21,736 reputation
1960
bio website math.ubc.ca/~israel
location Vancouver BC
age 64
visits member for 4 years, 3 months
seen 56 mins ago
Associate Professor Emeritus, University of British Columbia, and Optimization Algorithms Researcher, D-Wave Systems, Burnaby BC

6h
awarded  Nice Answer
1d
comment Is a specific sequentially closed subset of $M([0,1])$ closed?
Why $C_b$ rather than just $C$? $[0,1]$ and $[0,1]\times [0,1]$ are compact.
2d
answered Identities involving sums of Catalan numbers
2d
revised Determining if a matrix is orthogonal
added 536 characters in body
Jul
2
answered Determining if a matrix is orthogonal
Jul
1
comment When are the powers of 2 sum-free mod n?
@Seva If my program is correct, the first few odd $n$ with the property are 1, 3, 7, 15, 21, 31, 51, 63, 73, 85, 89, 91, 93, 105, 117, 127, 133, 151, 195. This sequence is not in the OEIS.
Jun
30
comment What conditions imply that a function over $\mathbb{Z}$ is a polynomial?
If $f$ is entire and there are at least two values that $f$ takes only finitely many times, then $f$ is a polynomial.
Jun
30
comment Is Every Holomorphic Near an Entire?
For your "plus sign" approximation, take $f(z) = z^3 g(z^4)$ where $g$ is a polynomial such that $|t^{3/4} (g(t) - t^{-1/2})| < \epsilon$ for $t \in [0,1]$. Such $g$ can be found using standard numerical approximation methods. For example, with $\epsilon \approx 0.1$, g(t) = 13.6602896164833+(-295.346171207092+(3061.90100782145+(-16221.4880068369+(48270.‌​4896476068+(-84097.0658600084+(85091.1281127053+(-46285.3324386071+10463.15607312‌​30*t)*t)*t)*t)*t)*t)*t)*t will work.
Jun
30
revised Generate Bernoulli vector with given covariance matrix
deleted 9 characters in body
Jun
30
answered Generate Bernoulli vector with given covariance matrix
Jun
30
comment Generate Bernoulli vector with given covariance matrix
Covariance matrices don't have to be diagonal. They do have to be positive semidefinite.
Jun
26
revised Arctangents of odd powers of the golden ratio
added 18 characters in body
Jun
26
revised Arctangents of odd powers of the golden ratio
edited body
Jun
26
revised Arctangents of odd powers of the golden ratio
deleted 19 characters in body
Jun
26
answered Arctangents of odd powers of the golden ratio
Jun
25
comment Are spherical harmonics uniformly bounded?
Which normalization are you using?
Jun
25
comment Can I find the gap between the two least eigenvalues of this special matrix A(t)?‎
How can this be unitary? Do you mean hermitian?
Jun
23
comment How do I evaluate this sum :$\sum_{n=0}^{\infty} \frac{\sin(n!)}{\cos(n!)}$ if it's not open problem?
@Zeraouliarafik I have no analytical proof for $\sum_n \tan(n!)$ diverging either. It seems to me very unlikely that Diophantine-approximation bounds for $\pi$ could be anywhere near good enough to prove this.
Jun
23
comment How do I evaluate this sum :$\sum_{n=0}^{\infty} \frac{\sin(n!)}{\cos(n!)}$ if it's not open problem?
If you want one that converges absolutely, try $\sum_{n=0}^\infty \tan(\pi (2n)! (e + 1/e)/2)$
Jun
23
comment How do I evaluate this sum :$\sum_{n=0}^{\infty} \frac{\sin(n!)}{\cos(n!)}$ if it's not open problem?
You mean $n!/e = (-1)^{n+1}/(n+1) + O(1/n^2) (\mod \mathbb Z)$, so $\tan(\pi n!/e) = (-1)^{n+1} \pi/(n+1) + O(1/n^2)$. Yes, the sum converges conditionally.