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Jun
7 |
asked | Lower bound for the probability that a certain component of a Gaussian vector dominates all others |
May
4 |
accepted | Positive roots of a polynomial |
May
4 |
comment |
Positive roots of a polynomial
Neat derivation! |
May
4 |
awarded | Nice Question |
May
3 |
comment |
Positive roots of a polynomial
@Greg Martin: $n=1$ does not satisfy the condition that not all $a_i$'s are equal. For $n=2$ we get $p(x)=\frac{1}{2} \left(a_1-a_2\right){}^2 x^2-\frac{1}{2} a_1 \left(a_1-a_2\right){}^2 a_2$ and so clearly the only positive root is $x_0=\sqrt{a_1 a_2}$. For $n=3$ I don't know already... |
May
3 |
awarded | Yearling |
May
3 |
revised |
Positive roots of a polynomial
added 55 characters in body |
May
3 |
comment |
Positive roots of a polynomial
@Seva some numerical evidence, I'll add this to the question |
May
3 |
asked | Positive roots of a polynomial |
May
1 |
comment |
Maximizing the discrepancy in Jensen's inequality for a certain function
@Sergei: see for instance Theorem 1 here: iub.edu/~caepr/RePEc/PDF/2012/CAEPR2012-004.pdf |
Apr
30 |
asked | Maximizing the discrepancy in Jensen's inequality for a certain function |
Jul
2 |
awarded | Curious |
Jun
5 |
answered | Property/Relations using Fourier series/transform, which give complete information about all the jump singularities of a function. |
Jun
2 |
accepted | Is the following conjecture regarding rotational iterates of collection of points on a circle true? |
Jun
2 |
comment |
Is the following conjecture regarding rotational iterates of collection of points on a circle true?
@Anthony Quas: This comes from estimating condition numbers of Vandermonde matrices with nodes on the circle. |
Jun
2 |
comment |
Is the following conjecture regarding rotational iterates of collection of points on a circle true?
Since your rescale everything to $[0,1)$, I think $\alpha$ should be multiplied by $\pi$. Also, could you please provide more intuition regarding the usage of the Dirichlet principle? Thanks! |
Jun
1 |
asked | Is the following conjecture regarding rotational iterates of collection of points on a circle true? |
May
12 |
comment |
Inverse of matrix of generalised harmonic numbers
@ChristianRemling: Unfortunately, this is not the case. $H^{-1}$ does have negative entries (as does the inverse of the Hilbert matrix), so even for a 2-by-2 case the matrix $H^{-1}R-I$ has $O(1)$ entries. |
May
11 |
comment |
Inverse of matrix of generalised harmonic numbers
@ChristianRemling: the problem is that one cannot write $R=H(I+O(1/n))$ in this case. Rather, $O(1/n)H$ stands for a matrix whose $i,j$-th entry is $O(1/n)$ times the $i,j$-th entry of $H$. |
May
11 |
awarded | Informed |