The parallelization of many algorithms can be obtained using space-time transformations which are applied on nested do-loops or on recurrence equations. In this paper, we analyze systems of linear recurrence equations, a generalization of uniform recurrence equations. The rst part of the paper describes a method for nding automatically whether such a system can be scheduled by an a ne timing fu...

Analysis of algorithms occasionally requires solving of rst-order two-dimensional linear homogeneous partial di erence equations. We survey solutions to special cases of the linear recurrence equation (am + bn + c)Fm;n = (dm + en + f)Fm 1;n + (gm + hn + i)Fm 1;n 1 in terms of known functions and establish equivalences between unsolved cases. The article also reviews solution techniques used to ...

This paper shows how to reason about streams concisely and precisely. Streams, infinite sequences of elements, live in a coworld: they are given by a coinductive datatype, operations on streams are implemented by corecursive programs, and proofs are typically concocted using coinduction. This paper offers an alternative to coinduction. Suitably restricted, stream equations possess unique soluti...

Each family of Gauss hypergeometric functions fn = 2F1(a + ε1n, b + ε2n; c + ε3n; z), n ∈ Z , for fixed εj = 0,±1 (not all εj equal to zero) satisfies a second order linear difference equation of the form Anfn−1 + Bnfn + Cnfn+1 = 0. Because of symmetry relations and functional relations for the Gauss functions, many of the 26 cases (for different εj values) can be transformed into each other. I...

The Amazon Basin experiences severe droughts that may become more common in the future. Little is known of the effects of such droughts on Amazon forest productivity and carbon allocation. We tested the prediction that severe drought decreases litterfall and wood production but potentially has multiple cancelling effects on belowground production within a 7-year partial throughfall exclusion ex...

We develop techniques that can be applied to find solutions to the recurrence ∣∣n k ∣∣ = ( n+ k + )∣∣n−1 k ∣∣+ ( ′n+ ′k + ′)∣∣n−1 k−1∣∣+ [n = k = 0]. Many interesting combinatorial numbers, such as binomial coefficients, both kinds of Stirling and associated Stirling numbers, Lah numbers, Eulerian numbers, and second-order Eulerian numbers, satisfy special cases of this recurrence. Our techniqu...

We present PLTplot, a plotting package for PLT Scheme. PLTplot provides a basic interface for producing common types of plots such as line and vector field plots from Scheme functions and data, an advanced interface for producing customized plot types, and support for standard curve fitting. It incorporates renderer constructors, transformers from data to its graphical representation, as values...