Search results for "convergence"

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.

Some approximation properties of a Durrmeyer variant ofq-Bernstein-Schurer operators

2016

On the Coefficients of Multiple Series with Respect to Vilenkin System

2017

Abstract We give a sufficient condition for coefficients of double series Σ Σ n,m an,m χ n,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.

Description of intermodulation generation of nonlinear responses beyond the validity of the power series expansion

2021

Weakly nonlinear responses are commonly described by a power series expansion. However, intermodulation distortion products that cannot be described by a power series have been observed in a variety of physical systems. As the power series description is only applicable within its radius of convergence, we choose an alternative approach based on Fourier coefficients to describe intermodulation levels beyond the convergence of the power series. The description over a wide power range allows us to make a decision about models and to determine previously inaccessible model parameters. We apply the approach to data obtained from the characterization of the nonlinear dielectric susceptibility of…

Adaptive Finite Temperature String Method in Collective Variables.

2017

Here we present a modified version of the on-the-fly string method for the localization of the minimum free energy path in a space of arbitrary collective variables. In the proposed approach the shape of the biasing potential is controlled by only two force constants, defining the width of the potential along the string and orthogonal to it. The force constants and the distribution of the string nodes are optimized during the simulation, improving the convergence. The optimized parameters can be used for umbrella sampling with a path CV along the converged string as the reaction coordinate. We test the new method with three fundamentally different processes: chloride attack to chloromethane…

On numerical broadening of particle size spectra: a condensational growth study using PyMPDATA 1.0

2021

Abstract. The work discusses the diffusional growth in particulate systems such as atmospheric clouds. It focuses on the Eulerian modeling approach in which the evolution of the probability density function describing the particle size spectrum is carried out using a fixed-bin discretization. The numerical diffusion problem inherent to the employment of the fixed-bin discretization is scrutinized. The work focuses on the applications of MPDATA family of numerical schemes. Several MPDATA variants are explored including: infinite-gauge, non-oscillatory, third-order-terms and recursive antidiffusive correction (double pass donor cell, DPDC) options. Methodology for handling coordinate transfor…

Late Quaternary Variations in the South American Monsoon System as Inferred by Speleothems—New Perspectives using the SISAL Database

2019

Here we present an overview of speleothem δ18O records from South America, most of which are available in the Speleothem Isotopes Synthesis and Analysis (SISAL_v1) database. South American tropical and subtropical speleothem δ18O time series are primarily interpreted to reflect changes in precipitation amount, the amount effect, and consequently history of convection intensity variability of convergence zones such as the Intertropical Convergence Zone (ITCZ) and the South America Monsoon System (SAMS). We investigate past hydroclimate scenarios in South America related to the South American Monsoon System in three different time periods: Late Pleistocene, Holocene, and the last tw…

How much is enough? : The convergence of finite sample scattering properties to those of infinite media

2021

We study the scattering properties of a cloud of particles. The particles are spherical, close to the incident wavelength in size, have a high albedo, and are randomly packed to 20% volume density. We show, using both numerically exact methods for solving the Maxwell equations and radiative-transfer-approximation methods, that the scattering properties of the cloud converge after about ten million particles in the system. After that, the backward-scattered properties of the system should estimate the properties of a macroscopic, practically infinite system. (C) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.o…

A little walk between Early Jurassic sponges and corals: a confusing morphological convergence.

2019

24 pages; International audience; Hispaniastraea Turnšek et Geyer, 1975 is a unique coral genus from the Early Jurassic Epoch (Liassic). Corals of this genus are characterised by a highly dominant major septum and a set of eleven minor septa that are very short or even abortive. Initially discovered in Spain, new samples of this genus were depicted from Morocco by Beauvais in 1980; however, this genus was interpreted as a synonym of Pseudoseptifer Fischer, 1970, a chaetetid sponge (i.e., a sponge with siliceous spicules embedded in a calcareous skeleton). The skeleton of Pseudoseptifer is composed of adjacent tubules that increase by fissiparity by means of a pseudoseptum. Based on the stud…

The analysis of convergence in ecological indicators: An application to the Mediterranean fisheries

2017

9 pages, 4 figures, 3 tables