517 reputation
310
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location NYC
age
visits member for 2 years, 6 months
seen 7 hours ago

Jul
2
awarded  Curious
May
31
comment Minimizing functionals with constraints
I am not an expert, but I came across this the other day. You may find sections 10 and 11 especially relevant. maths.ed.ac.uk/~jmf/Teaching/Lectures/CoV.pdf
Mar
6
awarded  Self-Learner
Feb
8
answered Classsifying 1- and 2- dimensional Algebras, up to Isomorphism
Jan
1
awarded  Yearling
Oct
28
comment The question about the word of “Mathematics”.
I think there are actually 8! string which contain the sub-string "math". We count the number of permutation of the 8 objects {e,m,a,t,i,c,s,math}.
Oct
4
asked Understanding Dini continuity for lifts of circle endomorhpisms
May
17
accepted Quotient rings of Gaussian integers $\mathbb{Z}[i]/(2)$, $\mathbb{Z}[i]/(3)$, $\mathbb{Z}[i]/(5)$,
May
17
comment Quotient rings of Gaussian integers $\mathbb{Z}[i]/(2)$, $\mathbb{Z}[i]/(3)$, $\mathbb{Z}[i]/(5)$,
That's helpful, thanks. Since R/(2) has just 4 elements, if it were isomorphic to a product of fields, then it would necessarily be isomorphic to Z/(2)xZ/(2). But $i^2=1$ in R/(2), and every element of Z/(2)xZ/(2) when squared equals itself. So... From the unusual phrasing of the question, I suppose R/(5) is isomorphic to a product of fields. Is this right? Would that product be Z/(5)/Z/(5)?
May
17
asked Quotient rings of Gaussian integers $\mathbb{Z}[i]/(2)$, $\mathbb{Z}[i]/(3)$, $\mathbb{Z}[i]/(5)$,
May
16
awarded  Caucus
Jan
1
awarded  Yearling
Sep
3
accepted $f,g$ continuous functions, $f$ strictly increasing, non-vanishing: $\int_a^bg(x)(f(x))^n\,dx=0$ for all $n$ $\Rightarrow g\equiv 0$
Sep
3
comment $f,g$ continuous functions, $f$ strictly increasing, non-vanishing: $\int_a^bg(x)(f(x))^n\,dx=0$ for all $n$ $\Rightarrow g\equiv 0$
Wow, great answer. I really did not understand the Stone-Weierstrass theorem until now - now that I see how powerful it is. Thank you!
Sep
3
revised $f,g$ continuous functions, $f$ strictly increasing, non-vanishing: $\int_a^bg(x)(f(x))^n\,dx=0$ for all $n$ $\Rightarrow g\equiv 0$
edited title
Sep
3
asked $f,g$ continuous functions, $f$ strictly increasing, non-vanishing: $\int_a^bg(x)(f(x))^n\,dx=0$ for all $n$ $\Rightarrow g\equiv 0$
Aug
21
accepted Lebesgue measure: $\mu(f-g(D))=0\Rightarrow\mu(f(D))=\mu(g(D))$
Aug
21
comment Lebesgue measure: $\mu(f-g(D))=0\Rightarrow\mu(f(D))=\mu(g(D))$
Of course! Thank you!
Aug
21
asked Lebesgue measure: $\mu(f-g(D))=0\Rightarrow\mu(f(D))=\mu(g(D))$
Jul
22
answered analytic on a disc with a hole