Search results for "Lagrange"

On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation

2009

Abstract The Deslauriers–Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers–Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l ∞ -stability bounds for the multiresolution transform. A variety of tests indicate that these l ∞ bounds are closer to numerical estimates than those obtained with other approaches.

A rank theorem for analytic maps between power series spaces

1994

Hypergestures in Complex Time: Creative Performance Between Symbolic and Physical Reality

2015

Musical performance and composition imply hypergestural transformation from symbolic to physical reality and vice versa. But most scores require movements at infinite physical speed that can only be performed approximately by trained musicians. To formally solve this divide between symbolic notation and physical realization, we introduce complex time (\(\mathbb {C}\)-time) in music. In this way, infinite physical speed is “absorbed” by a finite imaginary speed. Gestures thus comprise thought (in imaginary time) and physical realization (in real time) as a world-sheet motion in space-time, corresponding to ideas from physical string theory. Transformation from imaginary to real time gives us…

On the nonarchimedean quadratic Lagrange spectra

2018

We study Diophantine approximation in completions of functions fields over finite fields, and in particular in fields of formal Laurent series over finite fields. We introduce a Lagrange spectrum for the approximation by orbits of quadratic irrationals under the modular group. We give nonarchimedean analogs of various well known results in the real case: the closedness and boundedness of the Lagrange spectrum, the existence of a Hall ray, as well as computations of various Hurwitz constants. We use geometric methods of group actions on Bruhat-Tits trees. peerReviewed

Applications and numerical convergence of the partial inverse method

2006

In 1983, J.E. Spingarn introduced what he called the Partial Inverse Method in the framework of Mathematical Programming. Since his initial articles, numerous applications have been given in various fields including Lagrangian multipliers methods, location theory, convex feasibility problems, analysis of data, economic equilibrium problems. In a first part of this paper we give a survey of these applications. Then by means of optimization problems relevant to location theory such as single and multifacility minimisum or minimax location problems, we examine the main advantages of the algorithm and we point out its drawbacks mainly concerning the rate of convergence. We study how different p…

Exposition : René Lagrange

2021

A penalty-based interface technology

2009

Modern computers have enabled engineers to perform large scale analyses of complex structures like entire aircrafts, automobiles, and ships. One issue that arises often is the need to perform a unified analysis of a structural assembly using sub-structural models created independently. These sub-structural models are frequently designed by different engineers, thus they are likely to be incompatible at their interfaces. Finite element interface technology has been developed to facilitate the joining of independently modeled substructures. Here an effective and robust interface element is presented. This method has been developed using penalty constraints and allows computationally efficient…

MLML2R: an R package for maximum likelihood estimation of DNA methylation and hydroxymethylation proportions.

2019

Abstract Accurately measuring epigenetic marks such as 5-methylcytosine (5-mC) and 5-hydroxymethylcytosine (5-hmC) at the single-nucleotide level, requires combining data from DNA processing methods including traditional (BS), oxidative (oxBS) or Tet-Assisted (TAB) bisulfite conversion. We introduce the R package MLML2R, which provides maximum likelihood estimates (MLE) of 5-mC and 5-hmC proportions. While all other available R packages provide 5-mC and 5-hmC MLEs only for the oxBS+BS combination, MLML2R also provides MLE for TAB combinations. For combinations of any two of the methods, we derived the pool-adjacent-violators algorithm (PAVA) exact constrained MLE in analytical form. For the…

Thermalization of Random Motion in Weakly Confining Potentials

2010

We show that in weakly confining conservative force fields, a subclass of diffusion-type (Smoluchowski) processes, admits a family of "heavy-tailed" non-Gaussian equilibrium probability density functions (pdfs), with none or a finite number of moments. These pdfs, in the standard Gibbs-Boltzmann form, can be also inferred directly from an extremum principle, set for Shannon entropy under a constraint that the mean value of the force potential has been a priori prescribed. That enforces the corresponding Lagrange multiplier to play the role of inverse temperature. Weak confining properties of the potentials are manifested in a thermodynamical peculiarity that thermal equilibria can be approa…

Thermodynamic approach to vortex production and diffusion in inhomogeneous superfluid turbulence

2014

In this paper, we use a non-equilibrium thermodynamic framework to generalize a previous nonlocal model of counterflow superfluid turbulence to incorporate some new coupled terms which may be relevant in the evolution of inhomogeneous vortex tangles. The theory chooses as fundamental fields the energy density, the heat flux, and the averaged vortex line length per unit volume. The constitutive quantities are assumed to depend on the fundamental fields and on their first spatial derivatives, allowing us to describe thermal dissipation, vortex diffusion and a new contribution to vortex formation. The restrictions on the constitutive relations are deduced from the entropy principle, using the …