The elliptic norm curve Qn in space S„_i admits a group G2ni of collineations, and in fact there is a single infinity of such curves which admit the same group. A particular Qn of the family is distinguished by a value of the parameter t , itself an elliptic modular function defined by the modular group congruent to identity (mod. n). In the group G2n2, there are certain involutory collineation...

Let w be a morphic word over a finite alphabet Σ, and let ∆ be a nonempty subset of Σ. We study the behavior of maximal blocks consisting only of letters from ∆ in w, and prove the following: let (ik, jk) denote the starting and ending positions, respectively, of the k’th maximal ∆-block in w. Then lim supk→∞(jk/ik) is algebraic if w is morphic, and rational if w is automatic. As a result, we s...

We prove a new result about the mutual behavior of irrationality measure functions $\psi_{\alpha_j}(t)$ for $n$ different real numbers $\alpha_j, j = 1, \dots, n$.

The sequence of (terminating balanced) hypergeometric sums an = n ∑ k=0 ( n k )2( n+ k k )2 , n = 0, 1, . . . , appears in Apéry’s proof of the irrationality of ζ(3). Another example of hypergeometric use in irrationality problems is Ramanujan-type identities for 1/π, like ∞ ∑ k=0 ( 2k k )3 (4k + 1) (−1) 26k = 2 π . These two, seemingly unrelated but both beautiful enough, hypergeometric series...

We investigate the extent to which the “bubbles” and “crashes” in the experimental asset markets are due to individual irrationality and lack of common knowledge of rationality. We do so by comparing between the forecasted prices initially submitted by subjects in two market environments: (a) All the six traders are human subjects (6H) and (b) One human subject is interacting with five rational...

Assumptions of individual rationality and preference stability provide the foundation for a convenient and tractable modeling approach. While both of these assumptions have come under scrutiny in distinct literatures, the two lines of research remain disjointed. This study begins by explicitly linking the two literatures while providing insights into perhaps the central issue facing behavioral ...

Neuroeconomic conditions for "rational addiction" (Becker & Murphy 1988) have been unknown. This paper derived the conditions for "rational addiction" by utilizing a nonlinear time-perception theory of "hyperbolic" discounting, which is mathematically equivalent to the q-exponential intertemporal choice model based on Tsallis' statistics. It is shown that (i) Arrow-Pratt measure for temporal co...

If somehow you have not yet seen that proof, please ask someone, for example me, to show it to you. (Or maybe look at [2]. Well, meanwhile you can also extract it as a special case (substitute a = b and then n = 1) of what appears below in Section 2.) I learned this proof from Yoram Sagher who had learned it from John Conway. While we can consider it merely as a geometric realization of one of ...

The historical shift towards a scientific revolution after the eighteenth century in Europe has discarded societal and cultural folklore from its dictionary of knowledge. The Oxford Dictionary defines science as “the intellectual and practical activity encompassing the systematic study of the structure and behavior of the physical and natural world through observation and experiment” (2017). Th...

As we shall see later, Thomae’s function is not differentiable on the irrationals. In this note, we address whether there is a modification of Thomae’s function which is differentiable on a subset of the irrationals. In Section 2, we prove that Thomae’s function is not differentiable on the irrationals and define modified versions of Thomae’s function. In Section 3, we show that for each of our...