We propose a definition of branching-type stationary stochastic processes on rooted trees and related definitions hyper-positivity for functions the unit circle set non-negative integers. then obtain (1) necessary sufficient condition tree existence non-trivial it, (2) complete criterion hyper-positive in setting homogeneous terms variant classical Herglotz-Bochner Theorem, (3) prediction theor...

We study the following question posed by Turán. Suppose Ω is a convex body in Euclidean space Rd which is symmetric in Ω and with value 1 at the origin; which one has the largest integral? It is probably the case that the extremal function is the indicator of the half-body convolved with itself and properly scaled, but this has been proved only for a small class of domains so far. We add to thi...

In [2] we presented a Definite Integral Table Lookup (the DITLU) for parametric functions, including a minimal prototype implementation demonstrating its capabilities. In this paper we present a possible application of a DITLU, which would extend its utility for a modest investment of effort. The naive algorithm for indefinite integration of rational functions (see e.g. [12, 2.10]) can be imple...

This note illustrates theoretical worst-case scenarios for groundness analyses obtained through abstract interpretation over the abstract domains of definite (Def) and positive (Pos) Boolean functions. For Def, an example is given for which any Def-based abstract interpretation for groundness analysis follows a chain which is exponential in the number of argument positions as well as in the num...