Search results for "predicate"
showing 10 items of 216 documents
An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications
2020
Author's accepted manuscript. This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bergelson, V., Knutson, I. J. H. & Son, Y. (2020). An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications. International Mathematics Research Notices, 2021(19), 14965-15018 is available online at: https://academic.oup.com/imrn/article/2021/19/14965/5775499 and https://doi.org/10.1093/imrn/rnaa035. Generalized polynomials are mappings obtained from the conventional polynomials by the use of the operations of addition and multiplication and taking th…
Binary Patterns in Infinite Binary Words
2002
In this paper we study the set P(w) of binary patterns that can occur in one infinite binary word w, comparing it with the set F(w) of factors of the word. Since the set P(w) can be considered as an extension of the set F(w), we first investigate how large is such extension, by introducing the parameter ?(w) that corresponds to the cardinality of the difference set P(w) \ F(w). Some non trivial results about such parameter are obtained in the case of the Thue-Morse and the Fibonacci words. Since, in most cases, the parameter ?(w) is infinite, we introduce the pattern complexity of w, which corresponds to the complexity of the language P(w). As a main result, we prove that there exist infini…
Attracting sets in a deterministic discrete traffic model
2001
The fundamental diagram of the Nagel-Schreckenberg traffic model is derived analytically for the deterministic case using methods and concepts from nonlinear dynamics. It is shown that the possible states of the long-term behaviour form a globally attractive subset which can be well characterized. This attractive set of states is composed of coexisting attractors. The attractor concept is applied to a slow-to-start extension of the model. For this example it is shown that the attractive set consists of coexisting attractors with different macroscopic properties, that can be determined analytically.
A High Level Language for Pyramidal Architectures
1986
In the paper are described the syntax and some implementation features of a high level language for pyramidal architectures called Pyramid B Language (PCL). The language is an extension of the B and include data type, set of instructions and builtin functions oriented to the pyramidal architectures. Some notes on the implementation for the PAPIA machine are also given.
Progressive and predicative constructions with gerund in Romance. A contrastive analysis
2018
Progressive and predicative constructions formed with gerund are present in numerous Romance languages. In the literature, these two types of construction have often been considered as syntactically analogous. Through the application of syntactic tests, this study will show that, despite a number of similarities, progressive and predicative constructs with gerund are characterized by a different structure.
Quasi conjunction and p-entailment in nonmonotonic reasoning
2010
We study, in the setting of coherence, the extension of a probability assessment defined on n conditional events to their quasi conjunction. We consider, in particular, two special cases of logical dependencies; moreover, we examine the relationship between the notion of p-entailment of Adams and the inclusion relation of Goodman and Nguyen. We also study the probabilistic semantics of the QAND rule of Dubois and Prade; then, we give a theoretical result on p-entailment.
Testing a model for the monitoring of worked-out algebra-problem examples: from behaviours to outcomes on a math task
2021
This study aimed at testing an extension of a theoretical model for the metacognitive monitoring mechanism implied in the detection of inconsistencies when the information provided includes abstract symbols in addition to plain text. Ninety-four postgraduates of STEM specialities were asked to read a worked-out algebra-problem example and to report any incoherence, inconsistency, or error detected in the statement or in the solving procedure. A set of model inspired indexes was defined to describe participants¿ behaviour along the task. The Read & Answer software was used to record online individual processing data and participants¿ reports. Results supported model predictions. Indexes corr…
Towards Axiomatic Basis of Inductive Inference
2001
The language for the formulation of the interesting statements is, of course, most important. We use first order predicate logic. Our main achievement in this paper is an axiom system which we believe to be more powerful than any other natural general purpose discovery axiom system. We prove soundness of this axiom system in this paper. Additionally we prove that if we remove some of the requirements used in our axiom system, the system becomes not sound. We characterize the complexity of the quantifier prefix which guaranties provability of a true formula via our system. We prove also that if a true formula contains only monadic predicates, our axiom system is capable to prove this formula…
Design of the CGAL Spherical Kernel and application to arrangements of circles on a sphere
2009
International audience; This paper presents a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs. The paper makes three contributions. First, the mathematics underlying two non trivial predicates are presented. Second, the design of the kernel concept is developed, and the connexion between the mathematics and this design is established. In particular, we show how two different frameworks can be combined: one for the general setting, and one dedicated to the case where all the objects handled lie on a reference sphere. Finally, an assessment about the efficacy of the \sk\ is made through the calculation of the exact arrangement of circles on a sphere. On average …
Sign test of independence between two random vectors
2003
A new affine invariant extension of the quadrant test statistic Blomqvist (Ann. Math. Statist. 21 (1950) 593) based on spatial signs is proposed for testing the hypothesis of independence. In the elliptic case, the new test statistic is asymptotically equivalent to the interdirection test by Gieser and Randles (J. Amer. Statist. Assoc. 92 (1997) 561) but is easier to compute in practice. Limiting Pitman efficiencies and simulations are used to compare the test to the classical Wilks’ test. peerReviewed