbb{R}$ be a continuous function such that $f(0) = 0$. Which of the following statements are true?
You can't take $f(t)=\sin nt$ since $f$ is fixed and $n$ is varying (notice th for all $n$).
Jan
26
comment Pyramid Question
Ok, then as you write in the second paragraph, the "top" of the pyramid may be at any height, thus all side will not be equal, in general
Jan
17
comment are $f(f(x))=f(x)$ and $f(x)=x$ equivalent?
Try $f(x)=|x|$.
Jan
2
comment Gaussian Quadrature
If $ax_1 + bx_2 + cx_3 + dx_4 = 0$ for any choice of $x_1,x_2,x_3,x_4$, then $a=b=c=d=0$. To see why, simply let $x_1=1$ and $x_2=x_3=x_4=0$, thus $a=0$, etc.
Dec
28
comment Scalar product and uniform convergence of polynomials
Wow! I'll need some time to digest this :-) Very clever. Thank you! [Just one question, in the inequality with the sup, isn't it $1/C_n$ in the RHS?]
Dec
27
comment Is this a known number-theoretic function?
@MichaelHardy You are right. :-) Maybe you can do something with Chinese remainder theorem, but I doubt it would give you the shortest sequence.
Dec
27
comment Entire function $f(z)$ bounded for $\mathrm{Re}(z)^2 > 1$?
I have removed the images to follow advice from this answer about copyright on Meta. I'm quite sensitive on copyright issues, and would not like to infringe any law. I'll rework the proof in LaTeX this week-end: in the meantime, there is still the link to Google Books, or even the book itself for those who can find it in a nearby library!
Dec
26
comment A logical problem I can't solve. Please help. (About money)
You give back $2\times 23=46$ euros the next day, that is 1 euro more than you spent at the restaurant. This is the "missing" euro.
Dec
26
comment How to sketch $y = \left\lfloor \sqrt{2-x^2} \right\rfloor$?
Yes, it's the domain, but notice it's small. To sketch it, you just have to find on which intervals it can take which value. First, notice it's an even function. Then, if $x>1$, obviously $\sqrt{2-x^2}<1$ thus the "floor" is 0. And if $0<x<1$, obviously $1<\sqrt{2-x^2}<\sqrt{2}$, thus the "floor" is 1. Should not be that difficult to plot a function that is 1 on ]-1,1[ and 0 elsewhere. Just be careful with interval endpoints.
Dec
26
comment How to sketch $y = \left\lfloor \sqrt{2-x^2} \right\rfloor$?
Hint: it's only defined for $|x|\le\sqrt{2}$. And 2nd hint: it must be a step function.
Dec
26
comment Multiple context available for the AC?
AC is independent of ZF, not only of Peano arithmetic. So you can accept it or reject it. Some mathematicians reject it because it gives only "existence proofs", without any construction. Regarding Wiles'proof, see math.stackexchange.com/questions/151895/…
Dec
26
comment Counterexample that $a\in G$, $a^n\notin H$, for $H$ a subgroup of finite index $n$ in $G$.
Are you looking for an $a\in G$ such that $a\not\in H$ but $a^n \in H$? If so, take $G=\Bbb Z/4\Bbb Z=\{0,1,2,3\}$, $H=\{0,2\}$ and $a=1$.
Dec
26
comment To evaluate $\int_0^{+\infty} \frac{\;dx}{\sqrt[3]{x^3+a^3}\sqrt[3]{x^3+b^3}\sqrt[3]{x^3+c^3}}$
Very impressive. Thank you very much!
Dec
25
comment Scalar product and uniform convergence of polynomials
@timur Thank you for the hints! I'll have a look at this tomorrow. But I have to admit I know nothing about Petrov-Galerkin of Babuska-Brezzi. Do you have some references to recommend on this? Happy Christmas ;-)
Dec
25
comment On the sequence arctan (tan (n))
@GitGud I'm a bit puzzled: for you tan must not be periodic otherwise it has no inverse. But then, do you admit sine and cosine are periodic? I hope so, otherwise, you'll have to throw away Fourier series, among others. So, how do you define arcsine and arccosine? I hope you will give up, not the discussion, but your claim that "my stuff isn't standard at all". Mathematics is all about learning and discovering, I hope you have discovered something today. Happy Christmas.
Dec
24
comment What is the meaning of $n\in \aleph$
@AsafKaragila Sure, but to provide a well-ordering, you will often need the axiom of choice. Admittedly, my previous sentence was not clear at all on this.
Dec
24
comment On the sequence arctan (tan (n))
@GitGud Sure, it's why it has an inverse only on ]-pi/2,pi/2[, where it is bijective. You should draw a graph of $\tan(x)$, or ask WolframAlpha to do it for you.
Dec
24
comment Mclaurin on $\arccos(\frac{n^2-1}{n^2+1})$
@malloc Done...