Related papers: Recent advances in rigorous computation of Poincar…
In this paper we report some important results that help in analizing the border collision bifurcations that occur in n-dimensional discontinuous maps. For this purpose, we use the piecewise linear approximation in the neighborhood of the…
Some parts of stochastic analysis on curved spaces are revisted. A concise proof of the quasi-invariance of the Wiener measure on the path spaces over a Riemannian manifold is presented. The shifts are allowed to be in the Cameron-Martin…
We study the theoretical and practical aspects of computing braids described by approximate descriptions of paths in the plane. Exact algorithms rely on the lexicographic ordering of the points in the plane, which is unstable under…
The aim of this note is to show that Poincar\'e inequalities imply corresponding weighted versions in a quite general setting. Fractional Poincar\'e inequalities are considered, too. The proof is short and does not involve covering…
We study the Poincare-Bendixson theorem for two-dimensional continuous dynamical systems in compact domains from the point of view of computation, seeking algorithms for finding the limit cycle promised by this classical result. We start by…
This paper presents a computationally feasible method to compute rigorous bounds on the interval-generalisation of regression analysis to account for epistemic uncertainty in the output variables. The new iterative method uses machine…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Maps have always been an essential component of autonomous driving. With the advancement of autonomous driving technology, both the representation and production process of maps have evolved substantially. The article categorizes the…
A conformal description of Poincare-Einstein manifolds is developed: these structures are seen to be a special case of a natural weakening of the Einstein condition termed an almost Einstein structure. This is used for two purposes: to shed…
Interval arithmetic is a simple way to compute a mathematical expression to an arbitrary accuracy, widely used for verifying floating-point computations. Yet this simplicity belies challenges. Some inputs violate preconditions or cause…
Immersed boundary methods have attracted substantial interest in the last decades due to their potential for computations involving complex geometries. Often these cannot be efficiently discretized using boundary-fitted finite elements.…
In this paper, we propose a new and simple approach to the approximation algorithms that are modified and improved from our published results. The computational and graphical examples are presented with the aid of Maple procedures.
We investigate the character of the linear constraints which are needed for Poincar\'e and Korn type inequalities to hold. We especially analyze constraints which depend on restriction on subsets of positive measure and on the trace on a…
We present some classical and weighted Poincar\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric…
Gradual numbers have been introduced recently as a means of extending standard interval computation methods to fuzzy intervals. The literature treats monotonic functions of fuzzy intervals. In this paper, we combine the concepts of gradual…
Contour maps are widely used to display estimates of spatial fields. Instead of showing the estimated field, a contour map only shows a fixed number of contour lines for different levels. However, despite the ubiquitous use of these maps,…
A brief summary of recent developments in mathematical diffraction theory is given. Particular emphasis is placed on systems with aperiodic order and continuous spectral components. We restrict ourselves to some key results and refer to the…
We prove a new general Poincar\'e-type inequality for differential forms on compact Riemannian manifolds with nonempty boundary. When the boundary is isometrically immersed in Euclidean space, we derive a new inequality involving mean and…
In Pires {\it et al.} [Phys. Rev. E 84, 066210 (2011)] intermittent maps are considered, and the tight relationship between correlation decay of smooth observables and large deviations estimates, as for instance employed in Artuso and…
The space mapping technique is used to efficiently solve complex optimization problems. It combines the accuracy of fine model simulations with the speed of coarse model optimizations to approximate the solution of the fine model…