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pro vyhledávání: '"Cohen Alex"'
Let $p_1,\ldots,p_n$ be a set of points in the unit square and let $T_1,\ldots,T_n$ be a set of $\delta$-tubes such that $T_j$ passes through $p_j$. We prove a lower bound for the number of incidences between the points and tubes under a natural regu
Externí odkaz:
http://arxiv.org/abs/2409.07658
Autor:
Cohen, Alex, Mani, Nitya
In the 1960s Moser asked how dense a subset of $\mathbb{R}^d$ can be if no pairs of points in the subset are exactly distance 1 apart. There has been a long line of work showing upper bounds on this density. One curious feature of dense unit distance
Externí odkaz:
http://arxiv.org/abs/2407.05071
For sufficiently large $n$, we show that in every configuration of $n$ points chosen inside the unit square there exists a triangle of area less than $n^{-8/7-1/2000}$. This improves upon a result of Koml\'os, Pintz and Szemer\'edi from 1982. Our app
Externí odkaz:
http://arxiv.org/abs/2305.18253
Autor:
Cohen, Alex
We prove that if a fractal set in $\mathbb{R}^d$ avoids lines in a certain quantitative sense, which we call line porosity, then it has a fractal uncertainty principle. The main ingredient is a new higher dimensional Beurling-Malliavin multiplier the
Externí odkaz:
http://arxiv.org/abs/2305.05022
A Lee-Yang polynomial $ p(z_{1},\ldots,z_{n}) $ is a polynomial that has no zeros in the polydisc $ \mathbb{D}^{n} $ and its inverse $ (\mathbb{C}\setminus\overline{\mathbb{D}})^{n} $. We show that any real-rooted exponential polynomial of the form $
Externí odkaz:
http://arxiv.org/abs/2303.03201
Autor:
Cohen, Alex
We prove that a self-similar Cantor set in $\mathbb{Z}_N \times \mathbb{Z}_N$ has a fractal uncertainty principle if and only if it does not contain a pair of orthogonal lines. The key ingredient in our proof is a quantitative form of Lang's conjectu
Externí odkaz:
http://arxiv.org/abs/2206.14131
Autor:
Pugh, Samuel L., Chandler, Chelsea, Cohen, Alex S., Diaz-Asper, Catherine, Elvevåg, Brita, Foltz, Peter W.
Publikováno v:
In Psychiatry Research November 2024 341
Autor:
Siegel, Joshua S., Cohen, Alex S., Szabo, Steven T., Tomioka, Sasagu, Opler, Mark, Kirkpatrick, Brian, Hopkins, Seth
Publikováno v:
In Psychiatry Research October 2024 340
Autor:
Cohen, Alex S., Rodriguez, Zachary, Opler, Mark, Kirkpatrick, Brian, Milanovic, Snezana, Piacentino, Daria, Szabo, Steven T., Tomioka, Sasagu, Ogirala, Ajay, Koblan, Kenneth S., Siegel, Joshua S., Hopkins, Seth
Publikováno v:
In Psychiatry Research October 2024 340