(0, 2) trialities

2 0 2 2 0 2 0 0 0

An optimization problem for systems that are subject to perturbations where both state observations and control actions are impulsive is here addressed. The dynamics equation is given by a differential inclusion ( ) ( , ( )) x t F t x t ∈ and the optimal strategy is the minimizer of the worst viable perturbation process (minimax). Such formulation is appropriate when noise is barely known but l...

F 0 1 2 3 2 N ? 2 2 N ? 1 0 0 0 0 0 0 0 1 1 2 2 2 2 2

13 Proof: R private (f) C private (f) since in any protocol the parties send at least one bit per round. On the other hand, for every privately computable function f the bound R private (f) is achieved by the protocol A f. In any round of this protocol the parties send a message with size at most n. (Note that in steps (2a) and (2b) of A f we may save one bit per round by omitting the most sign...

Maps admitting trialities but not dualities

We use group theory to construct infinite families of maps on surfaces which are invariant under Wilson’s map operations of order 3 but not under the operations of order 2, such as duality and Petrie duality. MSC classification: Primary 05C25, secondary 05C10, 20B25.

2 0 0 0 T O 2 0 0 6

Christopher H. Wheeler is a research officer in the Research division of the Bank. He previously was an assistant professor of economics at Tulane University in New Orleans. Wheeler received his doctoral and master’s degrees in economics from the University of Wisconsin-Madison in 1998 and 1995, respectively, and his bachelor’s degree in economics from Colby College in Waterville, Maine, in 199...

0 0 0 0 0 0 0 T 0 0 2 0 0 0 0 0 0 C 0 0 0 4 2 2 0