Search

Your search keyword '"Natural number"' showing total 5,435 results
Start Over Descriptor "Natural number"
5,435 results on '"Natural number"'

101. On the (In)Dependence of the Peano Axioms for Natural Numbers

Author

Petrucio Viana, Guilherme Silveira, Márcia R. Cerioli, and Hugo Nobrega

Subjects
Combinatorics, Mathematics::Logic, History, Sequence, History and Philosophy of Science, Peano axioms, Independence (mathematical logic), Natural number, Mathematics
Abstract

We investigate two notions of independence—(usual) independence and complete independence—applied to the Peano axioms for the sequence of natural numbers. We review the results that, although they ...

Published
2021

102. Semisimplicity of the Deformations of the Subcharacter Algebra of an Abelian Group

Author

İsmail Alperen Öğüt

Subjects
Finite group, General Mathematics, Primary 19A22, Secondary 16B50, Zero (complex analysis), Structure (category theory), Cyclic group, Natural number, Field (mathematics), Algebra, FOS: Mathematics, Representation Theory (math.RT), Abelian group, Simple module, Mathematics - Representation Theory, Mathematics
Abstract

For those deformations that satisfy a certain non-degeneracy condition, we describe the structure of certain simple modules of the deformations of the subcharacter algebra of a finite group. For finite abelian groups, we prove that the deformation given by the inclusion of the natural numbers, which corresponds to the algebra generated by the fibred bisets over a field of characteristic zero, is not semisimple. In the cyclic group of prime order case, we provide a complete description of the semisimple deformations.

Published
2021

103. A complexity of compact 3-manifolds via immersed surfaces

Author

Gennaro Amendola

Subjects
Pure mathematics, General Mathematics, Natural number, Mathematics::Geometric Topology, Manifold, Connected sum, symbols.namesake, Subadditivity, symbols, Mathematics::Differential Geometry, Ideal (ring theory), Möbius strip, Mathematics::Symplectic Geometry, Finite set, Mathematics
Abstract

We generalise the surface-complexity of closed 3-manifolds to the compact case. This generalisation preserves the (natural generalisation of the) properties holding in the closed case: the surface-complexity on compact 3-manifolds is a natural number measuring how much the manifolds are complicated, it is subadditive under connected sum and it is finite-to-one on $$\mathbb {P}^2$$ -irreducible and boundary-irreducible manifolds without essential annuli and Mobius strips. Moreover, for these manifolds, it equals the minimal number of cubes in an ideal cubulation of the manifold, except for a finite number of cases. We will also give estimations of the surface-complexity by means of ideal triangulations and Matveev complexity.

Published
2021

104. Novel Theorems and Algorithms Relating to the Collatz Conjecture

Author

Michael R. Schwob, Peter J. S. Shiue, and Rama Venkat

Subjects
Conjecture, Article Subject, Mathematics - Number Theory, Natural number, Collatz conjecture, Mathematics (miscellaneous), Integer, Simple (abstract algebra), FOS: Mathematics, QA1-939, Number Theory (math.NT), Peak value, Algorithm, Mathematics
Abstract

Proposed in 1937, the Collatz conjecture has remained in the spotlight for mathematicians and computer scientists alike due to its simple proposal, yet intractable proof. In this paper, we propose several novel theorems, corollaries, and algorithms that explore relationships and properties between the natural numbers, their peak values, and the conjecture. These contributions primarily analyze the number of Collatz iterations it takes for a given integer to reach 1 or a number less than itself, or the relationship between a starting number and its peak value., 17 pages, 4 figures, 4 tables, 3 algorithms, 10 theorems, 2 corollaries, GitHub code

Published
2021

105. The strong law of large numbers for sums of randomly chosen random variables

Author

Agnieszka M. Gdula and Andrzej Krajka

Subjects
Independent and identically distributed random variables, Combinatorics, Sequence, Number theory, Law of large numbers, General Mathematics, Dependent random variables, Natural number, Almost surely, Random variable, Mathematics
Abstract

