A pointed endofunctor (and in particular a reflector) (R, r) in a category X is direct iff for each morphism f : X→ Y the pullback of Rf against rY exists and the unique fill-in morphism u from X to the pullback is such that Ru is an isomorphism. (This is close to the concept of a simple reflector introduced by Cassidy, Hébert and Kelly in 1985.) We give sufficient conditions for directness, an...

For any Thurston map with exactly four postcritical points, we present an algorithm to compute the Weil-Petersson boundary values of the corresponding Thurston pullback map. This procedure is carried out for the Thurston map f(z) = 3z 2 2z3+1 originally studied by Buff, et al. The dynamics of this boundary map are investigated and used to solve the analogue of Hubbard’s Twisted Rabbit problem f...

The purpose of this paper is to give a purely equivariant definition of orbifold Chow rings of quotient Deligne-Mumford stacks. This completes a program begun in [JKK] for quotients by finite groups. The key to our construction is the definition (Section 6.1), of a twisted pullback in equivariant K-theory, KG(X) → KG(I2G(X)) taking non-negative elements to non-negative elements. (Here I G (X) =...

We previously identified several members of the SLC7 transporter family as potential system c transporters based on immunofluorescence data and, for functionally characterized members, on cysteamine-cysteine competition experiments. CAT2A, CAT2B, an orphan CAT-like protein named SLC7A14 and, to a lesser extent, CAT1 appeared as good system c candidates. However, it is still unknown which of the...

The construction of a Lyapunov function characterizing the pullback attraction of a cocycle attractor of a nonautonomous discrete time dynamical system involving Lipschitz continuous mappings is presented.

The CSRE (carbon source-responsive element) is a sequence motif responsible for the transcriptional activation of gluconeogenic structural genes in Saccharomyces cerevisiae. We have isolated a regulatory gene, DIL1 (derepression of isocitrate lyase, = CAT8), which is specifically required for derepression of CSRE-dependent genes. Expression of CAT8 is carbon source regulated and requires a func...