In the present paper, synchronous, tabled chain code picture systems based on Lindenmayer systems (sT0L system) are studied with respect to the finiteness of their picture languages. The finiteness is proved to be decidable. Additionally, a method is given for deciding whether or not an sT0L system generates a finite picture language. © 2006 Elsevier B.V. All rights reserved.

We study the relationship between potential equivalence and character theory; we observe that of a representation ρ \rho is deter...

Our main result asserts that for any given numbers C and D the class of simply connected closed smooth manifolds of dimension m < 7 which admit a Riemannian metric with sectional curvature bounded in absolute value by |K| ≤ C and diameter uniformly bounded from above by D contains only finitely many diffeomorphism types. Thus in these dimensions the lower positive bound on volume in Cheeger’s F...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g&apos;.$ the converse of schur&apos;s theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur&apos;s theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

We view and provide further evidence for a number of Swampland criteria, including the Weak Gravity Conjecture, Distance Conjecture bounds on finiteness quantum gravity vacua from prism black hole entropy. Furthermore we propose that at least all these statements may be more fundamentally consequence amplitudes.