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location New York, NY
age 29
visits member for 3 years, 7 months
seen 9 hours ago

Data Scientist @ Explorer Media


16h
comment How prove this $x_{1}+x_{2}+\cdots+x_{n}<\frac{5}{3}$
Here is my failed attempt: $$ (x_1 + \dots x_n)^2 = \sum_{i,j} x_i x_j \leq \sum_{i,j} 4^{-|i-j|} = n + 2 \big[ (n-1)\;4^{-1} + \dots + 1 \cdot4^{n-1} \big]$$
Jul
23
comment periodicity of an interval exchange transformation(IET)
Is the number of segments in the interval exchange finite?
Jul
22
revised Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane
added 279 characters in body; edited tags
Jul
22
comment Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane
@DanielRust I thought I was simplifying by using $[-1,1]^3$ instead of a unit cube which would be $[-\tfrac{1}{2}, \tfrac{1}{2}]$.
Jul
22
comment Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane
Is it possible your answer can be simplified since $e_x, e_y, e_z$ are orthonormal?
Jul
22
comment Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane
@DanielRust Can you expand that into an answer below? Basically, I need to know how the projections $p(e_i)$ change with the normal vector $\mathbf{n} \in S^2$.
Jul
22
asked Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane
Jul
22
comment An inequality on sequences with each term dividing sum of two neighbouring terms
@shadow10 You can subsitute $\frac{x_{i+1}}{x_i} = k_i - \frac{1}{\frac{x_{i-1}}{x_i}} = k_i - \cfrac{1}{k_{k-1} - ...}$ and keep substituting to get some kind of continued fraction. Or maybe you can start from: $$ 2X \equiv 2(x_1 + \dots x_n) = k_1 x_1 + \dots k_n x_n $$ So there is an average of the $\mathbb{E}[k_i]=2$
Jul
22
comment Sign convention for derivatives in a $\mathbb{Z}_2$ graded space
@vkarve $\theta \cdot \theta g'(t) = 0$ since $\theta^2 = 0$. Maybe you also need $\tfrac{d\theta}{dt} = 0$ and are left with $\theta g'(t)$.
Jul
22
comment A Cauchy-Schwartz type inequality
What about setting $x_1 = \dots = x_n = 1$ then $A = \frac{n}{k}$.
Jul
22
answered Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
Jul
22
answered Sign convention for derivatives in a $\mathbb{Z}_2$ graded space
Jul
19
asked Probability of heads given we observe HTH?
Jul
14
answered A problem from Komal
Jul
9
comment Why is Volume^2 at most product of the 3 projections?
Here is a proof in the notes of Guth on the Polynomial Method the cube $\square$ seems to be a natural shape for this type of projection inequality. Notes by Noga Alon on combinatorial nullstellensatz seem similar in spirit, though I do like the geometric flavor of the original result.
Jul
7
answered Area of the Limiting Polygon
Jul
7
comment Check membership in a matrix group
Are these $2\times 2$ matrices? are these $n \times n$ ?
Jul
7
answered How would you count a base > 36 system?
Jul
6
revised Probability of $\alpha\beta\gamma=\gamma\beta\alpha$ for random permutations of a finite set?
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Jul
6
revised Probability of $\alpha\beta\gamma=\gamma\beta\alpha$ for random permutations of a finite set?
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