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location Albany, CA
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visits member for 2 years, 7 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.


1h
comment Continuity of translation on $L^1$ on the reals ($\int |f(x+h)-f(x)|\,dx\to 0$)
A standard approach is to use the fact that compactly supported continuous functions are dense in $L^1$.
3h
comment Calculating the mass of the earth
Also, you have the value for acceleration as $9.8^2$, it should be just $9.8$. You Java programmers.
3h
comment Calculating the mass of the earth
You could use scientific notation as in bigG = 6.673e-11; Also, you have $r$ in km, it should be in m, so r=6371e3;
3h
comment Calculating the mass of the earth
This is really not about mathematics...
9h
comment Show that S is a real vector space using the standard operations on R3 (what are “standard operations” on R3?)
Not usually. You already have a vector space, $\mathbb{R}^3$, you just need to show that $S$ is a subspace. In particular, if $x \in S$, check that $\lambda x \in S$ for any scalar $\lambda$, and if $x,y \in S$, check that $x+y \in S$.
9h
comment Show that S is a real vector space using the standard operations on R3 (what are “standard operations” on R3?)
You could show that $S = \ker \phi$, where $\phi((x,y,z)) = z$.
9h
comment Show that S is a real vector space using the standard operations on R3 (what are “standard operations” on R3?)
Appendectomy, hemorrhoidectomy, tonsillectomy are the most common.
14h
comment Segments on a real line
No problem, much appreciated!
14h
comment Segments on a real line
I wonder if you could re-select Hagen's answer please? He was first, you had previously selected his answer and I was adding my answer as an alternative, not to capture the vote. Much appreciated.
14h
comment Showing a set is a subspace
Well, the kernel is automatically a subspace, which is why I did it this way. You could show directly that if $\phi_k(f) = 0$ then $\phi_k(\lambda f) = 0$ and if $\phi_k(f) = 0$, $\phi_k(g) = 0$ then $\phi_k(f+g) = 0$. This would show that the $f$ satisfying $\phi_k(f) = 0$ form a subspace.
15h
comment CHECK: Let $G=\frac{(\mathbb{Z},+)/12\mathbb{Z}}{3\mathbb{Z}/12\mathbb{Z}}$. How many elements are there in $G$?
And explicitly, $G= \{ \{ \{k + 3n \}+ 12 \mathbb{Z} \}_{n=0}^3 \}_{k=0}^2$.
17h
comment indefinite integral and inequality
No, take $g=f = 0$. Then, since you have indefinite integrals, $\int f = 0+c_1, \int g =0+c_2$, but the $c_k$ are unspecified constants, so it can't be true unless you require that $c_1 \le c_2$.
1d
comment State space and linearization
Sorry, I don't know how to help since I'm not sure what you are trying to achieve.
1d
comment Pairwise disjoint proof
For (a), note that $x \in A_x$. One direction is immediate from the definition. For (b), show that if $A_x$ and $A_y$ intersect, then they are the same.
1d
comment Normality of a metric space
If $f(x) \ge 0$, you can see that $f^{-1}([0,\alpha)) = f^{-1}((-1,\alpha))$. Since $(-1,\alpha)$ is open, it follows that $V$ would be open too.
1d
comment State space and linearization
Again, I really don't know what you are trying to do, but if you can measure $x$ you can build an observer to estimate $\dot{x}$. The reference signal must be an input???
1d
comment State space and linearization
Can you measure $x$ or some linear functional of $x,\dot{x}$?
1d
comment Pairwise disjoint proof
You need to use mathjax to do the formatting. See meta.math.stackexchange.com/questions/5020/… for example.
1d
comment State space and linearization
Well, if you need to control $x$ then you have no choice but to include it in the state space representation. However, I am still not clear about why you think this is a problem with the representation.
1d
comment State space and linearization
You need to provide more info. about what you are trying to do and what you are trying to control/design. Is your state $x,\dot{x}$ or just $\dot{x}$, does $u$ have some nominal value, etc, etc...