Search results for " Mathematics"

Trial Methods for Nonlinear Bernoulli Problem

1997

In this article we consider a free boundary problem which is related to formation of waves on a fluid surface (for example the ship waves). We study the possibility to construct ‘trial’ methods where one solves a sequence of standard flow problems formulated in different geometries that converge to the final free boundary. Furthermore, we use the shape optimization techniques to analyse the convergence of the fixed point iteration near a fixed point. For stream function case we conclude that the fast convergence can be obtained by using non-standard boundary conditions and we present numerical results to confirm the analysis.

Turán type inequalities for generalized inverse trigonometric functions

2013

In this paper we study the inverse of the eigenfunction $\sin_p$ of the one-dimensional $p$-Laplace operator and its dependence on the parameter $p$, and we present a Tur\'an type inequality for this function. Similar inequalities are given also for other generalized inverse trigonometric and hyperbolic functions. In particular, we deduce a Tur\'an type inequality for a series considered by Ramanujan, involving the digamma function.

Eight-membered Rings with Two Heteroatoms 1,3

2008

This chapter deals with heterocine rings with two heteroatoms in a 1,3-relationship, namely 1,3-diazocine, 2H-1,3-oxazocine, 2H-1,3-thiazocine, 4H-1,3-dioxocin, and 4H-1,3-dithiocin. On the 4H-1,3-oxathiocin ring system, belonging to the diheterocine family, in the past decade, no chemistry was reported. This chapter covers the literature from 1996 to 2006 and also reports those articles published in 1995 which were not reported in CHEC-II(1996). In this edition, in addition to the uncondensed derivatives, eight-membered 1,2-heterocycles fused to five-, six-, and seven-membered carbocycles or heterocycles are covered. Bridged heterocines, which actually constitute the majority of the compou…

IWCFTA2012 Keynote Speech I - Hidden attractors in dynamical systems: From hidden oscillation in Hilbert-Kolmogorov, Aizerman and Kalman problems to …

2012

Summary form only given. In this survey an attempt is made to reflect the current trends in the synthesis of analytical and numerical methods to develop efficient analytical-numerical methods, based on harmonic linearization, applied bifurcation theory and numerical methods, for searching hidden oscillations.

Attracteurs et bifurcations en dynamique holomorphe

2019

Big Data in metagenomics: Apache Spark vs MPI.

2020

The progress of next-generation sequencing has lead to the availability of massive data sets used by a wide range of applications in biology and medicine. This has sparked significant interest in using modern Big Data technologies to process this large amount of information in distributed memory clusters of commodity hardware. Several approaches based on solutions such as Apache Hadoop or Apache Spark, have been proposed. These solutions allow developers to focus on the problem while the need to deal with low level details, such as data distribution schemes or communication patterns among processing nodes, can be ignored. However, performance and scalability are also of high importance when…

FASTA/Q data compressors for MapReduce-Hadoop genomics: space and time savings made easy

2021

Abstract Background Storage of genomic data is a major cost for the Life Sciences, effectively addressed via specialized data compression methods. For the same reasons of abundance in data production, the use of Big Data technologies is seen as the future for genomic data storage and processing, with MapReduce-Hadoop as leaders. Somewhat surprisingly, none of the specialized FASTA/Q compressors is available within Hadoop. Indeed, their deployment there is not exactly immediate. Such a State of the Art is problematic. Results We provide major advances in two different directions. Methodologically, we propose two general methods, with the corresponding software, that make very easy to deploy …

Choosing Optimal Seed Nodes in Competitive Contagion.

2019

International audience; In recent years there has been a growing interest in simulating competitive markets to find out the efficient ways to advertise a product or spread an ideology. Along this line, we consider a binary competitive contagion process where two infections, A and B, interact with each other and diffuse simultaneously in a network. We investigate which is the best centrality measure to find out the seed nodes a company should adopt in the presence of rivals so that it can maximize its influence. These nodes can be used as the initial spreaders or advertisers by firms when two firms compete with each other. Each node is assigned a price tag to become an initial advertiser whi…

Estimation of total electricity consumption curves of small areas by sampling in a finite population

2016

International audience; Many studies carried out in the French electricity company EDF are based on the analysis of the total electricity consumption curves of groups of customers. These aggregated electricity consumption curves are estimated by using samples of thousands of curves measured at a small time step and collected according to a sampling design. Small area estimation is very usual in survey sampling. It is often addressed by using implicit or explicit domain models between the interest variable and the auxiliary variables. The goal here is to estimate totals of electricity consumption curves over domains or areas. Three approaches are compared: the rst one consists in modeling th…

Computation of the area in the discrete plane: Green’s theorem revisited

2017

International audience; The detection of the contour of a binary object is a common problem; however, the area of a region, and its moments, can be a significant parameter. In several metrology applications, the area of planar objects must be measured. The area is obtained by counting the pixels inside the contour or using a discrete version of Green's formula. Unfortunately, we obtain the area enclosed by the polygonal line passing through the centers of the pixels along the contour. We present a modified version of Green's theorem in the discrete plane, which allows for the computation of the exact area of a two-dimensional region in the class of polyominoes. Penalties are introduced and …