On $\star $- associated comonotone functions

Ondrej Hutník; Jozef Pócs

Displaying similar documents to “On $☆$ - associated comonotone functions”

Regular elements and Green's relations in Menger algebras of terms

Klaus Denecke, Prakit Jampachon (2006)

Discussiones Mathematicae - General Algebra and Applications

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Defining an (n+1)-ary superposition operation $S^{n}$ on the set $W_{τ} (X_{n})$ of all n-ary terms of type τ, one obtains an algebra $n - c l o n e τ : = (W_{τ} (X_{n}); S^{n}, x_{1}, . . ., x_{n})$ of type (n+1,0,...,0). The algebra n-clone τ is free in the variety of all Menger algebras ([9]). Using the operation $S^{n}$ there are different possibilities to define binary associative operations on the set $W_{τ} (X_{n})$ and on the cartesian power $W_{τ} {(X_{n})}^{n}$ . In this paper we study idempotent and regular elements as well as Green’s relations in semigroups of terms with these binary associative...

$ℱ$ -hypercyclic and disjoint $ℱ$ -hypercyclic properties of binary relations over topological spaces

Marko Kostić (2020)

Mathematica Bohemica

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We examine various types of $ℱ$ -hypercyclic ( $ℱ$ -topologically transitive) and disjoint $ℱ$ -hypercyclic (disjoint $ℱ$ -topologically transitive) properties of binary relations over topological spaces. We pay special attention to finite structures like simple graphs, digraphs and tournaments, providing a great number of illustrative examples.

On the number of finite algebraic structures

Erhard Aichinger, Peter Mayr, R. McKenzie (2014)

Journal of the European Mathematical Society

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We prove that every clone of operations on a finite set $A$ , if it contains a Malcev operation, is finitely related – i.e., identical with the clone of all operations respecting $R$ for some finitary relation $R$ over $A$ . It follows that for a fixed finite set $A$ , the set of all such Malcev clones is countable. This completes the solution of a problem that was first formulated in 1980, or earlier: how many Malcev clones can finite sets support? More generally, we prove that every finite algebra...

Properties of unique information

Johannes Rauh, Maik Schünemann, Jürgen Jost (2021)

Kybernetika

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We study the unique information function $U I (T : X ∖ Y)$ defined by Bertschinger et al. within the framework of information decompositions. In particular, we study uniqueness and support of the solutions to the convex optimization problem underlying the definition of $U I$ . We identify sufficient conditions for non-uniqueness of solutions with full support in terms of conditional independence constraints and in terms of the cardinalities of $T$ , $X$ and $Y$ . Our results are based on a reformulation of the first...

Algorithm for the complement of orthogonal operations

Iryna V. Fryz (2018)

Commentationes Mathematicae Universitatis Carolinae

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G. B. Belyavskaya and G. L. Mullen showed the existence of a complement for a $k$ -tuple of orthogonal $n$ -ary operations, where $k < n$ , to an $n$ -tuple of orthogonal $n$ -ary operations. But they proposed no method for complementing. In this article, we give an algorithm for complementing a $k$ -tuple of orthogonal $n$ -ary operations to an $n$ -tuple of orthogonal $n$ -ary operations and an algorithm for complementing a $k$ -tuple of orthogonal $k$ -ary operations to an $n$ -tuple of orthogonal $n$ -ary operations. Also...

From binary cube triangulations to acute binary simplices

Brandts, Jan, van den Hooff, Jelle, Kuiper, Carlo, Steenkamp, Rik

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Cottle’s proof that the minimal number of $0 / 1$ -simplices needed to triangulate the unit $4$ -cube equals $16$ uses a modest amount of computer generated results. In this paper we remove the need for computer aid, using some lemmas that may be useful also in a broader context. One of the $0 / 1$ -simplices involved, the so-called antipodal simplex, has acute dihedral angles. We continue with the study of such acute binary simplices and point out their possible relation to the Hadamard determinant problem. ...

Representation functions for binary linear forms

Fang-Gang Xue (2024)

Czechoslovak Mathematical Journal

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Let $ℤ$ be the set of integers, $ℕ_{0}$ the set of nonnegative integers and $F (x_{1}, x_{2}) = u_{1} x_{1} + u_{2} x_{2}$ be a binary linear form whose coefficients $u_{1}$ , $u_{2}$ are nonzero, relatively prime integers such that $u_{1} u_{2} \neq \pm 1$ and $u_{1} u_{2} \neq - 2$ . Let $f : ℤ \to ℕ_{0} \cup {\infty}$ be any function such that the set $f^{- 1} (0)$ has asymptotic density zero. In 2007, M. B. Nathanson (2007) proved that there exists a set $A$ of integers such that $r_{A, F} (n) = f (n)$ for all integers $n$ , where $r_{A, F} (n) = | {(a, a^{'}) : n = u_{1} a + u_{2} a^{'} : a, a^{'} \in A} |$ . We add the structure of difference for the binary linear form $F (x_{1}, x_{2})$ .

