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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 ?