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The complexity of divisibility
Linear Algebra and Its Applications, 2016 We address two sets of long-standing open questions in probability theory, from a computational complexity perspective: divisibility of stochastic maps, and divisibility and decomposability of probability distributions. We prove that finite divisibility of stochastic maps is an NP-complete problem, and extend this result to nonnegative matrices, and ...
Toby Cubitt, Johannes Bausch
exaly +6 more sources
Operational Characterization of Divisibility of Dynamical Maps
Physical Review Letters, 2016 Divisibility of dynamical maps turns out to be a fundamental notion in characterising Markovianity of quantum evolution, although the decision problem for divisibility itself is computationally intractable.
Joonwoo Bae, Dariusz Chruściński
exaly +3 more sources
Linear divisibility sequences and Salem numbers [PDF]
, 2017 We study linear divisibility sequences of order 4, providing a characterization by means of their characteristic polynomials and finding their factorization as a product of linear divisibility sequences of order 2.
Abrate, Marco +3 more
core +2 more sources
Robin Criterion on Divisibility [PDF]
The Ramanujan Journal, 2021 Robin criterion states that the Riemann Hypothesis is true if and only if the inequality $\sigma(n) < e^{\gamma } \times n \times \log \log n$ holds for all $n > 5040$, where $\sigma(n)$ is the sum-of-divisors function and $\gamma \approx 0.57721$ is the Euler-Mascheroni constant. This is known as the Robin inequality.
openaire +17 more sources
Finite transducers for divisibility monoids [PDF]
, 2006 Divisibility monoids are a natural lattice-theoretical generalization of Mazurkiewicz trace monoids, namely monoids in which the distributivity of the involved divisibility lattices is kept as an hypothesis, but the relations between the generators are ...
Picantin, Matthieu
core +3 more sources
DIVISIBILITY TESTS FOR SMARANDACHE SEMIGROUPS [PDF]
, 2002 Two Divisibility Tests for Smarandache semigroups are given. Further, the notion of divisibility of elements in a semigroup is applied to characterize the Smarandache semigroups.
Rao, Chandra Sekhar
core +1 more source
Perfect divisibility and 2‐divisibility
Journal of Graph Theory, 2018 AbstractA graph G is said to be 2‐divisible if for all (nonempty) induced subgraphs H of G, can be partitioned into two sets such that and . (Here denotes the clique number of G, the number of vertices in a largest clique of G). A graph G is said to be perfectly divisible if for all induced subgraphs H of G, can be partitioned into two sets such ...
Maria Chudnovsky, Vaidy Sivaraman
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Psychiatric Bulletin, 1980 The Summer Quarterly Meeting of the Irish Division took place in St Brendan's Hospital, Dublin, on 2 July 1982.
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Risk justice: Boosting the contribution of risk management to sustainable development
Risk Analysis, EarlyView., 2023 Abstract Comprehensively addressing different aspects of justice is essential to enable risk management to contribute to sustainable development. This article offers a new conceptual framework called risk justice that comprises procedural, distributive, and corrective justice in four dimensions related to sustainable development: social, ecological ...
Mathilde de Goër de Herve +2 more
wiley +1 more source
On Exact Division and Divisibility Testing for Sparse Polynomials [PDF]
Proceedings of the 2021 International Symposium on Symbolic and Algebraic Computation, 2021 No polynomial-time algorithm is known to test whether a sparse polynomial G divides another sparse polynomial $F$. While computing the quotient Q=F quo G can be done in polynomial time with respect to the sparsities of F, G and Q, this is not yet sufficient to get a polynomial-time divisibility test in general.
Giorgi, Pascal +2 more
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