Search results for "Convergence"

A case of possible vocal convergence between frogs and a bird in Himalayan torrents

1984

Several species of frogs of the subgenusRana (Paa) and one species of bird of the genusPhylloscopus, which are calling in or near torrents in the Himalayas, show striking similarities in their vocal signals: 1) The calls are composed of short sequences of notes separated by periods of silence; 2) the notes are pure, short, and have a narrow frequency band; 3) within each sequence, the notes are rhythmically emitted. We suggest that these characteristics may be adaptive, the convergence being caused by the selective pressure of the acoustic constraints of the biotope.

Convergence in discrete Cauchy problems and applications to circle patterns

2005

A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.

Regularity of solutions of cauchy problems with smooth cauchy data

1988

Opinion dynamics in coalitional games with transferable utilities

2014

This paper studies opinion dynamics in a large number of homogeneous coalitional games with transferable utilities (TU), where the characteristic function is a continuous-time stochastic process. For each game, which we can see as a “small world”, the players share opinions on how to allocate revenues based on the mean-field interactions with the other small worlds. As a result of such mean-field interactions among small worlds, in each game, a central planner allocates revenues based on the extra reward that a coalition has received up to the current time and the extra reward that the same coalition has received in the other games. The paper also studies the convergence and stability of op…

Improving the QM/MM Description of Chemical Processes:  A Dual Level Strategy To Explore the Potential Energy Surface in Very Large Systems.

2005

Potential energy surfaces are fundamental tools for the analysis of reaction mechanisms. The accuracy of these surfaces for reactions in very large systems is often limited by the size of the system even if hybrid quantum mechanics/molecular mechanics (QM/MM) strategies are employed. The large number of degrees of freedom of the system requires hundreds or even thousands of optimization steps to reach convergence. Reactions in condensed media (such as enzymes or solutions) are thus usually restricted to be analyzed using low level quantum mechanical methods, thus introducing a source of error in the description of the QM region. In this paper, an alternative method is proposed, coupled to t…

Analytic calculation of the diagonal Born-Oppenheimer correction within configuration-interaction and coupled-cluster theory

2006

Schemes for the analytic calculation of the diagonal Born-Oppenheimer correction (DBOC) are formulated and implemented for use with general single-reference configuration-interaction and coupled-cluster wave function models. Calculations are reported to demonstrate the convergence of the DBOC with respect to electron-correlation treatment and basis set as well as to investigate the size-consistency error in configuration-interaction calculations of the DBOC. The importance of electron-correlation contributions to the DBOC is illustrated in the computation of the corresponding corrections for the reaction energy and activation barrier of the F + H2 --FH + H reaction as well as of the atomiza…

Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups

2020

We prove the local minimality of halfspaces in Carnot groups for a class of nonlocal functionals usually addressed as nonlocal perimeters. Moreover, in a class of Carnot groups in which the De Giorgi's rectifiability Theorem holds, we provide a lower bound for the $\Gamma$-liminf of the rescaled energy in terms of the horizontal perimeter.

Analytic high-order Douglas–Kroll–Hess electric field gradients

2007

In this work we present a comprehensive study of analytical electric field gradients in hydrogen halides calculated within the high-order Douglas-Kroll-Hess (DKH) scalar-relativistic approach taking picture-change effects analytically into account. We demonstrate the technical feasibility and reliability of a high-order DKH unitary transformation for the property integrals. The convergence behavior of the DKH property expansion is discussed close to the basis set limit and conditions ensuring picture-change-corrected results are determined. Numerical results are presented, which show that the DKH property expansion converges rapidly toward the reference values provided by four-component met…

The Cauchy problem for linear growth functionals

2003

In this paper we are interested in the Cauchy problem $$ \left\{ \begin{gathered} \frac{{\partial u}}{{\partial t}} = div a (x, Du) in Q = (0,\infty ) x {\mathbb{R}^{{N }}} \hfill \\ u (0,x) = {u_{0}}(x) in x \in {\mathbb{R}^{N}}, \hfill \\ \end{gathered} \right. $$ (1.1) where \( {u_{0}} \in L_{{loc}}^{1}({\mathbb{R}^{N}}) \) and \( a(x,\xi ) = {\nabla _{\xi }}f(x,\xi ),f:{\mathbb{R}^{N}}x {\mathbb{R}^{N}} \to \mathbb{R} \)being a function with linear growth as ‖ξ‖ satisfying some additional assumptions we shall precise below. An example of function f(x, ξ) covered by our results is the nonparametric area integrand \( f(x,\xi ) = \sqrt {{1 + {{\left\| \xi \right\|}^{2}}}} \); in this case …

LE AREE INTERNE PER LO SVILUPPO DEL TERRITORIO E LA COMPLEMENTARITÀ DI PROGRAMMI E STRUMENTI FRA LE POLITICHE EUROPEE DI SVILUPPO RURALE E DI COESIONE

Le Aree Interne rappresentano un tema particolarmente importante per la programmazione e la spesa dei fondi comunitari nel periodo 2014-2020 perché costituiscono il più grande esempio di complementarità fra le Politiche europee di sviluppo rurale e di coesione. Per lo sviluppo di queste Aree è stata creata una Strategia Nazionale per le Aree Interne (SNAI) che mira alla valorizzazione ed al recupero di tutti quei territori (rurali, montuosi, svantaggiati) dal carattere marginale rispetto alla disponibilità e all’offerta di servizi essenziali. La peculiarità di tale Strategia è quella di promuovere lo sviluppo di aree che sono uniformemente distribuite in tutto il comprensorio nazionale a di…