Finite effects

Radiation exits the monochromator and passes to the detector. As shown in Figure 10.12, a polychromatic source of radiation at the entrance slit is converted at the exit slit to a monochromatic source of finite effective bandwidth. The choice of... 

The dielectric constant is the electrostatic expression of the interaction of atoms and molecules with macroscopic electric fields rather than with the exceedingly strong fields of individual atoms and molecules. The interaction between the homogeneous outside field and electrically asymmetrical (polar) molecules results in a finite effect, since in these molecules the contributions of positive and negative charges do not cancel. 

In the nonlinear osmotic brush regime we combine the high-stretching (nonlinear) version of the chain elasticity in Eq. 22 with the nonhnear en-tropic effects of the counterions due to the finite volume of the polymer chains, i.e. we choose a finite effective diameter creff in Eq. 21. The final result for the equihbrium brush height is... 

Finite (year-end) cash flow and finite effective interest (0 of 15%. 

B) The case where the company demands a 20 percent finite effective end-of-year interest rate of return after taxes on any investment [i.e., profitability index (0 is 20 percent]. 

As stated in the introduction of this section, we use Hartmann-Hahn experiment as the generic term for transfer experiments that are based on the Hartmann-Hahn principle, that is, on matched effective fields. Because two vanishing effective fields are also matched, Hartmann-Hahn sequences need not have finite effective fields. Examples of Hartmann-Hahn sequences without effective spin-lock fields are MLEV-16 (Levitt et al, 1982), WALTZ-16 (Shaka et al., 1983b) and DIPSI-2 (Shaka et al., 1988). Note that the term Hartmann-Hahn sequence has also sometimes been used in the literature in a more restricted sense for experiments with matched but nonvanishing effective spin-lock fields (see, for example, Chandrakumar and Subramanian, 1985, and Griesinger and Ernst, 1988). 

In both the time-dependent and time-independent SCF perturbation theories the equations determining the effect of the perturbation look as if they can generate a finite effect with no applied perturbation. These cases of infinitesimal perturbations" are genuine ones which have important ramifications for the stabilities of the single-determinant states of a many-electron system. 

Freltoft, T., Kjems, J. K., and Sinha, S. K. 1986. Power-law correlations and finite effects in silica particle aggregates studied by small-angle neutron scattering. Phvs. Rev. B 33 269-75. 

The first criterion is most easily examined. In pure benzene vapor excited at 2536 A or longer wave lengths, both the quantum yield and the observed singlet state lifetime show only a very shallow dependence on benzene pressure above 10 torr. Addition of foreign gases such as hydrocarbons to these experiments also has little (but sometimes finite) effect on fluorescence yields " or lifetimes. Even in the extreme collisional limit of condensed phase at 77°K, the fluorescence yield of 0.2 matches that of the vapor. - (Condensed phase yields drop to about 0.05 at 300°K, but this is probably a special thermal effect somewhat apart from a collision-induced electronic decay. See Section IVC.)... 

Recently, however, a much more accurate determination has come from the CCFR Collaboration (CCFR, 1990a) also using an iron target. They obtain 2.66 0.03 0.08. The discrepancy (10%) is too large to attribute to the QCD correction. Moreover use of the more accurate expression (16.4.37) with allowance for finite effects wiU only reduce the RHS of (17.1.4,5) by about 1%. Thus theory and experiment are barely compatible and further data will be of great interest. 

Sulfur scavenging processes are typically batch operations. They make use of materials that capture and retain sulfur compounds, but have a finite effective capacity. When this capacity is reached, the spent sorbent (liquid or solid) must be removed and replaced with fresh material. The spent sorbent is normally disposed of as waste, and the production of an environmentally acceptable waste has become a key factor in the selection of. scavenging proces.ses for specific applications. Other important considerations are operating safety and reliability (unattended operation is often required) and, of course, capital and operating costs. 

Biomolecules are finite systems that gained much attention recently. These are rather small polymers and because of their functionalized chemical composition they sustain their size for all time. A finite-size scaling approach does not make sense at all. The folding of proteins, for example, is only due to finiteness effects under thermodynamic conditions. It is, therefore, necessary to develop or adapt concepts for nnderstanding cooperative effects also for systems on rather small and mesoscopic length scales (nm to pm) [58]. 

Now, if Q were either within the interior of the region of influence or somewhere outside of it, then small changes in the first derivatives would correspond to small changes in the second derivatives. If Q is on a characteristic line, however, even an infinitesimal change in the first derivatives may have a finite effect upon the second derivatives, requiring the matrix of (6.107) to be singular,... 

Diffusion current a (c(gaa) — Csurface)/Ax. For hydrodynamic reasons Ax can be approximated by a finite effective boundary thickness. At high voltages Csurface approaches zero and the signal is proportional to C(gag) (see also page 484). 

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