The $$\partial \bar \partial $$-Lemma under Surjective Maps

On Surjective Kernels of Partial Algebras

A partial algebra A = (A, F ) is called surjective if each of its elements lies in the range of some of its operations. By a transfinite iteration construction over the class of all ordinals it is proved that in each partial algebra A there exists the largest surjective subalgebra Skr A, called the surjective kernel of A. However, what might be found a bit surprising, for each ordinal α there i...

On Periodicity Lemma for Partial Words

We investigate the function L(h, p, q), called here the threshold function, related to periodicity of partial words (words with holes). The value L(h, p, q) is defined as the minimum length threshold which guarantees that a natural extension of the periodicity lemma is valid for partial words with h holes and (strong) periods p, q. We show how to evaluate the threshold function in O(log p + log...

Invariants of objects and their images under surjective maps

We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably. In the former case, we establish a constructible isomorphism between the al...

Bar recursion over finite partial functions

We introduce a new, demand-driven variant of Spector’s bar recursion in the spirit of the BerardiBezem-Coquand functional of [4]. The recursion takes place over finite partial functions u, where the control parameter φ, used in Spector’s bar recursion to terminate the computation at sequences s satisfying φ(ŝ) < |s|, now acts as a guide for deciding exactly where to make bar recursive updates, ...

Segment - Preserving Maps of Partial