ARCHIV DER MATHEMATIK, ISSN 0003-889X, 08/2019, Volume 113, Issue 2, pp. 157 - 168

In order to investigate multiplicative structures in additively large sets, Beiglbock et al. raised a significant open question as to whether or not every...

MATHEMATICS | Triveni triplet | Syndetic set | Geometric progression | Congruence

MATHEMATICS | Triveni triplet | Syndetic set | Geometric progression | Congruence

Journal Article

Periodica Mathematica Hungarica, ISSN 0031-5303, 6/2019, Volume 78, Issue 2, pp. 152 - 156

... density · Meager set Mathematics Subject Classiﬁcation Primary 40A35; Secondary 11B05 · 54A20 1 Introduction Oxtoby’s classical book [14] examines analogues and non...

54A20 | Statistical cluster points | Meager set | Statisical limit points | Mathematics, general | Mathematics | Primary 40A35 | Secondary 11B05 | Asymptotic density | MATHEMATICS | MATHEMATICS, APPLIED

54A20 | Statistical cluster points | Meager set | Statisical limit points | Mathematics, general | Mathematics | Primary 40A35 | Secondary 11B05 | Asymptotic density | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

Mathematika, ISSN 0025-5793, 01/2012, Volume 58, Issue 1, pp. 11 - 20

For a primitive root g modulo a prime p≥1 we obtain upper bounds on the gaps between the residues modulo p of the N consecutive powers agn, n=1,…,N, which is...

11T23 (secondary) | 11A07 (primary) | 11B50 | 11B05 | MATHEMATICS | MATHEMATICS, APPLIED

11T23 (secondary) | 11A07 (primary) | 11B50 | 11B05 | MATHEMATICS | MATHEMATICS, APPLIED

Journal Article

The Rocky Mountain journal of mathematics, ISSN 0035-7596, 2018, Volume 48, Issue 6, pp. 1951 - 1961

We define a class of so-called thinnable ideals I on the positive integers which includes several well-known examples, e.g., the collection of sets with zero...

Cluster point | Ideal convergence | Logarithmic density | Thinnable ideal | Summable ideal | Statistical convergence | Asymptotic density | Erdos-Ulam ideal | MATHEMATICS | summable ideal | ideal convergence | logarithmic density | CONVERGENT | statistical convergence | asymptotic density | thinnable ideal | SUBSEQUENCES

Cluster point | Ideal convergence | Logarithmic density | Thinnable ideal | Summable ideal | Statistical convergence | Asymptotic density | Erdos-Ulam ideal | MATHEMATICS | summable ideal | ideal convergence | logarithmic density | CONVERGENT | statistical convergence | asymptotic density | thinnable ideal | SUBSEQUENCES

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 06/2017, Volume 67, Issue 3, pp. 593 - 600

The concept of conditionally independent sets is introduced in this article. Its link with the concept of the conditional probability and with the concept of a...

conditional probability | Primary 11B05 | independent events | asymptotic density | Secondary 60A05 | independent sets | Fuzzy sets | Set theory | Research | Mathematical research | Conditional probability

conditional probability | Primary 11B05 | independent events | asymptotic density | Secondary 60A05 | independent sets | Fuzzy sets | Set theory | Research | Mathematical research | Conditional probability

Journal Article

Journal of Number Theory, ISSN 0022-314X, 08/2014, Volume 141, pp. 136 - 158

A beautiful theorem of Zeckendorf states that every positive integer can be uniquely decomposed as a sum of non-consecutive Fibonacci numbers {Fn}, where F1=1,...

Stirling numbers of the first kind | Gaussian behavior | Zeckendorf decompositions | Recurrence relations | MATHEMATICS | NUMBERS | EXPANSIONS | Mathematics - Number Theory

Stirling numbers of the first kind | Gaussian behavior | Zeckendorf decompositions | Recurrence relations | MATHEMATICS | NUMBERS | EXPANSIONS | Mathematics - Number Theory

Journal Article

08/2015

Involve 10 (2017) 125-150 Zeckendorf's theorem states that every positive integer can be uniquely decomposed as a sum of nonconsecutive Fibonacci numbers,...

Mathematics - Number Theory

Mathematics - Number Theory

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 08/2018, Volume 68, Issue 4, pp. 717 - 726

Weighted uniform densities are a generalization of the uniform density, which is also known as the Banach density. In this paper, we introduce the concept of...

filter | uniform density | Primary 11B05 | Darboux property | ideal | Secondary 40A35 | convergent series | ideal convergence | weighted uniform density | 40A05 | Banach density | P-ideal | MATHEMATICS | SERIES | CONVERGENCE | I-convergent series | Density | Sequences

filter | uniform density | Primary 11B05 | Darboux property | ideal | Secondary 40A35 | convergent series | ideal convergence | weighted uniform density | 40A05 | Banach density | P-ideal | MATHEMATICS | SERIES | CONVERGENCE | I-convergent series | Density | Sequences

Journal Article

Journal of Number Theory, ISSN 0022-314X, 05/2017, Volume 174, pp. 445 - 455

Let P(N) be the power set of N. An upper density (on N) is a nondecreasing and subadditive function μ⋆:P(N)→R such that μ⋆(N)=1 and μ⋆(k⋅X+h)=1kμ⋆(X) for all...

