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bio website mrcactu5.herokuapp.com/…
location New York, NY
age 29
visits member for 3 years, 10 months
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Data Scientist @ Explorer Media


Oct
14
comment Correctly transforming ODEs
@resu I was going to suggest $y+1 \mapsto y$ for the first step. Where did these equations come from? What text?
Oct
13
comment What is the value of $\sum_{m=1}^{19} \frac{1}{\zeta^{3m}+\zeta^{2m}+\zeta^{m}+1}$ with $\zeta=e^{2\pi i/19}$?
line 3 is very convenient that $x \mapsto x^k$ is the same as rearranging the terms
Oct
13
comment What is the value of $\sum_{m=1}^{19} \frac{1}{\zeta^{3m}+\zeta^{2m}+\zeta^{m}+1}$ with $\zeta=e^{2\pi i/19}$?
this is good you can use polynmial identity summing over the roots: $$ \frac{d}{dz} \big[\log p(z)\big]= \frac{p'(z)}{p(z)} = \sum \frac{1}{z-a} $$ where $p(z) = z^N-1$.
Oct
13
comment Show Laplace operator is rotationally invariant
@EmutheEmu By chain rule, your equation $u = x \cos \theta + y \sin \theta$ becomes $$\frac{\partial}{\partial u} = \frac{\partial}{\partial x} \cos \theta + \frac{\partial}{\partial y} \sin \theta $$ and a similar formula for second derivatives. Then you can plug in.
Oct
6
comment How to prove $\frac{(a_1 a_2\cdots a_n)^2-1}{8}\equiv\sum_{i=1}^n\frac{a^2_i -1}{8}\pmod 8$
Can you explain between step 2 and 3 - turning the product $\prod$ into sum $\sum$?
Sep
18
comment Harvard math 55 materials
@AlexBecker could it just be they are very smart?
Sep
15
comment Is $\int_{-1}^1 \frac{dx}{\sqrt{x^2 - 1}} $ divergent?
@AndréNicolas yes but why does it converge despite integrand tending to infinity? I think it's like $$\int_0^1 \frac{dx}{\sqrt{x}} = \sqrt{x}\bigg|_0^1 = 1$$
Sep
15
comment Is $\int_{-1}^1 \frac{dx}{\sqrt{x^2 - 1}} $ divergent?
up vote --- sorry for switching it up on you
Sep
6
comment Laplace transform on a finite interval $f(t)= \int_0^1 e^{-xt} f(x) \, dx$
@OmranKouba OK it is Laplace transform of $f(x)\mathbf{1}(x < 1)$. Using formulas from Laplace Transform Table. I am getting $(1 - e^{-t})\hat{f}(t)$ where $\hat{f}$ is the Laplace transform of $f$.
Sep
3
comment Minimum of $|az_x-bz_y|$
If $N_x$ and $N_y$ are very large, the minimum is the gcd.
Sep
3
comment Where can I learn about Mathematical Philosophy?
@AndresCaicedo I am arguing Voting theory and Social Choice theory are a kind of 'Mathematical Philosophy'. Instead of a book, I offered an online course. Hmm... maybe this is not metamathematics ?
Aug
23
comment Proving these trigonometric sums $\sum\limits_{k=0}^{n-1}\sin\frac{2k^2\pi}{n}=\frac{\sqrt{n}}{2}\left(\cos\frac{n\pi}{2}-\sin\frac{n\pi}{2}+1\right)$
@DavidH perhaps he is looking for more details
Aug
22
comment Analogue of $\zeta(2) = \frac{\pi^2}{6}$ for Dirichlet L-series of $\mathbb{Z}/3\mathbb{Z}$?
In arXiv:math-ph/9804010, $\sum (n^2 + \tfrac{n}{2})^{-1}$ by turning it into an integral, just as you described.
Aug
22
comment Analogue of $\zeta(2) = \frac{\pi^2}{6}$ for Dirichlet L-series of $\mathbb{Z}/3\mathbb{Z}$?
@JackD'Aurizio No I haven't. My proof extends to $L(2k,\chi_1)= (1 - \tfrac{1}{3^{2k}})\zeta(2k)$ but in the odd case, I am trying to add $$ L(1, \chi_2)= \sum \frac{1}{9n^2 + 9n + 2} $$ This type of problem has appeard on Math.SE I think.
Aug
4
comment Rank of Elliptic Curves
as a service to other readers - especially me - please define the 2-Selmber rank in your question? And I don't know what you mean by "congruent number family".
Aug
4
comment Rank of Elliptic Curves
when you say Clearly it is not known that the 2-Selmer rank is bounded, but is it known that it is unbounded in the congruent number family? do you have a reference?
Aug
4
comment What does the decomposition, weak union and contraction rule mean for conditional probability and what are their proofs?
@CharlieParker I was referring to a textbook on information theory by Raymond Yeung. slides from Daphne Koller's Coursera course suggest drawing the Bayesian net.
Jul
30
comment Entropy of the product of two random variables
what are the dimensions of our matrix $X$? Are all the entries independent? What is the size of your vector $Y$? @Lembik
Jul
30
comment Prove or find a counter example to the claim that for all sets A,B,C if A ∩ B = B ∩ C = A ∩ C = Ø then A∩B∩C ≠ Ø
It's clearly... true? I think you are proving his result
Jul
29
comment How prove this $x_{1}+x_{2}+\cdots+x_{n}<\frac{5}{3}$
Here is my failed attempt: $$ (x_1 + \dots x_n)^2 = \sum_{i,j} x_i x_j \leq \sum_{i,j} 4^{-|i-j|} = n + 2 \big[ (n-1)\;4^{-1} + \dots + 1 \cdot4^{n-1} \big]$$