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bio website mathtm.blogspot.com
location University of California Los Angeles, CA
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I am a recent graduate in applied mathematics at UCLA and currently trying to break into the quantitative investment/trading industry while also continuing to pursue advanced graduate-level mathematics as both a hobby and career necessity.


9h
awarded  Tenacious
Dec
3
answered Suppose that $f: \mathbb R \to \mathbb R$ is a continuous function and there is a number $p \in [a,b]$ so that $f(p) = q$.
Dec
3
comment Proving uniform convergence of an integral-defined function on compact sets
Ah, then you will have to adjust the limits in the integral accordingly to take into account the domain. But note for instance that if $f$ is supported on $K\subset\mathbb{R}$, then $f_{\epsilon}$ is supported on a subset $K_{\epsilon}\subset K$. The specific range of $f$ is irrelevant, only that it allows for $\int_{\mathbb{R}} f=1$ and that $f\geq0$.
Dec
2
revised Proving uniform convergence of an integral-defined function on compact sets
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Dec
2
comment Proving uniform convergence of an integral-defined function on compact sets
Actually, since uniform convergence is usually harder to demonstrate than pointwise convergence, a good starting point would be to prove pointwise convergence first, even if restricted to compact sets. I elaborated on my answer a bit; hopefully it will get you started.
Dec
2
revised If $\lim_{n \to \infty} f_n=f$ (Almost everywhere) then $\lim_{n \to \infty} f_n=f$ ( in measure on$E$)
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Dec
1
revised $y=ce^{y/x};\quad y'=y^2/(xy-x^2)$
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Dec
1
answered $y=ce^{y/x};\quad y'=y^2/(xy-x^2)$
Dec
1
revised If $\lim_{n \to \infty} f_n=f$ (Almost everywhere) then $\lim_{n \to \infty} f_n=f$ ( in measure on$E$)
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Dec
1
answered Proving uniform convergence of an integral-defined function on compact sets
Dec
1
answered If $\lim_{n \to \infty} f_n=f$ (Almost everywhere) then $\lim_{n \to \infty} f_n=f$ ( in measure on$E$)
Dec
1
comment Proving uniform convergence of an integral-defined function on compact sets
In the statement of your problem, does $f$ have compact support?
Dec
1
comment Orders of growth of typical sequences
Are you using the $\ll$ symbol to mean $P(n)\ll Q(n)$ if there is an absolute constant $C$ such that $P(n)\leq CQ(n)$ or that $P(n)/Q(n)\leq C$ for $n\geq N$ for some $N$ sufficiently large; or is it notation for one quantity being "much smaller" than the other? Also, are the numbers $p_{j},q_{j}$ and $a_{j},b_{j}$ arbitrary pairs with no relation between the indices?
Nov
20
comment Sum to infinity of the sum 1/n^2
Look to the right as you type this question and you'll see a ton of similar questions w/ answers. There's even one with literally dozens of solutions.
Nov
17
answered Equivalency of Norms and the Open Mapping Theorem
Nov
4
comment Resource on Pathwise Computations Involving Brownian Motion
Thanks - I edited my question to take some of this into account.
Nov
4
revised Resource on Pathwise Computations Involving Brownian Motion
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Nov
4
accepted Resource on Pathwise Computations Involving Brownian Motion
Nov
4
revised Resource on Pathwise Computations Involving Brownian Motion
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Oct
30
answered Solution to $\frac{d^2 y}{dt^2}+y=\sec\left(t\right)$