On the optimum design of piston rings

We study a family of control problems that arise in the design of dynamically loaded bearings which have a minimum power loss; in particular, we study the design of piston rings with minimum parasitic power loss.This research was partially supported by NSF Grant No. MCS-77-05624.     

On Brunovský's example

The example due to Brunovský [Eq. (1)] is analyzed, and further paradoxical properties are exhibited.     

A time-decomposition algorithm for a stiff linear two-point boundary-value problem and its application to a nonlinear optimal control problem

An algorithm is proposed to solve a stiff linear two-point boundary-value problem (TPBVP). In a stiff problem, since some particular solutions of the system equation increase and others decrease rapidly as the independent variable changes, the integration of the system equation suffers from numerical errors. In the proposed algorithm, first, the overall interval of integration is divided into several subintervals; then, in each subinterval a sub-TPBVP with arbitrarily chosen boundary values is solved. Second, the exact boundary values which guarantee the continuity of the solution are determined algebraically. Owing to the division of the integration interval, the numerical error is effectively reduced in spite of the stiffness of the system equation. It is also shown that the algorithm is successfully imbedded into an interaction-coordination algorithm for solving a nonlinear optimal control problem.The authors would like to thank Mr. T. Sera and Mr. H. Miyake for their help with the calculations.     

Lower closure and existence theorems for optimal control problems with infinite horizon

Lower closure theorems are proved for optimal control problems governed by ordinary differential equations for which the interval of definition may be unbounded. One theorem assumes that Cesari's property (Q) holds. Two theorems are proved which do not require property (Q), but assume either a generalized Lipschitz condition or a bound on the controls in an appropriateL _p-space. An example shows that these hypotheses can hold without property (Q) holding.     

Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms

In this paper, we introduce optimal control algorithm for the design of pulse sequences in NMR spectroscopy. This methodology is used for designing pulse sequences that maximize the coherence transfer between coupled spins in a given specified time, minimize the relaxation effects in a given coherence transfer step or minimize the time required to produce a given unitary propagator, as desired. The application of these pulse engineering methods to design pulse sequences that are robust to experimentally important parameter variations, such as chemical shift dispersion or radiofrequency (rf) variations due to imperfections such as rf inhomogeneity is also explained.     

Construction of universal rotations from point-to-point transformations

For a desired range of offsets, universal rotations of arbitrary flip angle can be constructed based on point-to-point rotations of I(y) with half the flip angle. This approach allows, for example, creation of broadband or bandselective refocusing pulses from broadband or bandselective excitation pulses. Furthermore, universal rotations about any axis can be obtained from point-to-point transformations that can easily be optimized using optimal control algorithms. The construction procedure is demonstrated on the examples of a broadband refocusing pulse, a broadband 120(x) degrees rotation and a z-rotation with offset pattern.     

Addition of secondary phosphines to a vinyl ether of diacetone-d-glucose: a new approach to optically active phosphines and their derivatives

Secondary phosphines react readily with a vinyl ether of diacetone-d-glucose under radical initiation conditions to give, in high yield, anti-Markovnikov adducts, diorganyl{2-[3-O-(1,2:5,6-di-O-isopropylidene)-d-glucofuranosyloxy]ethyl}phosphines, which oxidize almost quantitatively upon reacting with air oxygen or elemental sulfur to form the corresponding optically active phosphine oxides or sulfides.     

9H-Fluorene-9-carbodithioic acids and dithioates. First isolation and characterization of a gem-enedithiol

[2,7-Bis(octyloxy)fluoren-9-yliden]methanedithiol (1a) and its tautomer 2,7-bis(octyloxy)-9H-fluorene-9-carbodithioic acid (2a) can be isolated in pure form from the reaction of monolithiated 2,7-bis(octyloxy)-9H-fluorene with CS₂ followed by protonolysis with aqueous HCl. Compound 1a is the first isolated and unambiguously characterized gem-enedithiol. When 9H-fluorene, 2,7-di-tert-butyl-9H-fluorene or 2,7-dimethoxy-9H-fluorene are used, the same synthetic procedure yields the unstable dithioic acids, which can be converted to the piperidinium salts.     

Synthesis of optically active ring-A substituted tryptophans as IDO inhibitors

The first synthesis of optically active 7-methoxy-d-tryptophan as well as other ring-A substituted tryptophans is described.