13,260 reputation
22788
bio website lama.univ-savoie.fr/~bogosel
location Chambery, France
age 26
visits member for 3 years, 10 months
seen Dec 14 at 22:10

Third year Phd student at Universite de Savoie, France. Interests: free boundary problems, PDE, spectral optimization, numerical analysis.


Nov
25
comment Give the number of solutions of $x+y+z = 30$, for $4 \leq x \leq 14$, $3 \leq y \leq 17$, $10 \leq z \leq 25$.
Where do $x,y,z$ belong? If they are reals, then you cannot give the number of solutions. Are they integers?
Nov
25
comment Visual notion of tangential gradient
If you know what the normal derivative is, then the significance of the tangent derivative is straightforward. If you look at the gradient at a point on the boundary, you can decompose it in two parts: the parts in the normal direction and the rest. That rest is the tangential part.
Nov
19
comment Funny interconnection between a triangle and the ellipse inscribed
Here is the wikipedia article: en.wikipedia.org/wiki/Steiner_inellipse In the end, it mentions that the above theorem as Marden's theorem: en.wikipedia.org/wiki/Marden's_theorem Here is an elementary proof: dankalman.net/AUhome/pdffiles/mardenAMM.pdf
Nov
19
comment Funny interconnection between a triangle and the ellipse inscribed
Interesting :) I guess it is the conic which passes through the midpoints and is tangent to the sides of the triangle. The existence can be proved using affine transformations (from an equliateral triangle). The unicity follows from the fact that it passes through three points and is tangent to three lines. Anyway, it is interesting to see the connection with polynomials :)
Nov
18
comment Integral: $\displaystyle\int\dfrac{\sin^3\theta}{\sqrt{\cos\theta-2}}\,d\theta$
You could replace it with $\sqrt{2-\cos \theta}$. Maybe that's what the original question had.
Nov
18
comment Integral: $\displaystyle\int\dfrac{\sin^3\theta}{\sqrt{\cos\theta-2}}\,d\theta$
If you are working with real numbers, then $\sqrt{\cos \theta -2}$ makes no sense.
Nov
18
comment Dirichlet's principle- task.
I suppose that the second union is for $k \in B$.
Nov
18
comment If n $\geq2$, does G necessarily have an element of order $p^2$? Justify your answer.
@John Yes, but the counterexample still works :)
Nov
18
comment If n $\geq2$, does G necessarily have an element of order $p^2$? Justify your answer.
What is $G$, what is $p$?
Nov
10
comment Conditional probability elementary problem - check if I am right
But, indeed, the probability that a girl opens the door, is not equal to the probability that there exists a girl in the family.
Nov
10
comment Conditional probability elementary problem - check if I am right
If I use conditional probabilities for $(B)$ I get $P(\text{there are two boys} | \text{one child is a girl}) = P(\text{two boys and a girl})/P(\text{one child is a girl}) = \frac{3/8}{7/8}=\frac{3}{7}$.
Nov
10
comment Conditional probability elementary problem - check if I am right
:)) Yes. Sorry about that.
Sep
22
comment Is this bootstrap argument correct?
You said "the trace is preserved under weak convergence". Can you please give a reference where this result can be found?
Sep
15
comment basic question involving topology and the Hausdorff distance
If you can read a bit in French, I recommend springer.com/mathematics/book/978-3-540-26211-4 In chapter 2 there is a detailed discussion of different types of convergence of sets. There is an exercice which resembles your question. If you prove that $\Omega_n$ converges to $\Omega$ in the Hausdorff distance, then the convexity should imply the convergence of the boundaries.
Aug
15
comment Families of Square Roots of Identity Matrices
You can tackle the general case using reduction (diagonalization).
Aug
9
comment Distance between triangle's centroid and incenter, given coordinates of vertices
The sides of the triangle can be immediately calculated. After that, the coordinates of $G$ are just the averages of the coordinates of the vertices. For the incenter the formula is simple: you can find it here mathworld.wolfram.com/Incenter.html In my opinion there's no simpler way.
Jul
17
comment How prove $A^2=0$,if $AB-BA=A$
@Kelenner: I'm sorry. I didn't make all the computations.
Jul
17
comment How to find the determinant of this matrix
@user143993: This last equivalence you wrote is the definition of dependent vectors.
Jul
17
comment How to find the determinant of this matrix
@user143993: The statement you wrote is not right. The determinant is zero if and only if the columns (or the lines) are related. You can prove it like this: if the determinant is not zero, then any relation between the columns implies that the coefficients are zero (because the system has the unique solution of zeros). Therefore the columns are not related. Conversely, if the determinant is zero, then the system doesn't have a unique solution, i.e. has a non zero solution, i.e. you can find a relation between the column vectors.
Jul
17
comment How to find the determinant of this matrix
No, there is no $f$ here. The equation still defines a conic.