We show how the \rational" approach for integrating algebraic functions can be extended to handle elementary functions. The resulting algorithm is a practical decision procedure for determining whether a given elementary function has an elementary antiderivative, and for computing it if it exists.

The present longitudinal study tested the roles of early childhood executive control (EC) as well as exposure to poverty-related adversity at family and school levels as key predictors of low-income children's EC in elementary school (n = 391). Findings suggest that children's EC difficulties in preschool and lower family income from early to middle childhood are robust predictors of later EC d...

We give some new canonical representations for forms over C. For example, a general binary quartic form can be written as the square of a quadratic form plus the fourth power of a linear form. A general cubic form in (x1, . . . , xn) can be written uniquely as a sum of the cubes of linear forms `ij(xi, . . . , xj), 1 ≤ i ≤ j ≤ n. A general ternary quartic form is the sum of the square of a quad...

We present a new method for proving non-holonomicity of sequences, which is based on results about the number of zeros of elementary and of analytic functions. Our approach is applicable to sequences that are defined as the values of an elementary function at positive integral arguments. We generalize several recent results; e.g., non-holonomicity of the logarithmic sequence is extended to rati...

Kechris, A.S., Boundedness theorems for dilators and ptykes, Annals of Pure and Applied Logic 52 (1991) 79-92. The main theorem of this paper is: If f is a partial function from K, to X, which is Pi-bounded, then there is a weakly finite primitive recursive dilator D such that for all infinite a E domu), f(a) s D(a). The proof involves only elementary combinatorial constructions of trees. A gen...

We provide explicit formulas for asymptotic densities of d-dimensional isotropic Lévy walks, when d > 1. The densities of multidimensional undershooting and overshooting Lévy walks are presented as well. Interestingly, when the number of dimensions is odd the densities of all these Lévy walks are given by elementary functions. When d is even, we can express the densities as fractional derivativ...

We repeatedly toss a biased coin where the probability is p of observing “heads”. The probability of a certain event can be regarded as a function of p. L. Lovász asked for a characterization of the functions occurring as the probability of some “reasonable” event. We state this problem in precise terms by introducing the concept of an “observable” event. Our main theorem states that a function...

We give an explicit embedding of Schwarzschild exterior solution into pseudoEuclidean space, via elementary functions.

Received ; accepted – 2 – ABSTRACT We present a simplified solution to orbit determination of a binary system from astrometric observations. An exact solution was found by Asada, Akasaka and Kasai by assuming no observational errors. We extend the solution considering observational data. The generalized solution is expressed in terms of elementary functions, and therefore requires neither itera...

In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times. Keywords—Telegraph operator, Elementary solution, Distribution