Denis Serre
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Registered User
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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.
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1d |
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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. |
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1d |
revised |
Sequences equidistributed modulo 1 added 23 characters in body |
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2d |
answered | Which popular games are the most mathematical? |
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2d |
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Which popular games are the most mathematical? The French version of te game is "Le cochon qui rit". English translation "The laughing pig". |
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May 16 |
awarded | ● Nice Answer |
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May 14 |
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Matrix Inverse with Same Principal Minors I 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... |
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May 14 |
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Matrix Inverse with Same Principal Minors Sebastian, I changed deeply my answer, because there was a mistake in calculations. It is still nteresting, I hope, but in a different way. |
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May 13 |
awarded | ● Necromancer |
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May 6 |
awarded | ● Notable Question |
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May 6 |
revised |
cube + cube + cube = cube added 42 characters in body |
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May 6 |
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cube + cube + cube = cube @Joel. Yes, I can! |
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May 5 |
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cube + cube + cube = cube Actually, I should like to accept your answer. Unfortunately, I accepted already JHI's. |
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May 5 |
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cube + cube + cube = cube Beautiful! I'm especially impressed that you found a way to explain it in a convincing way by using 2-D figures. |
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Apr 29 |
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Verifying the correctness of a Sudoku solution (A2) doesn't work if three of the four subsquares are aligned. |
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Apr 26 |
awarded | ● Popular Question |
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Apr 25 |
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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". |
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Apr 21 |
awarded | ● Enlightened |
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Apr 21 |
awarded | ● Nice Answer |
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Apr 20 |
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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. |
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Apr 20 |
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Inverse of a totally unimodular matrix edited body |
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Apr 20 |
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Inverse of a totally unimodular matrix @qianchi. Of course you're right. I'll edit. |
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Apr 20 |
accepted | Inverse of a totally unimodular matrix |
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Apr 19 |
answered | Inverse of a totally unimodular matrix |
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Apr 17 |
revised |
cube + cube + cube = cube added 135 characters in body |
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Apr 12 |
accepted | A series question related to solution of Laplace equation |
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Apr 12 |
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How to solve this kinds of equations MO is not designed for posing exercises. |
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Apr 12 |
answered | A series question related to solution of Laplace equation |
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Apr 11 |
revised |
Fixed point theorems added 207 characters in body |
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Apr 10 |
answered | Fixed point theorems |
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Apr 10 |
revised |
Fixed point theorems added 1 characters in body |
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Apr 4 |
answered | Concavity of $\det^{1/n}$ over $HPD_n$. |
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Mar 29 |
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Geometric Interpretation of Trace However, this answer is somehow duplicate of that by Yemon Choi. |
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Mar 29 |
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Geometric Interpretation of Trace This 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. |
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Mar 28 |
awarded | ● Nice Answer |
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Mar 25 |
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Bounding the second derivative of the log-determinant About the entry of $B$ larger than $1$, is it diagonal ? |
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Mar 22 |
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eigenvalues of two nonnegative matrices trivial application of minmax formulae. |
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Mar 21 |
revised |
Examples of interesting false proofs added 2 characters in body |
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Mar 20 |
accepted | On the convexity of element-wise norm 1 of the inverse |
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Mar 19 |
answered | Examples of interesting false proofs |
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Mar 19 |
answered | On the convexity of element-wise norm 1 of the inverse |
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Mar 18 |
revised |
Motivating the Laplace transform definition edited body |
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Mar 18 |
answered | Motivating the Laplace transform definition |
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Mar 18 |
answered | Spectrum theorem for p-adic matrix analysis |
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Mar 15 |
revised |
The probability for a symmetric matrix to be positive definite added 17 characters in body |
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Mar 15 |
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The probability for a symmetric matrix to be positive definite @Federico. Right! I meant "among the Euclidian norms". |
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Mar 15 |
awarded | ● Popular Question |
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Mar 15 |
revised |
Distribution of the spectrum of large non-negative matrices edited title |
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Mar 11 |
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Behaviour of the gradient w.r.t. boundary conditions for elliptic PDEs Certainly not! You can add any linear function to one of both. |
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Mar 9 |
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What goes wrong for the Sobolev embeddings at $k=n/p$? actually, the embedding holds true in one critical case, namely $p=1$, $k=n$. |
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Mar 8 |
awarded | ● Popular Question |
