Search results for "Form."
showing 10 items of 43419 documents
Global Lp -integrability of the derivative of a quasiconformal mapping
1988
Let f be a quasiconformal mapping of an open bounded set U in Rn into Rn . Then f′ belongs to Lp(U) for some p > n provided that f satisfies (a) U is a uniform domain and fU is a John domain or (b) f is quasisymmetric and U satisfies a metric plumpness condition.
On Whitham and Related Equations
2017
The aim of this paper is to study, via theoretical analysis and numerical simulations, the dynamics of Whitham and related equations. In particular, we establish rigorous bounds between solutions of the Whitham and Korteweg–de Vries equations and provide some insights into the dynamics of the Whitham equation in different regimes, some of them being outside the range of validity of the Whitham equation as a water waves model.
The uniform convergence of a double sequence of functions at a point and Korovkin-type approximation theorems
2020
Abstract In this paper, we introduce an interesting kind of convergence for a double sequence called the uniform convergence at a point. We give an example and demonstrate a Korovkin-type approximation theorem for a double sequence of functions using the uniform convergence at a point. Then we show that our result is stronger than the Korovkin theorem given by Volkov and present several graphs. Finally, in the last section, we compute the rate of convergence.
Efficient generation of restricted growth words
2013
A length n restricted growth word is a word w=w"1w"2...w"n over the set of integers where w"1=0 and each w"i, i>1, lies between 0 and the value of a word statistics of the prefix w"1w"2...w"i"-"1 of w, plus one. Restricted growth words simultaneously generalize combinatorial objects as restricted growth functions, staircase words and ascent or binary sequences. Here we give a generic generating algorithm for restricted growth words. It produces a Gray code and runs in constant average time provided that the corresponding statistics has some local properties.
Removing the saturation assumption in Bank-Weiser error estimator analysis in dimension three
2020
International audience; We provide a new argument proving the reliability of the Bank-Weiser estimator for Lagrange piecewise linear finite elements in both dimension two and three. The extension to dimension three constitutes the main novelty of our study. In addition, we present a numerical comparison of the Bank-Weiser and residual estimators for a three-dimensional test case.
Análisis de la utilidad del algoritmo Gradient Boosting Machine (GBM) en la predicción del fracaso empresarial
2018
Este estudio, novedoso en cuanto a la utilizacion de la metodologia basada en la cultura de los algoritmos, prueba la capacidad de la tecnica ‘Gradient Boosting Machine’ (GBM) en la prediccion de l...
Adjacency matrices of random digraphs: singularity and anti-concentration
2017
Let ${\mathcal D}_{n,d}$ be the set of all $d$-regular directed graphs on $n$ vertices. Let $G$ be a graph chosen uniformly at random from ${\mathcal D}_{n,d}$ and $M$ be its adjacency matrix. We show that $M$ is invertible with probability at least $1-C\ln^{3} d/\sqrt{d}$ for $C\leq d\leq cn/\ln^2 n$, where $c, C$ are positive absolute constants. To this end, we establish a few properties of $d$-regular directed graphs. One of them, a Littlewood-Offord type anti-concentration property, is of independent interest. Let $J$ be a subset of vertices of $G$ with $|J|\approx n/d$. Let $\delta_i$ be the indicator of the event that the vertex $i$ is connected to $J$ and define $\delta = (\delta_1, …
Restricted compositions and permutations: from old to new Gray codes
2011
Any Gray code for a set of combinatorial objects defines a total order relation on this set: x is less than y if and only if y occurs after x in the Gray code list. Let @? denote the order relation induced by the classical Gray code for the product set (the natural extension of the Binary Reflected Gray Code to k-ary tuples). The restriction of @? to the set of compositions and bounded compositions gives known Gray codes for those sets. Here we show that @? restricted to the set of bounded compositions of an interval yields still a Gray code. An n-composition of an interval is an n-tuple of integers whose sum lies between two integers; and the set of bounded n-compositions of an interval si…
Statistics-preserving bijections between classical and cyclic permutations
2012
Recently, Elizalde (2011) [2] has presented a bijection between the set C"n"+"1 of cyclic permutations on {1,2,...,n+1} and the set of permutations on {1,2,...,n} that preserves the descent set of the first n entries and the set of weak excedances. In this paper, we construct a bijection from C"n"+"1 to S"n that preserves the weak excedance set and that transfers quasi-fixed points into fixed points and left-to-right maxima into themselves. This induces a bijection from the set D"n of derangements to the set C"n"+"1^q of cycles without quasi-fixed points that preserves the weak excedance set. Moreover, we exhibit a kind of discrete continuity between C"n"+"1 and S"n that preserves at each s…
Promotion et Développement d'un Master Erasmus Mundus - L'Exemple du VIBOT
2011
Cet article decrit l’offre de formation a l’internationale proposee au Centre Universitaire Condorcet du Creusot (Universite de Bourgogne) dans le domaine de la vision par ordinateur et de la robotique. Il presente l’organisation particuliere de ces formations et les actions de support mises en place pour en assurer la perennite.