Let {Xn,n ≥ 1} be a sequence of independent or identically distributed dependent random variables, and let {An,n ≥ 1} be a sequence of random subsets of natural numbers independent of {Xn, n ≥ 1}. In this paper, we describe the strong law of large numbers (SLLN) of the form $$ {\sum}_{i\in {A}_n}\left({X}_i-\mathrm{E}{\sum}_{i\in {A}_n}{X}_i\right)/{b}_n\to 0\ \mathrm{a}.\mathrm{s}. $$ ∑ i ∈ A n X i − E ∑ i ∈ A n X i / b n → 0 a . s . as n → ∞ for some sequence of nondecreasing positive numbers {bn, n ≥ 1}. There often arises an assumption that {An, n ≥ 1} are almost surely increasing: An ⊂ An + 1, a. s n ≥ 1.

Published
2021

106. Subpolygons in Conway–Coxeter frieze patterns

Author

Michael Cuntz and Thorsten Holm

Subjects
Combinatorics, Frieze, Mathematics::Combinatorics, Frieze group, Ptolemy's table of chords, Diagonal, Coxeter group, Regular polygon, Discrete Mathematics and Combinatorics, Natural number, Computer Science::Data Structures and Algorithms, Value (mathematics), Mathematics
Abstract

Friezes with coefficients are maps assigning numbers to the edges and diagonals of a regular polygon such that all Ptolemy relations for crossing diagonals are satisfied. Among these, the classic Conway-Coxeter friezes are the ones where all values are natural numbers and all edges have value 1. Every subpolygon of a Conway-Coxeter frieze yields a frieze with coefficients over the natural numbers. In this paper we give a complete arithmetic criterion for which friezes with coefficients appear as subpolygons of Conway-Coxeter friezes. This generalizes a result of our earlier paper with Peter Jorgensen from triangles to subpolygons of arbitrary size.

Published
2021

107. On the Ellis semigroup of a discrete dynamical system ([0, 1], f)

Author

S. Garcia-Ferreira and I. Vidal-Escobar

Subjects
Surjective function, Combinatorics, Algebra and Number Theory, Continuous function, Semigroup, Discrete space, High Energy Physics::Phenomenology, Natural number, Compactification (mathematics), Function (mathematics), Topological entropy, Mathematics
Abstract

The Ellis semigroup of a discrete dynamical system (X, f) is denoted by E(X, f). We only consider surjective continuous functions $$f:[0,1]\rightarrow [0,1]$$ such that $$\{ f^n : n\in {\mathbb {N}}\}$$ is infinite. The main result asserts that the Ellis semigroup E([0, 1], f) is always a compactification of the natural numbers with the discrete topology. We also prove some results estimating the cardinality of the Ellis semigroup of certain dynamical systems: we show that if $$f:[0,1]\rightarrow [0,1]$$ is a continuous function with positive topological entropy, then $$|E([0,1],f)|= 2^{2^{\aleph _0}}$$ , and if $$f:[0,1]\rightarrow [0,1]$$ is a $$2^{n}$$ -function for some $$n \in {\mathbb {N}}$$ , then $$|E([0,1],f)-\{f^n:n\in {\mathbb {N}}\}|=2^n.$$

Published
2021

129. Real Numbers

Author

Aksoy, Asuman G., Khamsi, Mohamed A., Aksoy, Asuman G., and Khamsi, Mohamed A.

