The Riemann integral can be approximated using partitions and a rule for assigning weighted sums of the function at points determined by the partition. Approximation methods commonly used include endpoint rules, the midpoint rule, the trapezoid rule, Simpson’s rule, and other quadrature methods. The rate of approximation depends to a large degree on the rule being used and the smoothness of the...

We give an overview of results, presented in the form of a poster at CSL03/KGC, about a general study of the notions of rule derivability and admissibility in Hilbert-style proof systems. The basis of our investigation consists in the concept of “abstract Hilbert system”, a framework for Hilbert-style proof systems in which it is abstracted from the syntax of formulas and the operational conten...

A single base rule representing a fundamental inter-relationship between variables within a dataset can generate a large number of derivative rules. These are rules that appear interesting only due to the inter-relationship that is best represented by the base rule. This phenomena is well understood with respect to derivative rules formed by adding unproductive conditions to the antecedent of t...

This paper introduces a new way of representing bankruptcy rules. These representations are used to show that the minimal overlap rule is a composition of the Ibn Ezra rule and the constrained equal losses rule, a result originally obtained by [1]. The residual minimal overlap rule is analysed as an alternative extension of the Ibn Ezra rule, by using a composition with the constrained equal aw...

Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the so-called “centipede game”, however, players frequently violate this principle. An alternative is a “dynamic level-k” model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level-k rule is a best-response to the l...

Applications of three-dimensional Galerkin boundary element methods require the numerical evaluation of many four-dimensional integrals. In this paper we explore the possibility of using extrapolation quadrature. To do so, one needs appropriate error functional expansions. The treatment here is limited to integration over a region T1×T2, where T1 and T2 are planar triangular elements in a hangi...

Time-integration for lumped parameter systems obeying implicit Bingham-Kelvin constitutive models is studied. The governing system of equations describing the lumped parameter system is a non-linear differential-algebraic equation and needs to be solved numerically. The response of this system is non-smooth and the kinematic variables can not be written in terms of the dynamic variables, explic...

The best Weibull distribution methods for the assessment of wind energy potential at different altitudes in desired locations are statistically diagnosed in this study. Seven different methods, namely graphical method (GM), method of moments (MOM), standard deviation method (STDM), maximum likelihood method (MLM), power density method (PDM), modified maximum likelihood method (MMLM) and equival...