Nuclear spin relaxation and magnetic shielding tensors of atoms constituting cyanogen bromide molecule

The temperature dependence of the correlation time describing reorientation kinetics of cyanogen bromide in CDCl₃ solution has been determined on the basis of the linewidths of the ¹⁴N NMR signal. It has been found that the longitudinal spin relaxation of the ¹⁵N nucleus occurs by shielding anisotropy and spin-rotation mechanisms, whereas for the ¹³C nucleus these mechanisms are of lesser importance. In the latter case the scalar relaxation of the second kind due to carbon-bromine coupling is the predominant relaxation mechanism. The parameter values: ¹ J(¹³C—⁷⁹Br) = 349 ± 10 Hz, T ₁ (⁷⁹Br, 303 K) = 2.31 ± 0.22 × 10^?7 s, Δσ(¹⁵N) = 565 ± 16 ppm and Δσ(¹³C) = 276 ± 120 ppm have been determined from the relaxation data analysis. The shielding anisotropy parameters Δσ(¹⁵N) = 580 ± 50 ppm and Δσ(¹³C) = 274 ± 9 ppm have been independently determined using ¹³C and ¹⁵N NMR in liquid crystalline solvent. The experimentally determined shielding tensors for sp-hybridized atoms in the investigated compound and in a series of bromoacetylenes have been compared with the results of quantum mechanical calculations [GIAO, DFT B3LYP/6-311 + +G(2d,p)]. The ‘heavy atom effect’ shielding bromine-bonded carbons is of the order of — 25 ppm and concerns mainly the σ⊥ component.     

Optimal control of a hyperbolic system with time-varying lags

In this paper, an optimal distributed control problem for ahyperbolic system in which time-varying lags appear in the stateequation and in the boundary condition simultaneously is considered.Making use of Lions' scheme, necessary and sufficient conditionsof optimality for the Neumann problem are derived.     

Optimal control of parabolic systems with time-varying lags

Various optimal control problems for linear parabolic systemswith time-varying lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwart's, the representation of the optimalfeedback control is given.     

Optimal Control of Distributed Parabolic Systems Involving Time Lags

Various optimal control problems for linear parabolic systemswith constant time lags are considered. Necessary and sufficientconditions of optimality are derived for the Neumann problem.The optimal control is obtained in the feedback form. Makinguse of the results of Schwartz, the representation of the optimalfeedback control is given. A simple example of application isalso provided.     

Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates |n〉, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state n^? with maximal quantum-classical distance; the value n^? decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.     

On some optimal control problem for a parabolic system with boundary condition involving a time-varying lag

An optimal boundary control problem for a distributed parabolicsystem with boundary condition involving a time-varying lagis considered. The initial condition of this equation is notgiven by a known function, but it belongs to a certain set.Necessary and sufficient conditions of optimality for the Neumannproblem with the quadratic performance functional are derived.A numerical example of application is also presented.     

SIMULTANEOUS GROWTH AND DECAY OF FREE RADICALS IN IRRADIATED PROTEINS

Abstract— The electron paramagnetic resonance signals due to free radicals created in illuminated keratin have been studied during illumination and also during the decay of the signal in the dark. A number of mechanisms suggested to account for the simultaneous growth and decay of radicals during illumination is considered but only one of these is capable of accounting for the experimental results.