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Displaying 1581 – 1600 of 1815

The Fourier transform of functions of the greatest common divisor.

Schramm, Wolfgang (2008)

Integers

The fractional part of $n θ + ø$ and Beatty sequences

Takao Komatsu (1995)

Journal de théorie des nombres de Bordeaux

The fundamental constituents of iteration digraphs of finite commutative rings

Jizhu Nan, Yangjiang Wei, Gaohua Tang (2014)

Czechoslovak Mathematical Journal

For a finite commutative ring $R$ and a positive integer $k ⩾ 2$ , we construct an iteration digraph $G (R, k)$ whose vertex set is $R$ and for which there is a directed edge from $a \in R$ to $b \in R$ if $b = a^{k}$ . Let $R = R_{1} \oplus ... \oplus R_{s}$ , where $s > 1$ and $R_{i}$ is a finite commutative local ring for $i \in {1, ..., s}$ . Let $N$ be a subset of ${R_{1}, \dots, R_{s}}$ (it is possible that $N$ is the empty set $\emptyset$ ). We define the fundamental constituents $G_{N}^{*} (R, k)$ of $G (R, k)$ induced by the vertices which are of the form ${(a_{1}, \dots, a_{s}) \in R : a_{i} \in D (R_{i})$ if $R_{i} \in N$ , otherwise $a_{i} \in U (R_{i}), i = 1, ..., s},$ where U $(R)$ denotes the unit group of $R$ and D $(R)$ denotes the zero-divisor set of $R$ . We investigate...

The gcd-sum function.

Broughan, Kevin A. (2001)

Journal of Integer Sequences [electronic only]

The general quasi-order algorithm in number theory.

Hilton, Peter, Pedersen, Jean (1986)

International Journal of Mathematics and Mathematical Sciences

The generalization and proof of Bertrand's postulate.

Giordano, George (1987)

International Journal of Mathematics and Mathematical Sciences

The Generation of Arithmetical Identities.

P.J. McCarthy (1960)

Journal für die reine und angewandte Mathematik

The geometry of non-unit Pisot substitutions

Milton Minervino, Jörg Thuswaldner (2014)

Annales de l’institut Fourier

It is known that with a non-unit Pisot substitution $σ$ one can associate certain fractal tiles, so-called Rauzy fractals. In our setting, these fractals are subsets of a certain open subring of the adèle ring of the associated Pisot number field. We present several approaches on how to define Rauzy fractals and discuss the relations between them. In particular, we consider Rauzy fractals as the natural geometric objects of certain numeration systems, in terms of the dual of the one-dimensional realization...

The Gergonne $m$ -pile trick and the base $m$ counting system. (El truco de $m$ pilas de Gergonne y el sistema de numeración de base $m$ .)

Quintero, Roy (2006)

Boletín de la Asociación Matemática Venezolana

The Golomb space is topologically rigid

Taras O. Banakh, Dario Spirito, Sławomir Turek (2021)

Commentationes Mathematicae Universitatis Carolinae

The Golomb space $ℕ_{τ}$ is the set $ℕ$ of positive integers endowed with the topology $τ$ generated by the base consisting of arithmetic progressions ${a + b n : n \geq 0}$ with coprime $a, b$ . We prove that the Golomb space $ℕ_{τ}$ is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.