Nicolas Essis-Breton
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 Jul 31 comment Sampling a Chebyshev polynomial with the discrete cosine transform @AnonSubmitter85 Can you say how I should zero-pad $a=[1,2,3]$ with three zeros? Do you mean that it should become either $[0,0,0,1,2,3]$ or $[1,2, 0, 0, 0, 3]$? Jul 5 comment How to do polynomial composition/substitution? (Vincent-Alesina-Galuzzi) @KerrekSB Thanks Kerrek, your comment made me realized. The theorem says to perform the substitution (1 + x)^n p( (a + b x) / (1 + x) ). This implies that there is no division, and I can adapt Horner. Jul 5 comment How to do polynomial composition/substitution? (Vincent-Alesina-Galuzzi) @KerrekSB, No, the coefficients of p(x) are randomly generated. Jun 7 comment Inscribed circle: find distance to circumscribed circle Also the tangent $T$ does not pass through the point $d$. And the distance $cd$ seems shorter than the distance $tT$ (at the tangencial contact point). Jun 7 comment Inscribed circle: find distance to circumscribed circle If I understand correctly, I draw the tangent $t$ at the point $c$. Then I draw a tangent $T$ of the great circle parallel to $t$. Let say $T$ is on the side of the point $d$. Then the distance between the tangencial contact points is the minimum distance from the point $c$ to the great circle. I don't see how this resolve the uniqueness of the length $cd$. Jun 4 comment smaller circle into larger circle : find length of common arc @YvesDaoust I made my question more precised. Does your assertion still hold with my precisions? Feb 10 comment Is finding the maximum of a polynomial of degree one a linear programming problem? Thank you, your answer really help. Feb 9 comment Is finding the maximum of a polynomial of degree one a linear programming problem? @MichaelC.Grant I see that my proposed equivalent is wrong. Can you indicate how to get, or if possible write as an answer, the equivalent problem using binary constraints? I tried to find my way with google, but I don't see how to do it. Feb 9 comment Is finding the maximum of a polynomial of degree one a linear programming problem? @MichaelC.Grant I think, the 'max' in the problem can be 'linearized' so that the problem becomes an LP (see edit). Is it true? Oct 20 comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space? @PrahladVaidyanathan Yes, thank you. I forgot to say that $X$ contains only bounded function. I added it. Oct 20 comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space? @PrahladVaidyanathan I see, I miswrite the max notation. I have corrected it, is it better now? Oct 20 comment What is the error when approximating $L^2([0,1])$ by a finite dimensional space? @PrahladVaidyanathan For my understanding, the error is in the orthogonal space. If I use your formula, the error will be too big: for any $f$, the closest $g \in X_n$ to $f$ is $\sum (f,v_i) v_i$, I think. Oct 1 comment Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$? @copper.hat Your answer shows an other side of the die. Please let it live. Oct 1 comment Is there a continuous bijection between an interval and a square: $[0,1] \mapsto [0,1] \times [0,1]$? @BobPego The bijection requirement was a first instinct. You made me realized I can forgo it. Thank you for your insightfull comment. Aug 31 comment Show that, for a random walk $X$ on $\mathbb Z_2$, $X_\infty$ is independent of the past $\left\{ X_t \right\}_{0\le t<\infty}$ By 'coincides', you mean in distribution: if $X$ is a random walk on $\mathbb Z_2$, as above, and $\left(Y_t\right)$ is an i.i.d sequence with uniform distribution on $\mathbb Z_2$. Then $X_t \buildrel{d}\over = Y_t, \forall t$. I don't see a proof for a stronger mode of convergence. Aug 31 comment Show that, for a random walk $X$ on $\mathbb Z_2$, $X_\infty$ is independent of the past $\left\{ X_t \right\}_{0\le t<\infty}$ @Did I tagged too much. Thanks For letting me know. May 20 comment Finding the range of a vector valued function What is then the conclusion, once $\det J_f=0$ on the line $y=x$? May 13 comment Maximum likelihood in exponential family: $\partial_{\theta,\theta} \ln L = -\mathrm{Var}(T)$, $T$ sufficient for $\theta$ @Caran-d'Ache I think you mean $$\mathrm{Var}(T) \ge (E(-\partial_{\theta,\theta} \ln L))^{-1},$$ the Cramer-Rao lower for the variance of $T$. From my calculation, this works, and it explains why they are inverse of each other. Thanks for your input, combine with Did comment, I better understand what is going on. Apr 29 comment $X_n \sim \text{Exponential}(\lambda_n)$, independent, $\sum 1/\lambda_n = \infty$, then, $\sum X_n=\infty$ a.s. Whoa! Of very great level. Thanks. Apr 22 comment Is it possible to construct a Loeb measure for $\{\epsilon: \epsilon\in[0,1], \epsilon \text{ infinitesimal}\}$? @user72694 How can I string finite numbers to get say $A=\{\frac{1}{\omega},\frac{2}{\omega}$\}? My thinking is $\mathrm{st}(A)=\{0,0\}$, so I don't see what to string.