Fundamental parameters

The eddy currents testing probe realization was satisfactory at the sight of the control and the testing results of coating samples. The fundamental parameters to keep in mind for a probe construction are ... 

The reactivity ratios of a copolymerization system are the fundamental parameters in terms of which the system is described. Since the copolymer composition equation relates the compositions of the product and the feedstock, it is clear that values of r can be evaluated from experimental data in which the corresponding compositions are measured. We shall consider this evaluation procedure in Sec. 7.7, where it will be found that this approach is not as free of ambiguity as might be desired. For now we shall simply assume that we know the desired r values for a system in fact, extensive tabulations of such values exist. An especially convenient source of this information is the Polymer Handbook (Ref. 4). Table 7.1 lists some typical r values at 60°C. 

In addition to the fundamental parameters of selectivity, capacity, and mass-transfer rate, other more practical factors, namely, pressure drop characteristics and adsorbent life, play an important part in the commercial viabiUty of a practical adsorbent. 

The fundamental parameters in the two main methods of achieving ignition are basically the same. Recent advances in the field of combustion have been in the development of mathematical definitions for some of these parameters. For instance, consider the case of ignition achieved by means of an electric spark, where electrical energy released between electrodes results in the formation of a plasma in which the ionized gas acts as a conductor of electricity. The electrical energy Hberated by the spark is given by equation 2 (1), where V = the potential, V 7 = the current. A 0 = the spark duration, s and t = time, s. 

The methodical elaboration is included for estimation of random and systematic errors by using of single factor dispersion analysis. For this aim the set of reference samples is used. X-ray analyses of reference samples are performed with followed calculation of mass parts of components and comparison of results with real chemical compositions. Metrological characteristics of x-ray fluorescence silicate analysis are established both for a-correction method and simplified fundamental parameter method. It is established, that systematic error of simplified FPM is less than a-correction method, if the correction of zero approximation for simplified FPM is used by preliminary established correlation between theoretical and experimental set data. 

Methods, those include theoretical corrections, fundamental parameters, regression in different modification. 

In this section, we summarize the fundamental parameters for carbon nanotubes, give the basic relations... 

A fundamental parameter characterizing the usefulness of a given precolumn for enrichment purposes is the breakthrough volume, Vg. This volume can be determined by monitoring continuously or discretely the detector signal at the outlet of the precolumn (35-37). The breakthrough volume can be defined by the following expression (37) ... 

The value Pcr, critical pressure, is a fundamental parameter of the nature of gas-containing melt flows below this critical point, the flow becomes two-phase. This point was established by C. D. Han and C. A. Villamizer [8] by direct observations of the flow in a transparent channel. Data presented by these authors pertain to the case of incomplete decomposition of the blowing agent prior to its entrance into the channel. Obviously, Pcr depends on the amount of gas. 

This fundamental parameter quantifies the relative affinity of an ion in the two phases, but it is not directly accessible experimentally because it is associated with a single ionic component. Therefore, to make or logP ° amenable to direct measurement,... 

Quantitative XRF analysis has developed from specific to universal methods. At the time of poor computational facilities, methods were limited to the determination of few elements in well-defined concentration ranges by statistical treatment of experimental data from reference material (linear or second order curves), or by compensation methods (dilution, internal standards, etc.). Later, semi-empirical influence coefficient methods were introduced. Universality came about by the development of fundamental parameter approaches for the correction of total matrix effects... 

Alternatively, fundamental parameter methods (FPM) may be used to simulate analytical calibrations for homogeneous materials. From a theoretical point of view, there is a wide choice of equivalent fundamental algorithms for converting intensities to concentrations in quantitative XRF analysis. The fundamental parameters approach was originally proposed by Criss and Birks [239]. A number of assumptions underlie the application of theoretical methods, namely that the specimens be thick, flat and homogeneous, and that, for calibration purposes, the concentrations of all the elements in the reference material be known (having been determined by alternative methods). The classical formalism proposed by Criss and Birks [239] is equivalent to the fundamental influence coefficient formalisms (see ref. [232]). In contrast to empirical influence coefficient methods, in which the experimental intensities from reference materials are used to compute the values of the coefficients, the fundamental influence coefficient approach calculates... 

There are two possible ways of XRF analysis used in fundamental parameter methods, namely analysis with and without standards. The intensity of the measured characteristic radiation 7 is related to the calculated intensity of radiation /icai... 

The use of fundamental parameters is attractive for various reasons. They impose fewer restrictions on the number of standards required for analysis. This simplifies the standardisation protocol for maintaining a XRF system, and permits greater flexibility in dealing with different types of materials. Inten-sity/concentration algorithms of the fundamental type, i.e. without recourse to the use of standards, have gradually developed [238-240] and are now widely available [241]. Functionality and quality of XRF software have reached a very high level, with a large variety of evaluation procedures and correction models for quantitative analysis, and calculation of fundamental parameter coefficients for effective matrix corrections. Nevertheless, there is still a need for accuracy improvement of fundamental parameters, such as the attenuation functions. 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

International or in-house standards in combination with fundamental parameters software, lead to the same accuracy as conventional analysis using regression analysis of standards. Provided that accurate standards are available, the main factors that determine the accuracy of XRF are the matrix absorption correction and (in the case of EDXRF) the spectrum evaluation programme, i.e. correction for spectral overlap and background. 

Thus, the fraction of dose absorbed is exponentially related to the absorption number. Equation (10) shows that the absorption number (and therefore the membrane permeability) is a fundamental parameter while other parameters such as the partition coefficient and pKa are useful guides but not fundamental parameters. For highly soluble drugs with linear absorption kinetics, dose and dissolution have no effect on the fraction of dose absorbed. In the case of drugs that are absorbed by a carrier-mediated process, a mean permeability should be used [30],... 

In conventional analyses of transport based on Fick s laws, the fundamental parameters that define the transport process are the solute diffusion coefficient in the polymer film, DM, and the partition coefficient, KP. Essentially, the diffusion coefficient defines how fast a solute molecule moves, and the partition coefficient... 

Fei He, Van Espen PJ (1991) General aspects for quantitative energy dispersive X-ray fluorescence analysis based on fundamental parameters. Anal Chem 63 2237... 

Absorption and clearance are two of the fundamental parameters that determine oral bioavailability. There are many in vitro methods to assess the absorption and metabolic potential of a given molecule, and it can be argued that a combination of these data should produce a model capable of predicting oral bioavailability. Such a model, based on a graphical approach has recently been published [26]. 

Fig. 2. The distribution of specific angular momentum in the dominant Galactic stellar populations. This indicates the similarity in this fundamental parameter, and presumably in origin, between bulge and halo (the two curves near the top left of the figure), and the quite distinct bahaviour of the Galactic thin and thick disks (the two curves through the centre of the figure). This figure is from Wyse Gilmore 1992.

Figure 2 above illustrates a similarity in at least one fundamental parameter between the Bulge and the stellar halo. The stellar halo traced by stars passing near the Sun is some 30% of its total mass of 2 x 109Mq. These stars are predominantly old and metal poor. They show remarkable uniformity in their relationship between the element ratios and the total metal abundance (Figure 1), with implications noted above. 

---