Search results for "convergence"
showing 10 items of 655 documents
A linearization technique and error estimates for distributed parameter identification in quasilinear problems
1996
The identification problem of a nonlinear functional coefficient in elliptic and parabolic quasilinear equations is considered. A distributed observation of the solution of the corresponding equation is assumed to be known a priori. An identification method is introduced, which needs only a linear equation to be solved in each iteration step of the optimization. Estimates of the rate of convergence for the proposed approach are proved, when the equation is discretized with the finite element method with respect to space variables. Some numerical results are given.
Convergence of Markovian Stochastic Approximation with discontinuous dynamics
2016
This paper is devoted to the convergence analysis of stochastic approximation algorithms of the form $\theta_{n+1} = \theta_n + \gamma_{n+1} H_{\theta_n}({X_{n+1}})$, where ${\left\{ {\theta}_n, n \in {\mathbb{N}} \right\}}$ is an ${\mathbb{R}}^d$-valued sequence, ${\left\{ {\gamma}_n, n \in {\mathbb{N}} \right\}}$ is a deterministic stepsize sequence, and ${\left\{ {X}_n, n \in {\mathbb{N}} \right\}}$ is a controlled Markov chain. We study the convergence under weak assumptions on smoothness-in-$\theta$ of the function $\theta \mapsto H_{\theta}({x})$. It is usually assumed that this function is continuous for any $x$; in this work, we relax this condition. Our results are illustrated by c…
2017
Abstract. We present a sensitivity study on transatlantic dust transport, a process which has many implications for the atmosphere, the ocean and the climate. We investigate the impact of key processes that control the dust outflow, i.e., the emission flux, convection schemes and the chemical aging of mineral dust, by using the EMAC model following Abdelkader et al. (2015). To characterize the dust outflow over the Atlantic Ocean, we distinguish two geographic zones: (i) dust interactions within the Intertropical Convergence Zone (ITCZ), or the dust–ITCZ interaction zone (DIZ), and (ii) the adjacent dust transport over the Atlantic Ocean (DTA) zone. In the latter zone, the dust loading show…
Introduction: Time, Space and Economics in the History of Latin America
2020
This book represents a contribution in, at least, three dimensions: quantitative, historical and conceptual. From a quantitative point of view, the volume presents an extensive data set corresponding to 9 countries, 182 regions (states, provinces, departments) and around 14 benchmark years from the end of the nineteenth century to the beginning of the twenty-first century. This constitutes a substantial contribution to quantitatively analyse the economic development of Latin America, identifying the evolution of regional inequality and studying economic convergence and the formation of convergence clubs (clusters of poor and rich regions). Second, the volume combines a regional and supranat…
When a convergence of filters is measure-theoretic
2022
Abstract Convergence almost everywhere cannot be induced by a topology, and if measure is finite, it coincides with almost uniform convergence and is finer than convergence in measure, which is induced by a metrizable topology. Measures are assumed to be finite. It is proved that convergence in measure is the Urysohn modification of convergence almost everywhere, which is pseudotopological. Extensions of these convergences from sequences to arbitrary filters are discussed, and a concept of measure-theoretic convergence is introduced. A natural extension of convergence almost everywhere is neither measure-theoretic, nor finer than a natural extension of convergence in measure. A straightforw…
Convergence for varying measures
2023
Some limit theorems of the type $\int_{\Omega}f_n dm_n -- --> \int_{\Omega}f dm$ are presented for scalar, (vector), (multi)-valued sequences of m_n-integrable functions f_n. The convergences obtained, in the vector and multivalued settings, are in the weak or in the strong sense.
Convergence Theorems for Varying Measures Under Convexity Conditions and Applications
2022
AbstractIn this paper, convergence theorems involving convex inequalities of Copson’s type (less restrictive than monotonicity assumptions) are given for varying measures, when imposing convexity conditions on the integrable functions or on the measures. Consequently, a continuous dependence result for a wide class of differential equations with many interesting applications, namely measure differential equations (including Stieltjes differential equations, generalized differential problems, impulsive differential equations with finitely or countably many impulses and also dynamic equations on time scales) is provided.
A regular non-weakly discretely generated $$P$$-space
2022
We construct a consistent example of a topological space Y= X∪ { ∞} such that: (1) Y is regular. (2) Every Gδ subset of Y is open. (3) The point ∞ is not isolated, but it is not in the closure of any discrete subset of X.
Free-surface flows solved by means of SPH schemes with numerical diffusive terms
2010
A novel system of equations has been defined which contains diffusive terms in both the continuity and energy equations and, at the leading order, coincides with a standard weakly-compressible SPH scheme with artificial viscosity. A proper state equation is used to associate the internal energy variation to the pressure field and to increase the speed of sound when strong deformations/compressions of the fluid occur. The increase of the sound speed is associated to the shortening of the time integration step and, therefore, allows a larger accuracy during both breaking and impact events. Moreover, the diffusive terms allows reducing the high frequency numerical acoustic noise and smoothing …
Testing for convergence from the micro-level
2011
Empirical convergence analysis is typically envisaged from a macro aggregate perspective. However, researchers have recently highlighted how investigating convergence at the disaggregate level may yield interesting insights into the convergence debate. In this paper, we suggest an approach that allows exploiting large micro panels to test for convergence. Compared to the traditional convergence analysis, this approach allows obtaining beta- and sigma-like convergence parameters for both the micro and the macro level of interest. We provide a practical example that analyses productivity convergence across firms and provinces using a large sample of Italian firms.