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pro vyhledávání: '"LEVIN, Mordechay B."'
Autor:
Levin, Mordechay B.
Let $ (X_n)_{n \geq 0} $ be a digital $(t,s)$-sequence in base $2$, $\mathcal{P}_m =(X_n)_{n=0}^{2^m-1} $, and let $D(\mathcal{P}_m, Y )$ be the local discrepancy of $\mathcal{P}_m$. Let $T \oplus Y$ be the digital addition of $T$ and $Y$, and let $$
Externí odkaz:
http://arxiv.org/abs/2012.14004
Autor:
Levin, Mordechay B.
Let $(H(n))_{n \geq 0} $ be a $2-$dimensional Halton's sequence. Let $D_{2} ( (H(n))_{n=0}^{N-1}) $ be the $L_2$-discrepancy of $ (H_n)_{n=0}^{N-1} $. It is known that $\limsup_{N \to \infty } (\log N)^{-1} D_{2} ( H(n) )_{n=0}^{N-1} >0$. In this pap
Externí odkaz:
http://arxiv.org/abs/2012.14002
Autor:
Levin, Mordechay B.
Let $p_1,...,p_{s+1}$ be distinct primes and let $T_{p_i}$ be the von Niemann - Kakutani adding machine $(1 \leq i \leq s)$, $T_{\mathcal{P}}(\mathbf{x}) =(T_{p_1}(x_1),..., T_{p_s}(x_s))$. Let $y_i \in (0,1)$ be a $p_{s+1}$-rational $(1 \leq i \leq
Externí odkaz:
http://arxiv.org/abs/2001.00796
Autor:
LEVIN, Mordechay B.
Publikováno v:
Journal de Théorie des Nombres de Bordeaux, 2022 Jan 01. 34(1), 163-187.
Externí odkaz:
https://www.jstor.org/stable/48676930
Autor:
Levin, Mordechay B.
Let ${\bf x}_0,{\bf x}_1,...$ be a sequence of points in $[0,1)^s$. A subset $S$ of $[0,1)^s$ is called a bounded remainder set if there exist two real numbers $a$ and $C$ such that, for every integer $N$, $$ | {\rm card}\{n
Externí odkaz:
http://arxiv.org/abs/1901.00135
Autor:
Levin, Mordechay B.
Let ${\bf x}_0,{\bf x}_1,...$ be a sequence of points in $[0,1)^s$. A subset $S$ of $[0,1)^s$ is called a bounded remainder set if there exist two real numbers $a$ and $C$ such that, for every integer $N$, $$ | {\rm card}\{n
Externí odkaz:
http://arxiv.org/abs/1901.00042
Autor:
Levin, Mordechay B.
Let $(H_s(n))_{n \geq 1}$ be an $s-$dimensional Halton's sequence, and let ${\mathcal{H}}_{s+1,N}=(H_s(n),n/N)_{n=0}^{N-1}$ be the $s+1-$dimensional Hammersley point set. Let $D(\mathbf{x},(H_n)_{n=0}^{N-1} )$ be the local discrepancy of $(H_n)_{n=0}
Externí odkaz:
http://arxiv.org/abs/1806.11498
Autor:
Levin, Mordechay B.
Let $ (H_s(n))_{n \geq 1} $ be an $s-$dimensional generalized Halton's sequence. Let $\emph{D}^{*}_N$ be the discrepancy of the sequence $ (H_s(n) )_{n = 1}^{N} $. It is known that $D^{*}_{N} =O(\ln^s N)$ as $N \to \infty $. In this paper, we prove t
Externí odkaz:
http://arxiv.org/abs/1507.08529
Autor:
Levin, Mordechay B.
We find the exact lower bound of the discrepancy of shifted Niedereiter's sequences.
Comment: Minor changes
Comment: Minor changes
Externí odkaz:
http://arxiv.org/abs/1505.06610