Linearity demonstration

Case 1. Linearity demonstrated from 50% of the ICH reporting limit to a nominal concentration of drug substance in the sample solution. In addition, no significant v-in(creep is observed (Figure 3.6). In this case, area percent calculation is suitable because the linearity range covers the responses of related substances and that of the drug substance in the sample solution. Therefore, these responses can be used directly to calculate the area percentage of each related substance. 

Case 3. Linearity demonstrated from 50% of the ICH reporting limit to 150% of the shelf life specification of a related substance, and a significant y-intercept is observed (Figure 3.8). Due to the significant -intercept, a single-point calibration (e.g., high-low or one-point external standard calibration) is not suitable. In this case, multiple-point external standard calibration is the most appropriate. See Section 3.3.3 for more discussion of the significant y-intercept. 

Figure 1.1 Partial pressure diagram of ethanol, C2H5OH, in logarithmic scale. The small deviation of the curve partial pressure p versus temperature T from linearity demonstrates that p(T) is not exactly exponential. The ethanol concentration scale c as a volume ratio refers to an ambient pressure of 1.013 105 Pa.

Dilutional linearity Demonstrate that high-concentration samples can be diluted into range with no hook effect Demonstrate low- and high-concentration samples can be diluted into range with acceptable accuracy and precision Demonstrate low- and high-concentration samples can be diluted into range with acceptable accuracy and precision... 

Plots of 1/Aod vs. time, shown in Fig. 18, (Aod = od -odt), are linear demonstrating the second order character of the reaction their slopes give therefore the dimerization... 

Fig.6a shows that the optical density, at the maximum optical absorbance wavelength = 376 nm, increases linearly with film thickness, up to approximately 0.4 pm. The linearity demonstrates that the film structure is independent of the number of deposited layers. When film thickness is further increased, the absorbance becomes so larg that the Lambert-Beer law is no longer satisfied. In Fig.6b the square root of the relative second-harmonic intensity is plotted versus the number of bilayers. 

In Fig. 3, it is shown the computing time for the system 1 fkg distributed on a number of nodes between 1 and 10. The behavior of the net is almost linear demonstrating a perfect distribution of the docking. 

Now let us return to the Kolm variational theory that was introduced in section A3.11.2.8. Here we demonstrate how equation (A3.11.46) may be evaluated using basis set expansions and linear algebra. This discussion will be restricted to scattering in one dimension, but generalization to multidimensional problems is very similar. 

Two-photon excited fluorescence detection at the single-molecule level has been demonstrated for cliromophores in cryogenic solids [60], room-temperature surfaces [61], membranes [62] and liquids [63, 64 and 65]. Altliough multiphoton excited fluorescence has been embraced witli great entluisiasm as a teclmique for botli ordinary confocal microscopy and single-molecule detection, it is not a panacea in particular, photochemical degradation in multiphoton excitation may be more severe tlian witli ordinary linear excitation, probably due to absorjDtion of more tlian tire desired number of photons from tire intense laser pulse (e.g. triplet excited state absorjDtion) [61],... 

The rupture force measured in AFM experiments is given, therefore, by the average slope of the energy profile minus a correction related to the effects of thermal fluctuations. Equation (11) demonstrates that the rupture force measured in AFM experiments grows linearly with the activation energy of the system (Chilcotti et ah, 1995). A comparison of (10) and (11) shows that the unbinding induced by stiff springs in SMD simulations, and that induced by AFM differ drastically, and that the forces measured by both techniques cannot be readily related. 

In our treatment of molecular systems we first show how to determine the energy for a given iva efunction, and then demonstrate how to calculate the wavefunction for a specific nuclear geometry. In the most popular kind of quantum mechanical calculations performed on molecules each molecular spin orbital is expressed as a linear combination of atomic orhilals (the LCAO approach ). Thus each molecular orbital can be written as a summation of the following form ... 

It has been demonstrated that a given eleetronie eonfiguration ean yield several spaee- and spin- adapted determinental wavefunetions sueh funetions are referred to as eonfiguration state funetions (CSFs). These CSF wavefunetions are not the exaet eigenfunetions of the many-eleetron Hamiltonian, H they are simply funetions whieh possess the spaee, spin, and permutational symmetry of the exaet eigenstates. As sueh, they eomprise an aeeeptable set of funetions to use in, for example, a linear variational treatment of the true states. 

For both types of orbitals, the coordinates r, 0, and (j) refer to the position of the electron relative to a set of axes attached to the center on which the basis orbital is located. Although Slater-type orbitals (STOs) are preferred on fundamental grounds (e.g., as demonstrated in Appendices A and B, the hydrogen atom orbitals are of this form and the exact solution of the many-electron Schrodinger equation can be shown to be of this form (in each of its coordinates) near the nuclear centers), STOs are used primarily for atomic and linear-molecule calculations because the multi-center integrals < XaXbl g I XcXd > (each... 

The following short descriptions of the steps involved in the synthesis of a tripeptide will demonstrate the complexity of the problem amino acid units. In the later parts of this section we shall describe actual syntheses of well defined oligopeptides by linear elongation reactions and of less well defined polypeptides by fragment condensation. 

The swelling of the adsorbent can be directly demonstrated as in the experiments of Fig. 4.27 where the solid was a compact made from coal powder and the adsorbate was n-butane. (Closely similar results were obtained with ethyl chloride.) Simultaneous measurements of linear expansion, amount adsorbed and electrical conductivity were made, and as is seen the three resultant isotherms are very similar the hysteresis in adsorption in Fig. 4.27(a), is associated with a corresponding hysteresis in swelling in (h) and in electrical conductivity in (c). The decrease in conductivity in (c) clearly points to an irreversible opening-up of interparticulate junctions this would produce narrow gaps which would function as constrictions in micropores and would thus lead to adsorption hysteresis (cf. Section 4.S). 

Polyesters were initially discovered and evaluated ia 1929 by W. H. Carothers, who used linear aliphatic polyester materials to develop the fundamental understanding of condensation polymerisation, study the reaction kinetics, and demonstrate that high molecular weight materials were obtainable and could be melt-spun iato fibers (1 5). 

Subsequent studies (63,64) suggested that the nature of the chemical activation process was a one-electron oxidation of the fluorescer by (27) followed by decomposition of the dioxetanedione radical anion to a carbon dioxide radical anion. Back electron transfer to the radical cation of the fluorescer produced the excited state which emitted the luminescence characteristic of the fluorescent state of the emitter. The chemical activation mechanism was patterned after the CIEEL mechanism proposed for dioxetanones and dioxetanes discussed earher (65). Additional support for the CIEEL mechanism, was furnished by demonstration (66) that a linear correlation existed between the singlet excitation energy of the fluorescer and the chemiluminescence intensity which had been shown earher with dimethyl dioxetanone (67). 

---