Sensitivity functions defined

As with a SISO system, a sensitivity function may be defined... 

Sensitivity is defined as the exposure energy necessary for 50% resist thickness remaining in the exposed areas. Contrast values are assessed by measuring the slope of the linear portion of the curve obtained by plotting the thickness of the relief image as a function of the logarithm of the exposure energy (15). The film thickness was measured with a Nanospec AFT film thickness monitor (Nanometrics). 

The Fukui function or frontier function was introduced by Parr and Yang in 1984 [144], They generously gave it a name associated with the pioneer of frontier molecular orbital theory, who emphasized the roles of the HOMO and LUMO in chemical reactions. In a reaction a change in electron number clearly involves removing electrons from or adding electrons to the HOMO or LUMO, respectively, i.e. the frontier orbitals whose importance was emphasized by Fukui.4 The mathematical expression (below) of the function defines it as the sensitivity of the electron density at various points in a species to a change in the number of electrons in the species. If electrons are added or removed, how much is the electron density... 

Chiral auxiliaries play a key role in the scale up of initial samples of materials and for small quantities. In addition, this method of approach can be modified to allow for the preparation of closely related materials that are invariably required for toxicologic testing during a pharmaceutical s development. There are a number of advantages associated with the use of an established auxiliary The scope and limitations of the system are well defined it is simple to switch to the other enantiomeric series (as long as mismatched pairs do not occur) concurrent protection of sensitive functionality can be achieved. This information can result in a short development time. The auxiliary s cost has the potential to be limited through recycles. However, the need to put on and take off the auxiliary unit adds two extra steps to a synthetic sequence that will reduce the overall yield. Most auxiliaries are not cheap, and this must be considered carefully when large amounts of material are needed. Finally, because the auxiliary has to be used on a stoichiometric scale, a by-product—recovered auxiliary—will be formed somewhere in the sequence. This byproduct has to be separated from the desired product sometimes, this is not a trivial task. 

Chemistry of Benzene and Toluene. One of our best defined chemical systems for C-H bond activation and C-H bond scission is that of benzene and toluene on nickel surfaces (9). The chemistry was a sensitive function of surface crystallography and of surface composition (9). 

The integration has proceeded successfully across tout. The values of U and UPRIME (including sensitivity functions when requested) have been computed at tout by interpolation. If you want to continue the integration, MAIN must define a new tout and call the code again. You cannot change the direction of integration without restarting. 

Spencer introduced the term functional sensitivity and defined it as the lowest concentration of an analyte for which clinically useful results can be reported (Spencer CA. Thyroid profiling for the 1990s free T4 estimate or sensitive TSH measurement. J Clin Immunoassay 1989 12 82-9.) This term has become widely adopted and used as one of the measures of the analytical performance of an immunoassay. 

To distinguish immunometric TSH assays from less sensitive RIAs, descriptive terms such as "sensitive, highly sensitive, ultrasensitive, and supersensitive have been used, generating much confusion as to the exact meaning of these terms. In 1991, a Nomenclature Committee of the American Thyroid Association recommended that the functional detection limit of serum TSH assays be determined on the basis of low-end interassay precision characteristics. Further, the committee recommended that precision at the lower reporting limit should optimally be 10% to 15% and preferably <20%. At present, functional sensitivity is defined as the lowest concentration of TSH at which an interassay coefficient of variation of 20% can be achieved. This functional detection hmit encompasses both analytical and... 

A consequence of the steepness of both functions defining the Gamow-peak is an extreme sensitivity of the Maxwellian-averaged cross section to temperature ... 

Another popular sensing methodology is based on spectral interrogation. It uses detection of displacements of spectral singularities in the presence of a measurand with respect to their positions for a zero measurand. This sensing approach is particularly effective in the resonant sensor configurations that feature sharp transmission or absorption peaks in their spectra. Defining /Ip( ) to be the position of a peak in a sensor transmission spectmm as a function of a measurand value spectral sensitivity function can be defined as ... 

The energy functional defines the second derivatives of equations (23)-(26), called the principal charge sensitivities, which determine the associated second differential of the Taylor expansion of equation (27) ... 

Loosely speaking, bandwidth may be defined as the frequency range [a>i, Wi] over which control is effective. In most cases we require tight control at steady state. Since coi=0 we call co the bandwidth. The word effective may be interpreted in different ways, giving rise to different definitions of bandwidth. The interpretation we use is that control is effective if we obtain some benefit in terms of performance. For example, considering the interpretation of the sensitivity function S, we arrive at the following definition ... 

Figure 3. Contours of the sensitivity parameter defined at the top of the figure as a function of temperature, T, and the induction parameter, T. ...

A sensitivity function describes the functional relationship between the change in an integral parameter caused by a fractional change in some input parameter, when the latter is expressed as a function of independent variables. For most applications a linear functional relationship is desirable. Perturbation theory formulations provide such a linear relationship. A sensitivity function can be defined for any integral parameter it can correspond to variations in any of the input parameters and it can be expressed in terms of any of the independent variables. Thus, the total number of sensitivity functions for a given system can be very large, and can be expressed in terms of different combinations of the independent variables. When the input parameter has discrete variations only, we shall refer to the sensitivity functions as sensitivity coefficients. 

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