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22881
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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.


2h
awarded  optimization
3h
comment Using arctan to prove equivalence of 3 definitions of a manifold
It is fairly straightforward to establish a homeomorphism between $B(0,1)$ and any other ball $B(x_0,r)$. Similarly between $B(0,1)$ and $\mathbb{R}^n$. So this gives $B \Leftrightarrow C$.
7h
comment Sphere in finit dimensional space
It is the injection given above?????
7h
comment Sphere in finit dimensional space
Perhaps I am missing something, but won't $H(x,t) = (1-t) i(x)$ work?
7h
comment complex problem in linear algebra
You may have edited the expression, but you haven't changed it. My comment above still applies.
10h
comment Inverse in a functional space
Well, in a Banach space you have no choice. In other space an unbounded inverse would be fine, just not continuous.
11h
comment Inverse in a functional space
Well, one proof for Banach spaces is base on the open mapping theorem.
11h
revised Is the inverse function continuous at a fixed point?
sp.
11h
comment Is the inverse function continuous at a fixed point?
The function $f$ is not surjective as a map $I \to \mathbb{R}$, so $f(I)$ is 'missing' many intervals. For example, there is no $\delta>0$ such that $f^{-1}$ is defined on $(1-\delta, 1+\delta)$.
12h
comment Equality of mixed partial derivatives
Very nice result here: math.stackexchange.com/a/47885/27978
20h
comment Show that weak local minimum of a convex function $\mathbb{R}^N\rightarrow \mathbb{R}$ is its weak global minimum.
What is a weak local minimum?
21h
answered Can a low-rank matrix set have nonempty interior?
21h
answered Find the continuous function such that the Riemann integrable is the same
21h
comment What does it mean to say the smallest σ-algebra?
Glad to be able to help.
21h
comment Interpretation of parametrization
Other than being a different parameterisation, it is hard to understand what you mean by interpretation.
21h
comment If $\sqrt{n}+ 8= n+1$, what is $n$?
I'm sure he could have used more steps :-).
21h
comment What does it mean to say the smallest σ-algebra?
It means that ${\cal F}$ consists of all subsets of $X$. Another notation is $2^X$ or ${\cal P}(X)$.
22h
answered Does being a local minimum imply a positive definite hessian?
22h
comment If $\sqrt{n}+ 8= n+1$, what is $n$?
This could take an infinite number of steps... Try $\sqrt{n} = n-7$, square both sides and this will reduce the number of possibilities you need to consider.
23h
answered Computing the limit of an alternating series,