Oct-

R. Pryde New Developments in Non-Destructive Testing of Hoisting Ropes.-Mine Hoisting 96, International Scientific and Technical Conf, 8-10 Oct. 1996, Gliwice, Poland, in 2 vol., vol. 2, pp. 22-24. 

O. VAILHEN, E. FLEUET, B. NOUAILHAS, A. SCHUMM TRAPPIST a standard open environment for multi-modal NDT data manipulation - Proceedings, 6th. ECND f, Nice, Oct. 94, pp. 45-49. 

Brasche, L, Smith, K Engine Titanium Consortium An Overview of the Contaminated Billet Study, Fall Conference of the American Society of Nondestructive Testing, Oct. 20-24, 1997, Pittsburgh, USA... 

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

In the OCT fomnilation, the TDSE written as a 2 x 2 matrix in a BO basis set, equation (Al.6.72). is introduced into the objective fiinctional with a Lagrange multiplier, x(x, t) [54]. The modified objective fiinctional may now be written as... 

The PdCli-catalyzed instantaneous rearrangement of A -carbethoxy-S-azabi-cyclo[5.1.0]oct-3-ene (60) takes place at room temperature to give A -car-bethoxy-8-azabicyclo[3.2.1]oct-2-ene (61)[50], The azepine 62 undergoes a smooth skeletal rearrangement to give 63, and the diazepine 64 is converted into the open-chain product[51]. Beckmann fission of the oxime 65 of ketones and aldehydes to give the nitrile 66 is induced by a Pd(0) complex and oxygen [52,53]. 

Acetyloxy)methyl]-7-[(5-amino-5-carboxy-l-oxopentyl)amino]-8-oxo-5-thia-l-a2abicyclo[4.2.0]oct-2-ene-2-carboxyhc acid... 

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