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bio website mathtm.blogspot.com
location University of California Los Angeles, CA
age
visits member for 1 year, 11 months
seen 14 hours ago

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.


19h
comment Integral of $\sin^{-1}(1/2 - \sin x) dx$
A quick check on Wolfram reveals that the answer is likely no (by solution, I assume you mean a closed formula for the indefinite integral).
Apr
1
comment Tensor notation and the “Zero-Value Theorem”
Does a proof follow the statement of the theorem?
Apr
1
comment Tensor notation and the “Zero-Value Theorem”
$V$ is arbitrary, so presumably he means over every open set $V$.
Feb
22
comment How to derive the formula to estimate the stock price probability distribution from call option prices?
@Raphael. The part where I mention "...as long as $\phi$ and $S\phi$ are integrable we're fine" is the justification for differentiation under the integral sign (see the link for Leibniz's rule).
Feb
22
comment How to derive the formula to estimate the stock price probability distribution from call option prices?
Sorry, wrote the answer too hastily and made a sign mistake at the end. Thanks Daniel Fischer for the edit.
Feb
22
comment The closure of $C^{1}_{0}(\mathbb R)$ in $L^{\infty}$?
I made an edit to my answer above which deals with the closure of $C^{1}_{0}$.
Feb
17
comment How to calculate this multivariate limit changing to polar coordiantes?
Simple examples: (1) $x^{2}+y^{2}=r^{2}\to0$ as $r\to0$ no matter what $\theta$ is; (2) $y(x^{2}+y^{2})=r^{3}\sin\theta\to0$ as $r\to0$ no matter what $\theta$ is; (3) $\frac{x^{2}y^{2}}{x^{4}+3y^{4}}=\frac{r^{4}\cos^{2}\theta\sin^{2}\theta}{r^{4}(‌​\cos^{4}\theta+3\sin^{4}\theta}=\frac{\sin^{2}(2\theta)}{4(\cos^{4}\theta+3\sin^{‌​4}\theta)}$ which depends on $\theta$ (and indeed, the limit does not exist as $(x,y)\to(0,0)$).
Feb
17
comment How to calculate this multivariate limit changing to polar coordiantes?
$(x,y)\to(0,0)$ is equivalent to $r\to0$. That's why we replace the limit by $r\to0$ when working polar coordinates. However, as you no doubt have seen, $(x,y)\to(0,0)$ can be accomplished in several different ways (paths), which can sometimes lead to different limiting values. When working in polar coordinates, $r\to0$ is approach along a ray to the origin. If $\theta$ is not involved, or if its presence in the limiting expression is dominated by $r\to0$, then there is no problem. If $\theta$ is involved, then the approach can vary depending on $\theta$, and this must be considered.
Feb
17
comment How to calculate this multivariate limit changing to polar coordiantes?
Fixed, thank you!
Dec
13
comment Solutions to Dirichlet problem on the half space with $L^{\infty}$ boundary data.
I assume it is just the restrition of $u$ to the boundary with the definition given as above; i.e. just act like $u$ is a function on the boundary and pair it with a test function defined there.
Dec
12
comment Probability of $\alpha\log n$ consecutive successes in a Bernoulli process for $\alpha$ small
It is finite when defining the $A_{n}$, and yes about the i.o.
Dec
10
comment What direction does the n vector (normal to the surface) have to be when doing Stokes' theorem?
Orientation; to get a real (rigorous) answer, however, you'll have to wait until you take differential geometry/topology. A simple answer is what you've already indicated: the curve is oriented clockwise, and therefore the surface normal is outward (a physicist would tell you to apply the right-hand rule). At the end of the day however, unless you're applying your result to other computations, it really doesn't matter since your answer will only differ by a sign.
Dec
6
comment A convergence result for functions in L^2
Cauchy-Schwarz and the pointwise bound $|f_{n}(x)||g(x)|\leq|x|^{-1/3}|g(x)|$ may be useful.
Dec
6
comment (Obvious?) Half-Space Poisson Kernel Estimate
I added the page where the theorem/proof appears. See (1)
Dec
6
comment (Obvious?) Half-Space Poisson Kernel Estimate
Sorry, I'm looking closer at the passage in the text and it looks like $y$ is actually held fixed. The reason I was tempted to say it is not is that in my linked question the equivalent of $y$ there (i.e. $t$) is allowed to vary, but that is why (I think) there is the additional constant involved in the estimate, namely $\beta$. So anyway, yes, $y$ is fixed.
Dec
6
comment (Obvious?) Half-Space Poisson Kernel Estimate
I believe $y>0$ is allowed to vary. $\alpha$ is the only parameter fixed, and $A$ is only allowed to depend on $\alpha$.
Dec
4
comment Constructing a Distributional Solution to the Inhomogeneous C.R. Equations
@Post - See the update to my question. I'd like to avoid any reference to complex analysis if it's possible.
Nov
20
comment Analytic functions of absolute value 1 on the boundary of the unit disc
(Or the strong form of the maximum modulus principle.)
Nov
18
comment Mean-value like theorem for holomorphic functions.
It implies the existence of some neighborhood $V$ of $z$ such that $g$ fails to be one to one and this implies the existence of distinct $s,t$ such that $g(s)=g(t)$, which is the desired conclusion. I'm thoroughly amused by the fact that all three questions I posted had solutions which depended on some suitably chosen auxiliary function and an application of some major theorem.
Nov
18
comment For $f\in H(U)$, find a bound on $|f(0)|$ given separate bounds of $|f|$ on $\partial U^{+}$ and $\partial U_{-}$.
How does $|g|$ being a constant imply $g$ is? What about $re^{it}$?