After-effect function

Thus the response of a spatially uniform system in thermodynamic equilibrium is always characterized by translationally invariant and temporaly stationary after-effect functions. This article is restricted to a discussion of systems which prior to an application of an external perturbation are uniform and in equilibrium. The condition expressed by Eq. (7) must be satisfied. Caution must be exercised in applying linear response theory to problems in double resonance spectroscopy where non-equilibrium initial states are prepared. Having dispensed with this caveat, we adopt Eq. (7) in the remainder of this review article. 

Once the after-effect function has been determined the response to any form of F(r, t) can be predicted. The after-effect function is an intrinsic dynamical property of the system, which is independent of the precise magnitude and form of the applied force, and which succinctly summarizes the way in which the constituent particles in a many-body system cooperate to give the observed response of the system to the external perturbation. 

That the after-effect function 0AB(r, t) is a real function of the space-time coordinates (r, t) can be deduced from the fact that, since A is an observable, the response [Pg.12]

Since the after-effect function is a real function of (r, t), the susceptibility can be written in terms of its real, XabQl> )> and imaginary, x ab(K ) parts,... 

It can be concluded that if eA = eB the after-effect function is an even function of the wave vector whereas if eA= — eB it is an odd function of the wave vector. 

Now that we have determined the quantum-mechanical form of the after-effect function for an equilibrium system, we can determine the response to a monochromatic field. This response has the same frequency... 

It can be demonstrated that the after-effect function < 4B(k, 0 can also be written as... 

Another important property of the after-effect function 0AB(k, t) can be derived. Note that... 

Our discussion so far refers to the case where the field is being switched on. Let us now consider the opposite case where a constant field E had been operative for a long time so that the induced moment is a(o°) and let us suppose that E is switched off at time t = 0. For t>0 the induced moment m(t) is Eo( ( oo) — (/)). This leads us to define the after-effect function b t) by the relation... 

The rate of polymerization in the dark, i.e., when the initiation is stopped, was used to uncouple the kinetic constants for termination and propagation. By performing these after-effect experiments (13-15) at various stages in the reaction, the kinetic constants for bimolecular carbon-carbon termination and propagation were characterized as a function of conversion. 

If R is known, it is possible to fit the parameters k, ktCC0, A, At, fcp and fct using kinetic data from a single experiment. Thus, if the reaction diffusion parameter is known from the unsteady state after-effect experiments, the kinetic constant evolution can be determined as a function of free volume, and thus conversion. More details about this method will be published elsewhere (18). 

The effect of zearalenone on crop development may be connected to its influence on the status and functioning of the photosynthetic apparatus (Koscielniak et al. 2008). The after-effects of zearalenone on the growth of soybean and wheat plants, net photosynthesis and transpiration rates, stomatal conductance, photochemical efficiency of photosystem 2 and on final seeds yield were determined. Modifications in leaf area were more pronounced in soybean than in wheat, and this tendency increases in successive developmental phases. The net photosynthesis was stimulated during the juvenile phase and during that of the final one by about 13.6% (average) in soybean plants. Stimulation of transpiration was also observed after... 

Chemicals are omnipresent in our world today. Chemical risk is a permanent issue in our everyday environment, obviously on work premises, and may also be caused by different circumstances of chemical assaults. Among all chemical accidents, eye projections are a specific issue because of the vulnerability of ocular structures and also because of the risk of major functional after-effects. Chemical Abstracts Service (CAS) is a division of the American Chemical Society. This International database of the American Chemical Society is a worldwide reference registering... 

The most serious adverse effect of protirelin is pituitary apoplexy (pituitary hemorrhage or infarction, characterized by severe headache, visual loss, and often by pituitary failure, hypotension, and coma). This complication has been described in 15 cases after pituitary function testing... 

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