Multiplicatively dependent triples of Tribonacci numbers

Carlos Alexis Ruiz Gómez, Florian Luca (2015)

Acta Arithmetica

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We consider the Tribonacci sequence $T : = {T_{n}}_{n \geq 0}$ given by T₀ = 0, T₁ = T₂ = 1 and $T_{n + 3} = T_{n + 2} + T_{n + 1} + T_{n}$ for all n ≥ 0, and we find all triples of Tribonacci numbers which are multiplicatively dependent.

On a special class of left-continuous uninorms

Gang Li (2018)

Kybernetika

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This paper is devoted to the study of a class of left-continuous uninorms locally internal in the region $A (e)$ and the residual implications derived from them. It is shown that such uninorm can be represented as an ordinal sum of semigroups in the sense of Clifford. Moreover, the explicit expressions for the residual implication derived from this special class of uninorms are given. A set of axioms is presented that characterizes those binary functions $I : {[0, 1]}^{2} \to [0, 1]$ for which a uninorm $U$ of this special...

A characterization of reflexive spaces of operators

Janko Bračič, Lina Oliveira (2018)

Czechoslovak Mathematical Journal

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We show that for a linear space of operators $ℳ \subseteq ℬ (ℋ_{1}, ℋ_{2})$ the following assertions are equivalent. (i) $ℳ$ is reflexive in the sense of Loginov-Shulman. (ii) There exists an order-preserving map $Ψ = (ψ_{1}, ψ_{2})$ on a bilattice $Bil (ℳ)$ of subspaces determined by $ℳ$ with $P \leq ψ_{1} (P, Q)$ and $Q \leq ψ_{2} (P, Q)$ for any pair $(P, Q) \in Bil (ℳ)$ , and such that an operator $T \in ℬ (ℋ_{1}, ℋ_{2})$ lies in $ℳ$ if and only if $ψ_{2} (P, Q) T ψ_{1} (P, Q) = 0$ for all $(P, Q) \in Bil (ℳ)$ . This extends the Erdos-Power type characterization of weakly closed bimodules over a nest algebra to reflexive spaces.

$(0, 1)$ -matrices, discrepancy and preservers

LeRoy B. Beasley (2019)

Czechoslovak Mathematical Journal

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Let $m$ and $n$ be positive integers, and let $R = (r_{1}, ..., r_{m})$ and $S = (s_{1}, ..., s_{n})$ be nonnegative integral vectors. Let $A (R, S)$ be the set of all $m \times n$ $(0, 1)$ -matrices with row sum vector $R$ and column vector $S$ . Let $R$ and $S$ be nonincreasing, and let $F (R)$ be the $m \times n$ $(0, 1)$ -matrix, where for each $i$ , the $i$ th row of $F (R, S)$ consists of $r_{i}$ 1’s followed by $(n - r_{i})$ 0’s. Let $A \in A (R, S)$ . The discrepancy of A, $disc (A)$ , is the number of positions in which $F (R)$ has a 1 and $A$ has a 0. In this paper we investigate linear operators mapping $m \times n$ matrices over...

Repdigits in generalized Pell sequences

Jhon J. Bravo, Jose L. Herrera (2020)

Archivum Mathematicum

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For an integer $k \geq 2$ , let ${(n)}_{n}$ be the $k -$ generalized Pell sequence which starts with $0, ..., 0, 1$ ( $k$ terms) and each term afterwards is given by the linear recurrence $n = 2 n - 1 + n - 2 + \dots + n - k$ . In this paper, we find all $k$ -generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence ${(P_{n}^{(2)})}_{n}$ . ...

The $ℒ_{n}^{m}$ -propositional calculus

Carlos Gallardo, Alicia Ziliani (2015)

Mathematica Bohemica

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T. Almada and J. Vaz de Carvalho (2001) stated the problem to investigate if these Łukasiewicz algebras are algebras of some logic system. In this article an affirmative answer is given and the $ℒ_{n}^{m}$ -propositional calculus, denoted by $ℓ_{n}^{m}$ , is introduced in terms of the binary connectives $\to$ (implication), $↠$ (standard implication), $\land$ (conjunction), $\lor$ (disjunction) and the unary ones $f$ (negation) and $D_{i}$ , $1 \leq i \leq n - 1$ (generalized Moisil operators). It is proved that $ℓ_{n}^{m}$ belongs to the class of standard systems...

Displaying similar documents to “On ☆ - associated comonotone functions”

Displaying similar documents to “On $☆$ - associated comonotone functions”