Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Lenny Fukshansky"'
Publikováno v:
Expositiones Mathematicae. 38:430-479
The Bateman–Horn conjecture is a far-reaching statement about the distribution of the prime numbers. It implies many known results, such as the prime number theorem and the Green–Tao theorem, along with many famous conjectures, such the twin prim
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::fb35b989094a7c7ec73c155251cef8a4
https://doi.org/10.1016/j.exmath.2019.04.005
https://doi.org/10.1016/j.exmath.2019.04.005
Autor:
Maxwell Forst, Lenny Fukshansky
We consider multivariable polynomials over a fixed number field, linear in some of the variables. For a system of such polynomials satisfying certain technical conditions we prove the existence of search bounds for simultaneous zeros with respect to
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::89027fd336e2fbe16daa135b449c50ce
http://arxiv.org/abs/2202.05916
http://arxiv.org/abs/2202.05916
Autor:
Albrecht Böttcher, Lenny Fukshansky
Publikováno v:
Research in Number Theory. 6
Let $$F(\varvec{x})$$ be a homogeneous polynomial in $$n \ge 1$$ variables of degree $$1 \le d \le n$$ with integer coefficients so that its degree in every variable is equal to 1. We give some sufficient conditions on F to ensure that for every inte
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::985da51925a0953182f31c6ed913a57b
https://doi.org/10.1007/s40993-020-00218-w
https://doi.org/10.1007/s40993-020-00218-w
Let $L$ be a lattice of full rank in $n$-dimensional real space. A vector in $L$ is called $i$-sparse if it has no more than $i$ nonzero coordinates. We define the $i$-th successive sparsity level of $L$, $s_i(L)$, to be the minimal $s$ so that $L$ h
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4fb833709422cd78fcd57a51cf78d637
Autor:
Lenny Fukshansky, David Kogan
Nearly orthogonal lattices were formally defined in [4], where their applications to image compression were also discussed. The idea of ``near orthogonality" in $2$-dimensions goes back to the work of Gauss. In this paper, we focus on well-rounded ne
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8a05f167aab6669473d66b470a252e5b
Autor:
Lenny Fukshansky, Alexander Hsu
We give a new deterministic construction of integer sensing matrices that can be used for the recovery of integer-valued signals in compressed sensing. This is a family of $n \times d$ integer matrices, $d \geq n$, with bounded sup-norm and the prope
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b751f8953651c425a30dc68e18a26a95
http://arxiv.org/abs/1912.10138
http://arxiv.org/abs/1912.10138
Publikováno v:
Proceedings of the American Mathematical Society. 146:4151-4163
Let Λ ⊂ R n \Lambda \subset \mathbb R^n be an algebraic lattice coming from a projective module over the ring of integers of a number field K K . Let Z ⊂ R n \mathcal Z \subset \mathbb R^n be the zero locus of a finite collection of polynomials
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c13f90100bbaa75a5326a6010749404b
https://doi.org/10.1090/proc/14110
https://doi.org/10.1090/proc/14110
Autor:
Lenny Fukshansky, A.A. Shaar
Publikováno v:
Advances in Mathematics of Communications. 12:181-188
We present a new family of one-coincidence sequence sets suitable for frequency hopping code division multiple access (FH-CDMA) systems with dispersed (low density) sequence elements. These sets are derived from one-coincidence prime sequence sets, s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::967b7f7b43ddbbea2e7ef4428d7b1946
https://doi.org/10.3934/amc.2018012
https://doi.org/10.3934/amc.2018012
Autor:
Albrecht Böttcher, Lenny Fukshansky
Publikováno v:
Linear Algebra and its Applications. 531:592-601
This note supplies additions to our paper quoted in the title on integral spans of tight frames in Euclidean spaces. In that previous paper, we considered the case of an equiangular tight frame (ETF), proving that if its integral span is a lattice th
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::d0204b6d62d9e91881c7f543ac5ff529
https://doi.org/10.1016/j.laa.2017.06.024
https://doi.org/10.1016/j.laa.2017.06.024
Publikováno v:
Discrete & Computational Geometry. 61:123-135
We consider lattices generated by finite Abelian groups. We prove that such a lattice is strongly eutactic, which means the normalized minimal vectors of the lattice form a spherical 2-design, if and only if the group is of odd order or if it is a po
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d0011edd6b810898cd9a0e40557658ca
https://doi.org/10.1007/s00454-017-9909-4
https://doi.org/10.1007/s00454-017-9909-4