Search results for "proofs"
showing 8 items of 8 documents
On an Inequality for Trigonometric Polynomials In Several Variables
1990
Publisher Summary This chapter presents trigonometric polynomials in n variables. Using the methods of approximation theory, an inequality can be extended to almost periodic functions and to still more general classes of functions as in the case for Bohr's inequality. However, no analogous result exists in the case of two variables. For the solution of problems containing small divisors, the estimate has to be completed by theorems concerning the best approximation of holomorphic functions by trigonometric polynomials in polystrips. The chapter also presents equations to provide an estimate for a differential operator.
Heyting-valued interpretations for Constructive Set Theory
2006
AbstractWe define and investigate Heyting-valued interpretations for Constructive Zermelo–Frankel set theory (CZF). These interpretations provide models for CZF that are analogous to Boolean-valued models for ZF and to Heyting-valued models for IZF. Heyting-valued interpretations are defined here using set-generated frames and formal topologies. As applications of Heyting-valued interpretations, we present a relative consistency result and an independence proof.
Mahonian STAT on words
2016
In 2000, Babson and Steingrimsson introduced the notion of what is now known as a permutation vincular pattern, and based on it they re-defined known Mahonian statistics and introduced new ones, proving or conjecturing their Mahonity. These conjectures were proved by Foata and Zeilberger in 2001, and by Foata and Randrianarivony in 2006.In 2010, Burstein refined some of these results by giving a bijection between permutations with a fixed value for the major index and those with the same value for STAT , where STAT is one of the statistics defined and proved to be Mahonian in the 2000 Babson and Steingrimsson's paper. Several other statistics are preserved as well by Burstein's bijection.At…
A Detailed Account of The Inconsistent Labelling Problem of Stutter-Preserving Partial-Order Reduction
2021
One of the most popular state-space reduction techniques for model checking is partial-order reduction (POR). Of the many different POR implementations, stubborn sets are a very versatile variant and have thus seen many different applications over the past 32 years. One of the early stubborn sets works shows how the basic conditions for reduction can be augmented to preserve stutter-trace equivalence, making stubborn sets suitable for model checking of linear-time properties. In this paper, we identify a flaw in the reasoning and show with a counter-example that stutter-trace equivalence is not necessarily preserved. We propose a stronger reduction condition and provide extensive new correc…
Thermal deformations of inhomogeneous elastic plates
1995
We consider thermal deformations of transversally inhomogenous elastic plates. Thin plate equations are derived as limits of full three-dimensional models both in the linear was well as in the non-linear case with appropriate convergence proofs. In the non-linear case also the corresponding von Karman equations are formulated. Its is obtained that the inhomogeneity leads to the loss of some symmetry properties at the von Karman equations
Energy-Efficiency and Coverage Quality Management for Reliable Diagnostics in Wireless Sensor Networks
2020
International audience; The processing of data and signals provided by sensors aims at extracting rnrelevant features which can be used to assess and diagnose the health state rnof the monitored targets. Nevertheless, Wireless Sensor Networks (WSNs) present rna number of shortcomings that have an impact on the quality of the gathered rndata at the sink level, leading to imprecise diagnostics rnof the observed targets. To improve data accuracy, two main critical and related issues, namely the energy consumption and coverage quality, need to be considered. The goal is to maximize the network lifetime while guaranteeing the complete coverage of all the targets. Unfortunately, these performance…
How much geometry it takes to reconstruct a 2-manifold in R 3
2009
Known algorithms for reconstructing a 2-manifold from a point sample in R 3 are naturally based on decisions/predicates that take the geometry of the point sample into account. Facing the always present problem of round-off errors that easily compromise the exactness of those predicate decisions, an exact and robust implementation of these algorithms is far from being trivial and typically requires employment of advanced datatypes for exact arithmetic, as provided by libraries like CORE, LEDA, or GMP. In this article, we present a new reconstruction algorithm, one whose main novelties is to throw away geometry information early on in the reconstruction process and to mainly operate combina…
Scientific writing for impact factor journals
2013
EASARCICAPLivre dispo. dans :hal-00832739, version 1; Publish or Perish. This old adage illustrates the importance of scientific communication; essential to research, it also represents a strategic sector for each country’s competitiveness. An often-neglected topic, scientific communication is of vital importance, with new information technologies accelerating and profoundly changing how knowledge is disseminated. The necessity of optimally disseminating experts’ findings has also become crucial to researchers, institutes and universities alike, which has prompted the recent advent of Impact Factors for the evaluation and financing of research, the goal being for scientific knowledge to be …