This paper is part of the general project of proof mining, developed by Kohlenbach. By ”proof mining” we mean the logical analysis of mathematical proofs with the aim of extracting new numerically relevant information hidden in the proofs. We present logical metatheorems for classes of spaces from functional analysis and hyperbolic geometry, like Gromov hyperbolic spaces, R-trees and uniformly ...

We establish the multifractal analysis of hyperbolic flows and of suspension flows over subshifts of finite type. A non-trivial consequence of our results is that for every Hölder continuous function noncohomologous to a constant, the set of points without Birkhoff average has full topological entropy.

A homogeneous real polynomial p is hyperbolic with respect to a given vector d if the univariate polynomial t → p(x − td) has all real roots for all vectors x. Motivated by partial differential equations, Gårding proved in 1951 that the largest such root is a convex function of x, and showed various ways of constructing new hyperbolic polynomials. We present a powerful new such construction, an...

Time discounting is the phenomenon that a desired result in the future is perceived as less valuable than the same result now. Economic theories can take this psychological fact into account in several ways. In the economic literature the most widely used type of additive time discounting is exponential discounting. In exponential discounting, the fall of valuation depends by a constant factor ...

A new discretization method for hyperbolic systems with stiff relaxation source terms (hyperbolic-relaxation equations) is introduced. The method is based on Huynh’s “upwind moment scheme” for hyperbolic conservation laws with implicit treatment of the source term. A Von Neumann analysis shows superiority in both stability and accuracy of the resulting fully discrete scheme over the method-of-l...

The application of hyperbolic Givens and Householder transformation ma-trices (see [1]) to different matrix factorizations namely, the hyperbolic QRalgorithm and the algorithm for hyperbolic singular value decomposition willbe described. An error analysis will be provided and the connection betweenthe condition number of the matrix and the rounding errors will be discussed.<...