Ewan Delanoy
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31,357
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 12h awarded Socratic 1d revised Problem with sum of projections deleted 29 characters in body 1d comment Problem with sum of projections @zyx It is very likely that there is. I've just asked a question about that here 1d asked Algebra defined by $a^2=a,b^2=b,c^2=c,(a+b+c)^2=a+b+c$ 1d comment Optimizing value of discrete harmonic function at a given point @HandeBruijn It is redundant indeed. If you don't like the normalization $f(0,0)=1$, replace this condition with "$f$ nonzero". Then it can be shown that $f(0,0)$ is nonzero. And maximize $\frac{f(1,0)}{f(0,0)}$ instead of $f(1,0)$ May 2 comment Problem on field extension related to irreducible polynomial Some assumptions are missing in your question. I suppose that $p$ must be irreducible over $\mathbb Q$, otherwise we could take $\gamma=0,\gamma'=\sqrt{5}$, $p=x(x^2-5)$. May 2 comment How to prove this result about the interlacing of eigenvalues. You’re right, I shouldn't have sad "interlacing in $A$" but rather simple eigenvalues for $A$. And yes, I presume that $\lambda_i > \mu_i > \lambda_{i+1}$ in this case (though I don't know how to prove it). May 2 comment How to prove this result about the interlacing of eigenvalues. It is likely that the interlacing will be strict in $C$ if it is already strict in $A$ and $0$ is not an eigenvalue for $A$. May 2 revised (Elegant) proof of an inequality: $h(x) \geq 1- (1-\frac{x}{1-x})^2$, where $h$ is the binary entropy function added 7 characters in body May 2 answered (Elegant) proof of an inequality: $h(x) \geq 1- (1-\frac{x}{1-x})^2$, where $h$ is the binary entropy function May 1 comment (Elegant) proof of an inequality: $h(x) \geq 1- (1-\frac{x}{1-x})^2$, where $h$ is the binary entropy function Your graph suggests that $g(x)\geq g(1-x)$ for $x\in[0,\frac{1}{2}]$, and a simple computation confirms that : $g(x)-g(1-x)=\left(\frac{x}{1-x}-\frac{1-x}{x}\right) \left(2-\frac{x}{1-x}-\frac{1-x}{x}\right)$ and this will be $\geq 0$ by AM-GM. Since $h(1-x)=h(x)$, it suffices to show the inequality for $x\in[0,\frac{1}{2}]$. May 1 accepted Rational function between a constant and a third root Apr 30 revised Rational function between a constant and a third root edited body Apr 30 revised Rational function between a constant and a third root edited body Apr 30 revised Rational function between a constant and a third root added 3 characters in body Apr 30 comment Rational function between a constant and a third root @MXYMXY Clearly the degree of $P$ must equal the degree of $Q$. Otherwise $f$ would either grow too fast for the upper bound or decrease too fast for the lower bound Apr 30 asked Rational function between a constant and a third root Apr 30 revised Optimizing value of discrete harmonic function at a given point added 20 characters in body Apr 30 answered How to prove this result about the interlacing of eigenvalues. Apr 27 comment Find smallest k for which the inequality holds What did you try ? What are your thoughts ?