Following a question of Brun, we consider the possibility of finding a first order statement that the rational summands in an infinite series can be checked against in order to give a sufficient condition for the series to sum to an irrational value. We show that such a statement can exist in structures that define the integers, but not in o-minimal structures. 2010 Mathematics Subject Classifi...

We prove that the binary complexity of solving ordinary polynomial differential equations in terms of Puiseux series is single exponential in the number of terms in the series. Such a bound was given in 1990 by Grigoriev for Riccatti differential polynomials associated to ordinary linear differential operators. In this paper, we get the same bound for arbitrary differential polynomials. The alg...

for some nonnegative integer k and complex numbers a0, . . . , ak, b1, . . . , bk ∈ C. Trigonometric polynomials and their series counterparts, the Fourier series, play an important role in many areas of pure and applied mathematics and are likely to be quite familiar to the reader. When reflecting on the terminology, however, it is reasonable to wonder why the term trigonometric polynomial is ...

We explore a function theory connected with the principal series representation of SL(2, R) in contrast to standard complex analysis connected with the discrete series. We construct counterparts for the Cauchy integral formula, the Hardy space, the Cauchy-Riemann equation and the Taylor expansion. ∗Supported by grant 3GP03196 of the FWO-Vlaanderen (Fund of Scientific ResearchFlanders), Scientif...

As medicine leans increasingly on mathematics no clinician can afford to leave the statistical aspects of a paper to the "experts." If you are numerate, try the "Basic Statistics for Clinicians" series in the Canadian Medical Association Journal,1 2 3 4 or a more mainstream statistical textbook.5 If, on the other hand, you find statistics impossibly difficult, this article and the next in this ...

We have first demonstrated that Debreu’s view regarding the publication of The Theory of Games and Economic Behavior by von Neumann and Morgenstern in 1944 as the birth of modern mathematical economics is not convincing. In this paper, we have proposed the hypothesis that the coordinated research programs in the 1930’s, initiated by the Econometric Society and the Cowles Commission for Research...