We present a novel way for reasoning about (possibly ir)rational quantifier-free non-linear arithmetic by a reduction to SAT/SMT. The approach is incomplete and dedicated to satisfiable instances only but is able to produce models for satisfiable problems quickly. These characteristics suffice for applications such as termination analysis of rewrite systems. Our prototype implementation, called...

In this paper we show how one can obtain simultaneous rational approximants for ζq(1) and ζq(2) with a common denominator by means of Hermite-Padé approximation using multiple little q-Jacobi polynomials and we show that properties of these rational approximants prove that 1, ζq(1), ζq(2) are linearly independent over Q. In particular this implies that ζq(1) and ζq(2) are irrational. Furthermor...

This paper extends earlier work on the definition of Wannier functions for Bloch electrons in a magnetic field. Extensions to irrational as well as rational magnetic fields are defined, and their properties investigated. The results are used to give a generalisation of the Peierls effective Hamiltonian which is valid when the magnetic flux per unit cell is close to any rational number. * Addres...

How people deal with risk and uncertainty has fuelled public and academic debate in recent decades. Researchers have shown that common distinctions between rational and 'irrational' strategies underestimate the complexity of how people approach an uncertain future. I suggested in 2008 that strategies in-between do not follow standards of instrumental rationality nor they are 'irrational' but fo...

Various studies (e.g., Becker, 1962, Ariely et al., 2003) have noted anomalies concerning the relationship between observed demand and the preferences presumed to motivate it. We reexamine these findings using experimental choice data. After separating our subjects’ choices into rational and irrational subsets based on consistency with the axioms of revealed preference, we estimate and compare ...

since the collapse of the soviet :union:, russia has been affected by intensifying regional and international developments than ever before. because of new opportunities and threats caused by these developments, russia faced with the problem of structural adoption whit systemic new realities, accompanying whit redefinition of its position and review of foreign policy approaches. conceptual and ...

We are the first paper to analyse and confirm the existence and extent of rational informational herding and rational informational contrarianism in a financial market experiment, and to compare and contrast these with the equivalent irrational phenomena. In our study, subjects generally behaved according to benchmark rationality. Moreover, traders who should herd or be contrarian in theory are...

I consider the Diophantine approximation problem of sup-norm simultaneous rational approximation with common denominator of a pair of irrational numbers, and compute explicitly some pairs with large approximation constant. One of these pairs is the most badly approximable pair yet computed. The theory of approximation of a single irrational number by rationals is well known, and for our purpose...