Published
2010
Full Text
View/download PDF

130. Aggregation of Bounded Fuzzy Natural Number-Valued Multisets

Author

Casasnovas, Jaume, Vicente Riera, J., Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Siekmann, Jörg, editor, Wahlster, Wolfgang, editor, Torra, Vicenç, editor, Narukawa, Yasuo, editor, and Daumas, Marc, editor

Published
2010
Full Text
View/download PDF

131. Least and Greatest Solutions of Equations over Sets of Integers

Author

Jeż, Artur, Okhotin, Alexander, Hutchison, David, editor, Kanade, Takeo, editor, Kittler, Josef, editor, Kleinberg, Jon M., editor, Mattern, Friedemann, editor, Mitchell, John C., editor, Naor, Moni, editor, Nierstrasz, Oscar, editor, Pandu Rangan, C., editor, Steffen, Bernhard, editor, Sudan, Madhu, editor, Terzopoulos, Demetri, editor, Tygar, Doug, editor, Vardi, Moshe Y., editor, Weikum, Gerhard, editor, Hliněný, Petr, editor, and Kučera, Antonín, editor

Published
2010
Full Text
View/download PDF

133. Basics of ring theory

Author

Awange, Joseph L., Grafarend, Erik W., Paláncz, Béla, Zaletnyik, Piroska, Awange, Joseph L., Grafarend, Erik W., Paláncz, Béla, and Zaletnyik, Piroska

Published
2010
Full Text
View/download PDF

138. Relativization of Real Numbers to a Universe

Author

Ishihara, Hajime, Hendricks, Vincent F., editor, Symons, John, editor, Van Dalen, Dirk, editor, Kuipers, Theo A.F., editor, Seidenfeld, Teddy, editor, Suppes, Patrick, editor, WoleńSki, Jan, editor, Lindström, Sten, editor, Palmgren, Erik, editor, Segerberg, Krister, editor, and Stoltenberg-Hansen, Viggo, editor

Published
2009
Full Text
View/download PDF

139. Frege’s Context Principle and Reference to Natural Numbers

Author

Linnebo, Øystein, Hendricks, Vincent F., editor, Symons, John, editor, Van Dalen, Dirk, editor, Kuipers, Theo A.F., editor, Seidenfeld, Teddy, editor, Suppes, Patrick, editor, WoleńSki, Jan, editor, Lindström, Sten, editor, Palmgren, Erik, editor, Segerberg, Krister, editor, and Stoltenberg-Hansen, Viggo, editor

Published
2009
Full Text
View/download PDF

140. The Measure of Scottish Neo-Logicism

Author

Shapiro, Stewart, Hendricks, Vincent F., editor, Symons, John, editor, Van Dalen, Dirk, editor, Kuipers, Theo A.F., editor, Seidenfeld, Teddy, editor, Suppes, Patrick, editor, WoleńSki, Jan, editor, Lindström, Sten, editor, Palmgren, Erik, editor, Segerberg, Krister, editor, and Stoltenberg-Hansen, Viggo, editor

Published
2009
Full Text
View/download PDF

141. On the Theory of Projective Planes

Author

Shirshov, A. I., Nikitin, A. A., Rota, Gian-Carlo, editor, Kung, Joseph P. S., editor, Bokut, Leonid, editor, Shestakov, Ivan, editor, Latyshev, Victor, editor, and Zelmanov, Efim, editor

Published
2009
Full Text
View/download PDF

142. On Special J-rings

Author

Shirshov, A. I., Rota, Gian-Carlo, editor, Kung, Joseph P. S., editor, Bokut, Leonid, editor, Shestakov, Ivan, editor, Latyshev, Victor, editor, and Zelmanov, Efim, editor

Published
2009
Full Text
View/download PDF

147. Numbers

Author

Axler, S., editor, Ribet, K. A., editor, and Childs, Lindsay N., editor

Published
2009
Full Text
View/download PDF

148. On Equations over Sets of Numbers and Their Limitations

Author

Lehtinen, Tommi, Okhotin, Alexander, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Sudan, Madhu, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Vardi, Moshe Y., Series editor, Weikum, Gerhard, Series editor, Diekert, Volker, editor, and Nowotka, Dirk, editor

Published
2009
Full Text
View/download PDF

Catalog

Books, media, physical & digital resources
See catalog results