Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds

The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construction as a carefully organized surgery on a link. In this paper, we work out the relationship between the twisted face-pairing description of closed 3-manifolds and the more common descriptions by surgery and Heegaard diagrams. We show that all Heegaard diagrams have a natural decomposition into subdiagrams called Heegaard cylinders, each of which has a natural shape given by the ratio of two positive integers. We characterize the Heegaard diagrams arising naturally from a twisted face-pairing description as those whose Heegaard cylinders all have integral shape. This characterization allows us to use the Kirby calculus and standard tools of Heegaard theory to attack the problem of finding which closed, orientable 3-manifolds have a twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm

A survey of the theory of the Earth's rotation

The theory of the Earth's rotation and the geophysical phenomena affecting it is examined. First principles are reviewed and the problem of polar motion and UT1 variations is formulated in considerable generality and detail. The effects of Earth deformations and the solid Earth tides are analyzed

Self-Tuning Adaptive-Controller Using Online Frequency Identification

A real time adaptive controller was designed and tested successfully on a fourth order laboratory dynamic system which features very low structural damping and a noncolocated actuator sensor pair. The controller, implemented in a digital minicomputer, consists of a state estimator, a set of state feedback gains, and a frequency locked loop (FLL) for real time parameter identification. The FLL can detect the closed loop natural frequency of the system being controlled, calculate the mismatch between a plant parameter and its counterpart in the state estimator, and correct the estimator parameter in real time. The adaptation algorithm can correct the controller error and stabilize the system for more than 50% variation in the plant natural frequency, compared with a 10% stability margin in frequency variation for a fixed gain controller having the same performance at the nominal plant condition. After it has locked to the correct plant frequency, the adaptive controller works as well as the fixed gain controller does when there is no parameter mismatch. The very rapid convergence of this adaptive system is demonstrated experimentally, and can also be proven with simple root locus methods

Deformation processes in forging ceramics Progress report, 19 Jun. - 19 Sep. 1969

Deformation processes involved in forging of polycrystalline oxide ceramic