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location Albany, CA
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visits member for 2 years, 8 months
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If I see further than most, it is because I have stood on the toes of giants and they kicked me high into the air...

However, there is nothing to suggest that I see further than most.

I am (inasmuch as one 'is' an occupation) an engineer. My mathematical skills are rather pedestrian, with a rare insight every now and then. I have been lucky enough to sit in the same room with some famous mathematicians & engineers. My Erdős number is 5, which undoubtedly makes me as unique as an Irishman in a pub. And I have been spotted in The Pub from time to time.

In professional circumstances, my value add has usually been the injection of common sense and completion of grunt work when perspectives and energies are unfocused.

My current age is the smallest number composed of the first two primes that would allow me to have watch on RTÉ the slightly contradictory small step for man and giant leap for mankind.

My real name is Joe Higgins. Apparently, my last name means 'of the Viking' in Irish.

My alma mater is University College, Cork in Ireland, and I had the additional privilege of obtaining my Phd. from the University of California at Berkeley under the enlightened tutelage of Lucien Polak.

I can be reached at joe dot higgins at gmail dot com.


3h
comment Find all 2 x 2 skew-symmetric matrices A
@RobertLewis: Yes indeed! Happy Turkey day to you too!
4h
comment Frechet-Hausdorff theorem reference from J.L. Kelley used in proof that each probability measure is inner regular
@Alen: I mean for any $\delta>0$ you can find a finite subset $x_1,...,x_n$ of $K_\epsilon$ such that for any $y \in K_\epsilon$ there is some $x_k$ such that $d(y,x_k) < \delta$. It is a little more restrictive than just boundedness.
4h
comment Find all 2 x 2 skew-symmetric matrices A
@HenningMakholm: Caffeine deficit. I am linearly dependent on my tea.
4h
comment Is this function is Invertible?
Read the first comment.
4h
comment Is this function is Invertible?
Since $f(x) \ge 0$ for any $x$, it cannot take any value $<0$.
4h
comment Frechet-Hausdorff theorem reference from J.L. Kelley used in proof that each probability measure is inner regular
@NateEldredge: I have always called it (loosely) the Heine Borel theorem.
5h
comment Let $r_0,r_1,…,r_m$ be the real roots of $a_nx^n+a_{n-1}x^{n-1}+…+a_0$.Is there a closed-form expression for $\sum_{i=1}^mr_i -\sum_{i=1}^m1/r_i$?
Harder for me :-). I don't know any trick for separating out the real roots...
5h
comment Prove that $F=\int_x^{x^2} \! \frac{\sin t}{t} \, \mathrm{d}t$ is differentiable.
@Ilya: Only in the best possible world...
5h
comment Let $r_0,r_1,…,r_m$ be the real roots of $a_nx^n+a_{n-1}x^{n-1}+…+a_0$.Is there a closed-form expression for $\sum_{i=1}^mr_i -\sum_{i=1}^m1/r_i$?
The algebra-precalculus tag made me wonder... Out of my depth...
5h
comment Let $r_0,r_1,…,r_m$ be the real roots of $a_nx^n+a_{n-1}x^{n-1}+…+a_0$.Is there a closed-form expression for $\sum_{i=1}^mr_i -\sum_{i=1}^m1/r_i$?
Did you intend to restrict to real roots only?
5h
comment Prove that $F=\int_x^{x^2} \! \frac{\sin t}{t} \, \mathrm{d}t$ is differentiable.
Leibnitz is your friend... en.wikipedia.org/wiki/Leibniz_integral_rule
5h
comment Is the empty set the only possible set for $A$ such that $A=\{x|x\not\in A\}$?
Doug would be happy.
5h
comment Generating function for the sequence $(0,0,0,1,2,…,2^{r-3},…)$
It is not clear to me what the general term in the sequence is?
6h
comment extension of trigonometric functions as basis functions to higher dimensions
Out of my range, sorry...
15h
comment Proving equivalence relation and classes
Note that $5 \mid a+4b$ iff $5 \mid a-b$. Hence $a R b$ iff $f(a) = f(b)$, where $f(n) = n \mod 5$.
16h
comment extension of trigonometric functions as basis functions to higher dimensions
You can show that the collection $\{ x \mapsto e^{i 2 \pi(n_1 x_1 + n_2 x_2)} \}_{n \in \mathbb{Z}^2}$ is an orthonormal basis for $L^2[0,1]^2$. (And similarly, $\{ x \mapsto e^{i 2 \pi \sum_{k=0}^d n_k x_k} \}_{n \in \mathbb{Z}^d}$ for $L^2[0,1]^d$).
1d
comment Sequence of $f_n \in R[0, 1]$ that converges pointwise to $f \in R[0, 1]$ such that $\lim_{n \to \infty} \int_0^1 f_n dx \neq \int_0^1 f dx$.
What is the question?
1d
comment completion of measure space, smallest sigma algebra
Depends on your definition.
2d
comment completion of measure space, smallest sigma algebra
If $\Omega$ is a $\sigma$- algebra, then it is the smallest $\sigma$- algebra containing $\Omega$? You just need to check that $\bar{\Omega}$ is a $\sigma$- algebra.
2d
comment Laplace transform of a differential equation??
Alternatively, you could expand $f$ in terms of its Fourier series, and then solve the above for $f(t) = e^{2 \pi i n t}$ and add. Justifying convergence is a little trickier, though. If you do pursue the Laplace transform approach, this will suggest the form of the solution.