63,913 reputation
22880
bio website
location Albany, CA
age
visits member for 2 years, 8 months
seen 1 hour ago

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.


Jul
19
comment Improper double integral evaluation by changing the order of integration
I cannot (quickly) find a satisfactory reference for the improper integral. Some approachs (inspired by Marsden's "Real analysis") is to let $f_M(x) = \min(f(x),M)$ and define $\int f = \lim_{M \to \infty} f_M$ (assuming the limit exists). Another would be to 'approximate' $R$ by smaller rectangles that 'converge' in some sense, so that $f$ is Riemann integrable on the smaller rectangles.
Jul
19
answered Improper double integral evaluation by changing the order of integration
Jul
19
comment Improper double integral evaluation by changing the order of integration
Are you using the Lebesgue integral? If so, then Tonelli says that you can swap the order regardless (since the underlying space is $\sigma$-finite and the integrand is non-negative).
Jul
19
answered Borel $\sigma$-algebra of subsets of [0,1]
Jul
19
comment Prove the inequality $\sum_{i,j = 1}^n {{A_{i,j}}({x_i}^2 - {x_i}{x_j})} \ge 0 $
Is $A$ symmetric? If so, I think a diagonal dominance argument can be used to show the above inequality is true.
Jul
19
revised Integrate $\int \sin^4x \cos^2x dx$
added missing square
Jul
19
comment Integrate $\int \sin^4x \cos^2x dx$
You can check your answer by differentiating. It is not correct. It is not true that $\int \cos^k x dx = {1 \over k+1} \cos^{k+1} x$.
Jul
19
comment Equivilent first order differential and initial condition?
I am afraid that three glasses of wine are pre-empting my ability to help at this moment :-). Will look again in the (my) morning time!
Jul
19
comment Equivilent first order differential and initial condition?
@ClaudeLeibovici: en.wikipedia.org/wiki/…
Jul
19
comment Equivilent first order differential and initial condition?
Can you answer the question posed in my first comment? (I am going to sleep shortly; I will help you now if you respond in a timely and reasonable manner.)
Jul
19
comment Equivilent first order differential and initial condition?
Well, I am willing to help, but we need some common point of overlap to start. You need to supply that.
Jul
19
revised Equivilent first order differential and initial condition?
added 226 characters in body
Jul
19
comment Equivilent first order differential and initial condition?
I can help you if you can elaborate what is confusing to you.
Jul
19
comment Equivilent first order differential and initial condition?
I have added an aside that hopefully shows some intuition behind the differentiation.
Jul
19
revised Equivilent first order differential and initial condition?
added 133 characters in body
Jul
19
comment Equivilent first order differential and initial condition?
(I was going to add some more detail, but can see I was headed in the wrong direction at the moment.)
Jul
19
comment Equivilent first order differential and initial condition?
An expression of the form $x \mapsto \int_1^x g(t) dt$ can be differentiated (assuming $g$ is sufficiently smooth). Do you know how to differentiate this expression?
Jul
19
revised Equivilent first order differential and initial condition?
added 133 characters in body
Jul
19
answered Equivilent first order differential and initial condition?
Jul
18
comment Finite union of measurable rectangles can be written as union of pairwise disjoint measurable rectangles?
Well, you are very welcome, albeit you did it yourself!