We consider optimal control problems for a class of hybrid systems with switches dependent on an external event process. In the case where all event times in this process are fully known, the solution to such problems was obtained in prior work. When event times are uncertain or unknown, we propose a Receding Horizon (RH) control scheme in which only some future event information is available w...

We formulate conditions on the geometry of a non-expanding horizon ∆ which are sufficient for the space-time metric to coincide on ∆ with the Kerr metric. We introduce an invariant which can be used as a measure of how different the geometry of a given non-expanding horizon is from the geometry of the Kerr horizon. Directly, our results concern the space-time metric at ∆ at the zeroth and the f...

Adiabatic (curvature) perturbations are produced during a period of cosmological inflation that is driven by a single scalar field, the inflaton. On particle physics grounds – though – it is natural to expect that this scalar field is coupled to other scalar degrees of freedom. This gives rise to oscillations between the perturbation of the inflaton field and the perturbations of the other scal...

The 3 ocelli of the blowfly Calliphora erythrocephala, grouped close together an the top of the head (Fig. 1), have large, extensively overlapping visual fields. Together they view the entire upper hemisphere of the surroundings plus part of the lower hemisphere (Figs. 5, 7). It is shown for the lateral ocelli that despite the underfocussing of the ocellar lens large patterns are imaged an the ...

We study the Hawking radiation in two dimensional dilaton black hole by means of quantum gravity holding near the apparent horizon. First of all, we construct the canonical formalism of the dilaton gravity in two dimensions. Then the Vaidya metric corresponding to the dilaton black hole is established where it is shown that the dilaton field takes a form of the linear dilaton. Based on the cano...

In this paper, I compare two di¤erent approaches to model implicit contracting, the in…nite-horizon approach typically used in the literature and a …nite-horizon approach building on an adverse-selection model. I demonstrate that even the most convincing result of the in…nite-horizon approach, namely that implicit contracting is improved, if the discount rate is lowered, does not carry over to ...

A control law is constructed for a linear time varying system by solving a two player zero sum diierential game on a moving horizon, the game being that which is used to construct an H 1 controller on a nite horizon. Conditions are given under which this controller results in a stable system and satisses an innnite horizon H 1 norm bound. A risk sensitive formulation is used to provide a state ...

This paper studies stochastic inventory problems with unbounded Markovian demands, ordering costs that are lower semicontinuous, and inventory/backlog (or surplus) costs that are lower semicontinuous with polynomial growth. Finite horizon problems, stationary and nonstationary discounted cost in nite horizon problems, and stationary long-run average cost problems are addressed. Existence of opt...

We review the anomaly induced effective action for dilaton coupled spinors and scalars in large N and s-wave approximation. It may be applied to study the following fundamental problems: construction of quantum corrected black holes (BHs), inducing of primordial wormholes in the early Universe (this effect is confirmed) and the solution of initial singularity problem. The recently discovered an...

This Letter analyzes 3-dimensional simulations of Kerr black hole magnetospheres that obey the general relativistic equations of perfect magnetohydrodynamics (MHD). Particular emphasis is on the event horizon magnetosphere (EHM) which is defined as the the large scale poloidal magnetic flux that threads the event horizon of a black hole (This is distinct from the poloidal magnetic flux that thr...