12,750 reputation
22482
bio website mathproblems123.wordpress.com
location Chambery, France
age 26
visits member for 3 years, 5 months
seen Jul 21 at 17:13

PHD - interests: PDE, Free boundaries, Shape Optimization


Dec
25
comment How many times is the digit $3$ repeated in $9^{666}$?
The answer seems to be 60. (done with pari-gp)
Dec
25
comment Proving continuity at a point $x_0$.
If you have a sequence in $A\cup B$ then there are a few cases: 1. All terms from a point on are in $A$. 2. All terms from a point on are in $B$. 3. There are two other sequences, one in $A$ and one in $B$ such that their union is the initial sequence.
Dec
25
comment Calculation of $\lambda$, If $x^2+2(a+b+c)\cdot x+3\lambda \cdot (ab+bc+ca) = 0$ has real roots
It seems that you wrote the inequalities backwards... The equilateral triangle doesnt verify that.
Dec
21
comment Proving that a polynomial $|P(x)|=e^x$ has a solution
@GinKin: The polynomial is a constant in the first case.
Dec
20
comment Examples of Baire class 2 functions
This paper contains some interesting facts about Baire class 1 functions: math.ucsd.edu/programs/undergraduate/1213_honors_presentations/… Maybe it can help you.
Dec
19
comment Show that there is a subspace $J$.
@evinda: It is nice to upvote the answers you receive if they are correct.
Dec
19
comment Show that there is a subspace $J$.
Of course. This is what everyone is saying in their answers.
Dec
16
comment Combinations math. What's the direct approach here?
Why not vote up and accept the answer you received??
Dec
14
comment Cover polygon with rectangles
Your question is not precise at all: how many rectangles do you want? What is their size? Are they equal rectangles? Do the sides of the covered polygon have only vertical or horizontal directions?
Dec
12
comment What is the maximum number of distinct roots does the characteristic polynomial have?
A characteristic polynomial of a $n \times n$ matrix has degree $n$ so it has at most $n$ solutions. A matrix that commutes with all matrices is a multiple of the identity matrix.
Dec
12
comment How prove this inequality $\frac{1}{n!}\sum\limits_{k=0}^{\infty}\frac{k^n}{k!}\ge e(C\ln{n})^{-n}$
You may try to use Stirling approximation: en.wikipedia.org/wiki/Stirling's_approximation
Dec
11
comment measurable sets
Looks like this is a duplicate.
Dec
11
comment Proving a combination of differentiability
I do not talk about the continuity of $f$, but of the possible extension by continuity of $f'$, which is a totally different thing. A function which is differentiable at $x_0$ is continuous at $x_0$. On the other hand, if $f'$ may exist at every point, but it may be discontinuous.
Dec
11
comment Proving a combination of differentiability
I will add in the question the sketch of the proof you search.
Dec
11
comment Simple Functional Equation $\frac{f(a)-f(b)}{a-b}\cdot(-a)+f(a)=-ab$
@chubakueno: Yes, you are right.
Dec
11
comment Simple Functional Equation $\frac{f(a)-f(b)}{a-b}\cdot(-a)+f(a)=-ab$
@NickKidman: You're right :) You don't need to verify in order not to lose points. What I wanted to say is that even at high levels verification is considered important. It doesn't mater that it is a trivial computation. You might find that your answer is wrong.
Dec
11
comment Differentiability at a point on a compact set implies difference quotients are bounded
Not necessarily. If the ratio is bounded then $f(x)=f(x_0)+g(x)(x-x_0)$ where $g$ is a bounded function. Pick a bounded continuous, non-differentiable function and you have found a counterexample.
Dec
10
comment Proving $(0,1) $ is not countable
@Inquest: Yes, but how do you prove that $\Bbb{R}$ is uncountable then?
Dec
8
comment Trigonometric equation: $2(\sin^6 x+\cos^6 x)-3(\sin^4 x+\cos^4 x)+1=0$
@dona12: then write it now. You can edit your question.
Dec
8
comment Trigonometric equation: $2(\sin^6 x+\cos^6 x)-3(\sin^4 x+\cos^4 x)+1=0$
Try to make the title about the question, not about begging for help.