Zobrazeno 1 - 10
of 10
pro vyhledávání: '"Mehdi Makhul"'
Autor:
Mehdi Makhul, Rom Pinchasi
Publikováno v:
Studia Scientiarum Mathematicarum Hungarica. 59:196-208
Let P be a set of n points in general position in the plane. Let R be a set of points disjoint from P such that for every x, y € P the line through x and y contains a point in R. We show that if is contained in a cubic curve c in the plane, then P
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ae226b465b81d127db2f4e24949b9430
https://doi.org/10.1556/012.2022.01527
https://doi.org/10.1556/012.2022.01527
Publikováno v:
Israel Journal of Mathematics. 248:39-66
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::78e93a3ee5d28b4c129bc66368838867
https://doi.org/10.1007/s11856-022-2291-9
https://doi.org/10.1007/s11856-022-2291-9
Autor:
Arne Winterhof, Mehdi Makhul
Publikováno v:
Research in Number Theory. 8
Let $$\varvec{F}_q$$ F q be the finite field of q elements, where $$q=p^r$$ q = p r is a power of the prime p, and $$\left( \beta _1, \beta _2, \dots , \beta _r \right) $$ β 1 , β 2 , ⋯ , β r be an ordered basis of $$\varvec{F}_q$$ F q over $$\v
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::7bcf344e5a69c478f50ef794897ab8f1
https://doi.org/10.1007/s40993-022-00335-8
https://doi.org/10.1007/s40993-022-00335-8
Autor:
Mehdi Makhul
Publikováno v:
Discrete & Computational Geometry. 66:1143-1149
Richard Guy asked the following question: can we find a triangle with rational sides, medians, and area? Such a triangle is called a \emph{perfect triangle} and no example has been found to date. It is widely believed that such a triangle does not ex
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b893526c0f2a6825bb2d99e806b1b627
https://doi.org/10.1007/s00454-020-00227-7
https://doi.org/10.1007/s00454-020-00227-7
Publikováno v:
The Electronic Journal of Combinatorics. 27
We give a construction of a non-degenerate polynomial $F\in \mathbb R[x,y,z]$ and a set $A$ of cardinality $n$ such that $F$ vanishes on $\Omega(n^{3/2})$ points of $A \times A \times A$, thus providing a new lower bound construction for the Elekes
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::16422c94904a96d597483ddd77638315
https://doi.org/10.37236/8668
https://doi.org/10.37236/8668
We study subsets of the $n$-dimensional vector space over the finite field $\mathbb{F}_q$, for odd $q$, which contain either a sphere for each radius or a sphere for each first coordinate of the center. We call such sets radii spherical Kakeya sets a
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3c7786bb9e4e04a3164d4353e6f31714
We study the probability for a random line to intersect a given plane curve, defined over a finite field, in a given number of points defined over the same field. In particular, we focus on the limits of these probabilities under successive finite fi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2395410e60620d4352dc91ec0f6e7ab2
https://hdl.handle.net/11368/3037695
https://hdl.handle.net/11368/3037695
Autor:
Mehdi Makhul
Publikováno v:
Mosc. J. Comb. Number Theory 8, no. 2 (2019), 143-149
We prove that if $g(x,y)$ is a polynomial of constant degree $d$ that $y_2-y_1$ does not divide $g(x_1,y_1)-g(x_2,y_2)$, then for any finite set $A \subset \mathbb{R}$ \[ |X| \gg_d |A|^2, \quad \text{where} \ X:=\left\{\frac{g(a_1,b_1)-g(a_2,b_2)}{b_
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c9b9b98b7406f2e01cae339a8df62891
Autor:
Konrad J. Swanepoel, Mehdi Makhul, Frank de Zeeuw, Aaron Lin, Hossein Nassajian Mojarrad, Josef Schicho
Publikováno v:
Discrete & Computational Geometry
An ordinary circle of a set $P$ of $n$ points in the plane is defined as a circle that contains exactly three points of $P$. We show that if $P$ is not contained in a line or a circle, then $P$ spans at least $\frac{1}{4}n^2 - O(n)$ ordinary circles.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::240cd60b29399c1c82c355094e81e4ef
Autor:
Jafar Shaffaf, Mehdi Makhul
Publikováno v:
Comptes Rendus Mathematique. 350:121-124
A rational set in the plane is a point set with all its pairwise distances rational. Ulam asked in 1945 if there is an everywhere dense rational set. Solymosi and de Zeeuw proved that every rational distance subset of the plane has only finitely many
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5b323956f36443f5ea1f87575cb9644c
https://doi.org/10.1016/j.crma.2012.01.010
https://doi.org/10.1016/j.crma.2012.01.010