From Sturmian and Christoffel words we derive a strictly increasing function ∆ : [0,∞) → R. This function is continuous at every irrational point, while at rational points, left-continuous but not right-continuous. Moreover, it assumes algebraic integers at rationals, and transcendental numbers at irrationals. We also see that the differentiation of ∆ distinguishes some irrationality measures o...

In contrast to Roth’s theorem that all algebraic irrational real numbers have approximation exponent two, the distribution of the exponents for the function field counterparts is not even conjecturally understood. We describe some recent progress made on this issue. An explicit continued fraction is not known even for a single non-quadratic algebraic real number. We provide many families of exp...

There is evidence that bidders fall prey to the winner’s curse because they fail to extract information from hypothetical events like winning an auction. This paper investigates experimentally whether bidders in a common value auction perform better when the requirements for this cognitive issue also denoted by contingent reasoning are relaxed, leaving all other parameters unchanged. The overal...

Most literature on time series classification assumes that the beginning and ending points of the pattern of interest can be correctly identified, both during the training phase and later deployment. In this work, we argue that this assumption is unjustified, and this has in many cases led to unwarranted optimism about the performance of the proposed algorithms. As we shall show, the task of co...

A family of orthogonal systems of irrational functions on the semi-infinite interval is introduced. The proposed orthogonal systems are based on Jacobi polynomials through an irrational coordinate transform. This family of orthogonal systems offers great flexibility to match a wide range of asymptotic behaviors at infinity. Approximation errors by the basic orthogonal projection and various oth...

The purpose of this study was to analyze the relationship between the sunk cost effect and ambiguity in investment situations. Starting from the sensemaking approach and the decision dilemma theory, our hypothesis is that a sunk cost affected decision can be “constructively" rational in ambiguous environments in the sense that decision makers have the opportunity, through actions, to enact an e...

An optimal artificial neural network (ANN) has been developed to predict the Nusselt number of non-Newtonian nanofluids. The resulting ANN is a multi-layer perceptron with two hidden layers consisting of six and nine neurons, respectively. The tangent sigmoid transfer function is the best for both hidden layers and the linear transfer function is the best transfer function for the output layer....