Characterizations of Bounded Ricci Curvature on Smooth and NonSmooth Spaces

There are two primary goals to this paper. In the first part of the paper we study smooth metric measure spaces (M^n,g,e^{-f}dv_g) and give several ways of characterizing bounds -Kg\leq \Ric+\nabla^2f\leq Kg on the Ricci curvature of the manifold. In particular, we see how bounded Ricci curvature on M controls the analysis of path space P(M) in a manner analogous to how lower Ricci curvature controls the analysis on M. In the second part of the paper we develop the analytic tools needed to in order to use these new characterizations to give a definition of bounded Ricci curvature on general metric measure spaces (X,d,m). We show that on such spaces many of the properties of smooth spaces with bounded Ricci curvature continue to hold on metric-measure spaces with bounded Ricci curvature

Space shuttle rudder/speedbrake actuation subsystem

The Rudder/Speedbrake (R/SB) Actuation Subsystem for use on the NASA Space Shuttle Orbiter is an electro-hydro-mechanical system which provides the control and positionary capability of the orbiter aero-dynamic primary flight control surface. The system is located in the vehicle's vertical stabilizer. The geared rotary actuators provide a power hinge feature of the split panel rudder. Actuation of both panels in the same direction provides conventional rudder control; actuating the panels differentially provides a speedbrake function intended to control both speed and pitch. The commands may be superimposed on one another. The system consists of one power drive unit which responds to quadredundant avionic signals to generate a rotary output, four geared rotary actuators, which develop rotary position and torque as outputs, and ten torque transmitting drive-shifts