Set functions | Darboux (or intermediate value) property | Asymptotic (or natural) density | Banach (or uniform) density | Subadditive functions | Upper and lower densities (and quasi-densities) | MATHEMATICS | INTEGERS

Set functions | Darboux (or intermediate value) property | Asymptotic (or natural) density | Banach (or uniform) density | Subadditive functions | Upper and lower densities (and quasi-densities) | MATHEMATICS | INTEGERS

Journal Article

Monatshefte für Mathematik, ISSN 0026-9255, 11/2016, Volume 181, Issue 3, pp. 577 - 599

We provide a framework for proofs of structural theorems about sets with positive Banach logarithmic density. For example, we prove that if $$A\subseteq...

Secondary 26E35 | Primary 11B05 | Logarithmic density | 37A45 | Nonstandard analysis | Mathematics, general | Mathematics | SUMSET PHENOMENON | MATHEMATICS | THEOREM | LARGE SETS | Computer science | Specific gravity | Analysis

Secondary 26E35 | Primary 11B05 | Logarithmic density | 37A45 | Nonstandard analysis | Mathematics, general | Mathematics | SUMSET PHENOMENON | MATHEMATICS | THEOREM | LARGE SETS | Computer science | Specific gravity | Analysis

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2017, Volume 67, Issue 5, pp. 1105 - 1128

In the present paper we introduce the upper and lower exponential density functions of subsets ⊆ ℕ*. We identify completely the form of the upper density and...

upper and lower asymptotic density | abscissa of convergence | fractional density | 26A24 | upper and lower exponential density | Primary 11K99 | 26A03 | Dirichlet series | 26A15 | 26A48 | Secondary 11B05 | α-fractional density | MATHEMATICS | alpha-fractional density | Fuzzy sets | Set theory | Functions | Research | Functional equations | Mathematical research | Density

upper and lower asymptotic density | abscissa of convergence | fractional density | 26A24 | upper and lower exponential density | Primary 11K99 | 26A03 | Dirichlet series | 26A15 | 26A48 | Secondary 11B05 | α-fractional density | MATHEMATICS | alpha-fractional density | Fuzzy sets | Set theory | Functions | Research | Functional equations | Mathematical research | Density

Journal Article

Positivity, ISSN 1385-1292, 3/2014, Volume 18, Issue 1, pp. 131 - 145

... · A-statistical convergence · Hausdorff spaces · Matrix summability Mathematics Subject Classiﬁcation (2000) Primary 54A20 · 40J05; Secondary 40A05 · 40G15 · 11B05...

Hausdorff spaces | 40J05 | Secondary 40A05 | Primary 54A20 | Mathematics | Matrix summability | A$$ -distributional convergence | 11B05 | Operator Theory | Fourier Analysis | A$$ -statistical convergence | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Econometrics | 40G15 | A-distributional convergence | A-statistical convergence | MATHEMATICS | STATISTICAL CONVERGENCE | Studies | Topological manifolds | Matrix

Hausdorff spaces | 40J05 | Secondary 40A05 | Primary 54A20 | Mathematics | Matrix summability | A$$ -distributional convergence | 11B05 | Operator Theory | Fourier Analysis | A$$ -statistical convergence | Potential Theory | Calculus of Variations and Optimal Control; Optimization | Econometrics | 40G15 | A-distributional convergence | A-statistical convergence | MATHEMATICS | STATISTICAL CONVERGENCE | Studies | Topological manifolds | Matrix

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2011, Volume 61, Issue 5, pp. 705 - 716

We investigate the sequence of integers x 1, x 2, x 3, … lying in {0, 1, …, [β]} in a so-called Rényi β-expansion of unity 1 = $\sum\limits_{j = 1}^\infty {x_j...

transcendental numbers | Secondary 11B05, 11J82 | Algebra | β -expansion | Diophantine exponent | Mathematics, general | Mathematics | Primary 11A63 | β-expansion | MATHEMATICS | beta-expansion

transcendental numbers | Secondary 11B05, 11J82 | Algebra | β -expansion | Diophantine exponent | Mathematics, general | Mathematics | Primary 11A63 | β-expansion | MATHEMATICS | beta-expansion

Journal Article

Journal of Number Theory, ISSN 0022-314X, 2008, Volume 128, Issue 6, pp. 1646 - 1654

Let e ⩾ 1 and b ⩾ 2 be integers. For a positive integer n = ∑ j = 0 k a j × b j with 0 ⩽ a j < b , define S e , b ( n ) = ∑ j = 0 k a j e . n is called ( e , b...

