Search results for "Numbers"
showing 10 items of 128 documents
Restricted 123-avoiding Baxter permutations and the Padovan numbers
2007
AbstractBaxter studied a particular class of permutations by considering fixed points of the composite of commuting functions. This class is called Baxter permutations. In this paper we investigate the number of 123-avoiding Baxter permutations of length n that also avoid (or contain a prescribed number of occurrences of) another certain pattern of length k. In several interesting cases the generating function depends only on k and is expressed via the generating function for the Padovan numbers.
Scaling properties of topologically random channel networks
1996
Abstract The analysis deals with the scaling properties of infinite topologically random channel networks (ITRNs) fast introduced by Shreve (1967, J. Geol. , 75: 179–186) to model the branching structure of rivers as a random process. The expected configuration of ITRNs displays scaling behaviour only asymptotically, when the ruler (or ‘yardstick’) length is reduced to a very small extent. The random model can also reproduce scaling behaviour at larger ruler lengths if network magnitude and diameter are functionally related according to a reported deterministic rule. This indicates that subsets of rrRNs can be scaling and, although rrRNs are asymptotically plane-filling due to the law of la…
Generating restricted classes of involutions, Bell and Stirling permutations
2010
AbstractWe present a recursive generating algorithm for unrestricted permutations which is based on both the decomposition of a permutation as a product of transpositions and that as a union of disjoint cycles. It generates permutations at each recursive step and slight modifications of it produce generating algorithms for Bell permutations and involutions. Further refinements yield algorithms for these classes of permutations subject to additional restrictions: a given number of cycles or/and fixed points. We obtain, as particular cases, generating algorithms for permutations counted by the Stirling numbers of the first and second kind, even permutations, fixed-point-free involutions and d…
Law of the Iterated Logarithm
2020
For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.
Risk Assessment of a compound feed process based on HAZOP analysis and linguistic terms
2016
[EN] The size and complexity of industrial plants, along with the characteristics of the products used, require a study, analysis and control of the existing risks in every industrial process. In this paper, a methodology for risk assessment in industrial plants, based on the combination of risks identification through the Hazard and Operability (HAZOP) analysis and the risks evaluation through linguistic variables and fuzzy numbers is applied to a case study consisting on a compound feed plant located in the town of Silla (Valencia, Spain). The results from this study show that the main risk in the compound feed production process is the formation of explosive atmospheres (ATEX). Therefore…
On the Talmud Division: Equity and Robustness
2008
The Talmud Division is a very old method of sharin g developed by the rabbis in the Talmud and brought to the fore in the modern area s ome authors, among them are Aumann and Maschler. One compares the Talmud Division to other methods, mainly here the most popular, Aristotle's Proportional Division, but also to the equal division. The Talmud Division is more egalitarian than the Proportional Division for smal l levels of estate and conversely and it protects the weakest -those who cannot place a non-zero clai m-. This suggests that claimants may choose among the claiming methods depending on their interest, what implies a metagame. Unlike other methods as the Proportional Division, the Talm…
Lenguaje vago: los números en la enseñanza de español como lengua extranjera
2018
The vague language, in addition to the attenuation, is a pragmatic content that is not worked enough during the lessons of Spanish as a Foreign Language. In fact, the Common European Framework of Reference for Languages nor the Plan Curricular of the Instituto Cervantes give it the relevance it has, especially at levels B and C. In this paper, a theoretical approach to vague language is made, more specifically to the use of numbers. The research shows part of a database in which oral texts have been compiled from Val.Es.Co. (Valencia Español Coloquial), from CREA (Corpus of Reference of t he Present Spanish) and from the research project Es.Var.Atenuación (Spanish Variation and Attenuation)…
Random Walk in a N-cube Without Hamiltonian Cycle to Chaotic Pseudorandom Number Generation: Theoretical and Practical Considerations
2017
Designing a pseudorandom number generator (PRNG) is a difficult and complex task. Many recent works have considered chaotic functions as the basis of built PRNGs: the quality of the output would indeed be an obvious consequence of some chaos properties. However, there is no direct reasoning that goes from chaotic functions to uniform distribution of the output. Moreover, embedding such kind of functions into a PRNG does not necessarily allow to get a chaotic output, which could be required for simulating some chaotic behaviors. In a previous work, some of the authors have proposed the idea of walking into a $\mathsf{N}$-cube where a balanced Hamiltonian cycle has been removed as the basis o…
Property prices index numbers and derived indices
2014
Purpose – A useful instrument to understand and examine the inner workings of the property trade is devising index numbers of property prices based on historical sequences of market prices. The present work aims at the definition of index numbers of property prices, proposing an innovative methodology compared with what usually recurs in literature. The purpose of this paper is to discuss these issues. Design/methodology/approach – The analysis proposed, based on the mechanisms of formation of stock indices, investigates the analogies between stock and property information, according to the peculiarities of the property trade, leading to a methodology approach, derived from Simple Price In…
The pruning-grafting lattice of binary trees
2008
AbstractWe introduce a new lattice structure Bn on binary trees of size n. We exhibit efficient algorithms for computing meet and join of two binary trees and give several properties of this lattice. More precisely, we prove that the length of a longest (resp. shortest) path between 0 and 1 in Bn equals to the Eulerian numbers 2n−(n+1) (resp. (n−1)2) and that the number of coverings is (2nn−1). Finally, we exhibit a matching in a constructive way. Then we propose some open problems about this new structure.