# Denis Serre

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## Registered User

 Name Denis Serre Member for 2 years Seen 3 hours ago Website Location Lyon, FRANCE Age 58
My research activity is mainly in PDEs, with applications to Physics, especially in Fluid Dynamics. I have written a 2-volume book on Conservation laws, and a book about the Hyperbolic IBVP (in collaboration with S. Benzoni-Gavage). I have edited in collaboration with S. Friedlander, a 4-volume Handbook of Mathematical Fluid Dynamics. I have a continuous interest in Matrix Analysis. I have written a Graduate Text about Matrices. The second edition has been released in November 2010.
 1d comment Strong convergence in the Bochner space L^p([0,T],X)Is the pointwise convergence $x_n(t)\rightarrow x(t)$ in $X$ a claim or an assumption? If it is a claim, it is false. 1d revised Sequences equidistributed modulo 1added 23 characters in body 2d answered Which popular games are the most mathematical? 2d comment Which popular games are the most mathematical?The French version of te game is "Le cochon qui rit". English translation "The laughing pig". May16 awarded ● Nice Answer May14 comment Matrix Inverse with Same Principal MinorsI eventually delete my answer. It seems that I described the set of involutory matrices! Fortunately, this was not a doctoral dissertation; see the MO question about urban legends... May14 comment Matrix Inverse with Same Principal MinorsSebastian, I changed deeply my answer, because there was a mistake in calculations. It is still nteresting, I hope, but in a different way. May13 awarded ● Necromancer May6 awarded ● Notable Question May6 revised cube + cube + cube = cubeadded 42 characters in body May6 comment cube + cube + cube = cube@Joel. Yes, I can! May5 comment cube + cube + cube = cubeActually, I should like to accept your answer. Unfortunately, I accepted already JHI's. May5 comment cube + cube + cube = cubeBeautiful! I'm especially impressed that you found a way to explain it in a convincing way by using 2-D figures. Apr29 comment Verifying the correctness of a Sudoku solution (A2) doesn't work if three of the four subsquares are aligned. Apr26 awarded ● Popular Question Apr25 comment What is the best *general triangle*?Related to this question is the observation that even if you succeed to draw a "general triangle" as described above, you can still "prove" that it has to equal sides (hence two equal angles). Of course, you cheat somewhere, but it is very subtle. This was shown to me by my math teacher when I was 12, and I never forget the argument. This teacher claimed that "Geometry is the art of making correct reasoning from wrong pictures"; in French "la Géométrie est l'art de raisonner juste sur des figures fausses". Apr21 awarded ● Enlightened Apr21 awarded ● Nice Answer Apr20 comment Inverse of a totally unimodular matrix@S. Sra. If you multiply modulo $2$, you cannot distinguish between $+1$ and $-1$. Therefore the minors are defined only modulo $2$, which means that they are either $0$ or $1$. Since every matrix should be TU modulo $2$, this notion in not interesting in ${\mathbb Z}_2$. It is only interesting in $\mathbb Z$, in which the product of TU matrices is not even unimodular in general. So the question about multiplication is just not a good one. Apr20 revised Inverse of a totally unimodular matrixedited body Apr20 comment Inverse of a totally unimodular matrix@qianchi. Of course you're right. I'll edit. Apr20 accepted Inverse of a totally unimodular matrix Apr19 answered Inverse of a totally unimodular matrix Apr17 revised cube + cube + cube = cubeadded 135 characters in body Apr12 accepted A series question related to solution of Laplace equation Apr12 comment How to solve this kinds of equationsMO is not designed for posing exercises. Apr12 answered A series question related to solution of Laplace equation Apr11 revised Fixed point theoremsadded 207 characters in body Apr10 answered Fixed point theorems Apr10 revised Fixed point theoremsadded 1 characters in body Apr4 answered Concavity of $\det^{1/n}$ over $HPD_n$. Mar29 comment Geometric Interpretation of TraceHowever, this answer is somehow duplicate of that by Yemon Choi. Mar29 comment Geometric Interpretation of TraceThis comment finds a wide extension in the notion of numerical measure of a matrix, which is supported by the numerical range. See Th. Gallay & D. S. Comm. Pure Appl. Math. 65 (2012), pp 287-336. Mar28 awarded ● Nice Answer Mar25 comment Bounding the second derivative of the log-determinantAbout the entry of $B$ larger than $1$, is it diagonal ? Mar22 comment eigenvalues of two nonnegative matricestrivial application of minmax formulae. Mar21 revised Examples of interesting false proofsadded 2 characters in body Mar20 accepted On the convexity of element-wise norm 1 of the inverse Mar19 answered Examples of interesting false proofs Mar19 answered On the convexity of element-wise norm 1 of the inverse Mar18 revised Motivating the Laplace transform definitionedited body Mar18 answered Motivating the Laplace transform definition Mar18 answered Spectrum theorem for p-adic matrix analysis Mar15 revised The probability for a symmetric matrix to be positive definiteadded 17 characters in body Mar15 comment The probability for a symmetric matrix to be positive definite@Federico. Right! I meant "among the Euclidian norms". Mar15 awarded ● Popular Question Mar15 revised Distribution of the spectrum of large non-negative matricesedited title Mar11 comment Behaviour of the gradient w.r.t. boundary conditions for elliptic PDEsCertainly not! You can add any linear function to one of both. Mar9 comment What goes wrong for the Sobolev embeddings at $k=n/p$?actually, the embedding holds true in one critical case, namely $p=1$, $k=n$. Mar8 awarded ● Popular Question