MATHEMATICS

MATHEMATICS

Journal Article

Experimental Mathematics, ISSN 1058-6458, 01/2006, Volume 15, Issue 4, pp. 421 - 444

Digital snowflakes are solidifying cellular automata on the triangular lattice with the property that a site having exactly one occupied neighbor always...

Secondary 68Q80, 11B05, 60K05 | macroscopic dynamics | exact solvability | thickness | growth model | Primary 37B15 | cellular automaton | Asymptotic density | Thickness | Cellular automaton | Growth model | Macroscopic dynamics | Exact solvability | MATHEMATICS | CELLULAR AUTOMATA | asymptotic density | 68Q80 | 60K05 | 37B15 | 11B05

Secondary 68Q80, 11B05, 60K05 | macroscopic dynamics | exact solvability | thickness | growth model | Primary 37B15 | cellular automaton | Asymptotic density | Thickness | Cellular automaton | Growth model | Macroscopic dynamics | Exact solvability | MATHEMATICS | CELLULAR AUTOMATA | asymptotic density | 68Q80 | 60K05 | 37B15 | 11B05

Journal Article

Communications in Algebra, ISSN 0092-7872, 08/2019, Volume 47, Issue 8, pp. 3056 - 3063

Let denote the set of positive integers that appear as the strong symmetric genus of a finite nilpotent group. We show that if g is not congruent to , then ....

strong symmetric genus | genus spectrum | nilpotent groups | Density | Primary 30F99 | Secondary 11B05 | MATHEMATICS | Integers | Lower bounds | Group theory

strong symmetric genus | genus spectrum | nilpotent groups | Density | Primary 30F99 | Secondary 11B05 | MATHEMATICS | Integers | Lower bounds | Group theory

Journal Article

Journal of Number Theory, ISSN 0022-314X, 04/2019, Volume 197, pp. 218 - 227

The quotient set, or ratio set, of a set of integers A is defined asR(A):={a/b:a,b∈A,b≠0}. We consider the case in which A is the image of Z+ under a...

p-adic numbers | Polynomials | Quotient set | Sum of powers | Denseness | MATHEMATICS

p-adic numbers | Polynomials | Quotient set | Sum of powers | Denseness | MATHEMATICS

Journal Article

Mathematica Slovaca, ISSN 0139-9918, 10/2008, Volume 58, Issue 5, pp. 535 - 540

In the paper, there are proved some properties of the asymptotic density using the permutations.

Primary 11B05 | Algebra | Mathematics, general | Mathematics | asymptotic density | Secondary 40C05 | permutation | DENSITY | MATHEMATICS

Primary 11B05 | Algebra | Mathematics, general | Mathematics | asymptotic density | Secondary 40C05 | permutation | DENSITY | MATHEMATICS

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 4/2018, Volume 110, Issue 4, pp. 343 - 349

.... We study the notion of van der Corput sets with respect to general compact groups. Mathematics Subject Classiﬁcation. Primary 11K06, Secondary 11B05, 37A45. Keywords...

Uniform distribution | Compact groups | 37A45 | Van der Corput sets | Primary 11K06 | Mathematics, general | Van der Corput’s theorem | Intersective sets | Mathematics | Secondary 11B05 | MATHEMATICS | DIFFERENCE THEOREM | Van der Corput's theorem

Uniform distribution | Compact groups | 37A45 | Van der Corput sets | Primary 11K06 | Mathematics, general | Van der Corput’s theorem | Intersective sets | Mathematics | Secondary 11B05 | MATHEMATICS | DIFFERENCE THEOREM | Van der Corput's theorem

Journal Article

Archiv der Mathematik, ISSN 0003-889X, 4/2017, Volume 108, Issue 4, pp. 341 - 350

... 11B05, 11N25, 11N37, 20F38, 30F99. Keywords. Strong symmetric genus, Riemann surface, Genus spectrum, Abelian groups, Asymptotic density, Unions of arithmetic...

Primary 57M60 | Mathematics | 30F99 | Unions of arithmetic progressions | Secondary 11B05 | Riemann surface | 11N25 | Abelian groups | Mathematics, general | 20F38 | 11N37 | Strong symmetric genus | Genus spectrum | Asymptotic density | MATHEMATICS

Primary 57M60 | Mathematics | 30F99 | Unions of arithmetic progressions | Secondary 11B05 | Riemann surface | 11N25 | Abelian groups | Mathematics, general | 20F38 | 11N37 | Strong symmetric genus | Genus spectrum | Asymptotic density | MATHEMATICS

Journal Article

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