Subject critical value

As we discussed previously that if the shear rate increases continuously, the film is subjected to a growing shear stress, which will eventually reach a critical value that results in the slip either at the wall-lubricant interface or within the films. This provides additional information about... 

In the duo-trio test one presents to each panellist (or subject ) an identified reference sample, followed by two coded samples, one of which matches the reference sample (Fig. 38.2). The subjects are asked to indicate which of the two coded samples matches the reference. If enough correct replies are obtained the two coded samples are perceived as different. Table 38.2 gives the critical values... 

For this reason, a number of analysts uses a further limit quantity, namely the limit of quantification, xLq, (limit of determination), from which on the analyte can be determined quantitatively with a certain given precision (Kaiser [1965, 1966] Long and Winefordner [1983] Currie [1992, 1995, 1997] IUPAC [1995] Ehrlich and Danzer [2006]). This limit is not a general one like the critical value and the detection limit which are defined on an objective basis. In contrast, the limit of quantification is a subjective measure depending on the precision, expressed by the reciprocal uncertainty xLq/AxLq = k, which is needed and set in advance. The limit of quantification can be estimated from blank measurements according to... 

Continuing from our previous discussion in Chapter 18 from reference [1], analogous to making what we have called (and is the standard statistical terminology) the a error when the data is above the critical value but is really from P0, this new error is called the [3 error, and the corresponding probability is called the (3 probability. As a caveat, we must note that the correct value of [3 can be obtained only subject to the usual considerations of all statistical calculations errors are random and independent, and so on. In addition, since we do not really know the characteristics of the alternate population, we must make additional assumptions. One of these assumptions is that the standard deviation of the alternate population (Pa) is the same as that of the hypothesized population (P0), regardless of the value of its mean. 

The [10°] off axis tension specimen shown in Fig 3.23 is another simple specimen similar in geometry to that of the [ 45 ]s tensile test. This test uses a unidirectional laminate with fibers oriented at 10° to the loading direction and the biaxial stress state (i.e. longitudinal, transverse and in-plane shear stresses on the 10° plane) occurs when it is subjected to a uniaxial tension. When this specimen fails under tension, the in-plane shear stress, which is almost uniform through the thickness, is near its critical value and gives the shear strength of the unidirectional fiber composites based on a procedure (Chamis and Sinclair, 1977) similar to the [ 45°]s tensile test. 

The null distribution for the t-test depended on the number of subjects in the trial. For the chi-square test comparing two proportions, and providing the sample size is reasonably large, this is not the case the null distribution is always x i- As a consequence we become very familiar with x i- The critical value for 5 per cent significance is 3.841 while 6.635 cuts off the outer 1 per cent probability and 10.83 cuts off the outer 0.1 per cent. 

Assuming normally distributed sampling and analysis errors (and no bias), the NIOSH accuracy standard is met if the true coefficient of variation of the total error, denoted by CVp, is no greater than 0.128. However, estimates of CVp (denoted by CVp), which were obtained in the laboratory validations, are themselves subject to appreciable random errors of estimation. Therefore, a "critical value" for the CVp was needed (i.e. the value not to be exceeded by an experimental CVp if the method is to be judged acceptable). 

The critical value of CVp has to be lower than the maximum permissible true value (e.g. lower than CVp 0.128 when there is no bias). The maximum permissible value of the true CVp will be referred to as its "target level". In order to have a confidence level of 95% that a subject method meets this required target level, on the basis of CVp estimated from laboratory tests, an upper confidence limit for CVp is calculated which must satisfy the following criterion reject the method (i.e. decide it does not meet the accuracy standard) if the 95% upper confidence limit for CVp exceeds the target level of CVp. Otherwise, accept the method. This decision criterion was implemented in the form of the Decision Rule given below which is based on assumptions that errors are normally distributed and the method is unbiased. Biased methods are discussed further below. 

Induction of New Phenomena by Imposed Gradients. Studies on the effects of imposed electric fields on chemical waves (see below on signal propagation) show that phenomena can be induced in the system by the imposed gradient that do not exist in the field free medium. For example, it was found (l l) that for a system wherein only one type of wave existed in the field free case, two stable types of waves exist in the system subject to the field. This "induction of multiplicity" implies that beyond a critical value of the applied field strength new phenomena may set in that are not simple distortions of field free patterns. Another strictly imposed field effect is found in the case of a new two dimensional crescent shaped wave that occurs when a circular wave is subjected to a supracritical field (15). 

Well-known yield criteria are the Tresca criterion and the Von Mises criterion. Discussion of this subject falls beyond the scope of this book, but a clear description is presented in, e.g. the monograph of Ward and Hadley (1993). If stresses increase above a certain value yield will occur. For metals this critical value is almost independent of pressure, whereas for polymers it is strongly dependent on pressure. An example is shown in Fig. 13.72 for PMMA in Sect. 13.5.4. 

All our discussion has assumed that our branched structures are robust. But they are in fact subjected to significant hydrodynamic tensions. Consider a star polymer under a current J largerthan Jcl. Then we shall meet situations where one (or a few) arm(s) has entered the tube, while the central nodule is still stuck at the entry as in Fig. 3b. If is the length of tube which has been invaded by the arm(as in Sect. 2.3), the hydrodynamic force qv/, may be large, and can possibly reach the threshold force xm for rupture near the nodule. This leads to a critical value m ... 

The use of adsorption isotherms is subject to both theoretical and experimental limitations. There is effectively a minimum relative pressure value specific to each adsorbate (e.g. P/Pq = 0.42 for nitrogen, 0,2 for CCI4) which corresponds to the minimum value of the surface tension for the phase to remain in liquid form. Below this critical value, the liquid adsorbate is unstable and vaporises spontaneously, an effect represented on the desorption curves by a sharp drop in the adsorbed volume. Depending on the significance of this variation, the porous distribution calculated from the desorption data may show an artefact in the pore size domain corresponding to this process (3-4 nm in diameter). For a porous solid where this phenomenon occurs, it is advisable to study the adsorption curve. 

Irwin (40) gave an alternative formulation to fracture by considering the distribution or field of stresses around a crack in an elastic material. He proposed that such a distribution could be expressed as a function of a parameter K, known as the stress intensity factor, and he established that the fracture would occur when K exceeds a critical value characteristic of each material. Figure 14.33 shows a sharp crack of length 2a in an infinite lamina subjected to a tensile stress ct. The equations defining the local stresses an, a22 < 12 are (42)... 

However, as noted in the discussion on the LRT (Section 12.6.1), the test tends to be conservative for fixed effects, suggesting that the actual critical value for the LRT statistic may be larger than 3.84. Moreover, the number of samples per subject and the sample size may also affect the theoretical critical value, as the likelihood ratio is asymptotically distributed. Previous work also indicated that the likelihood... 

Sample Size Subjects on Interacting Drug (%) Interindividual Variability (%CV) Type I Error Empirica Critical Value... 

Thus, for two free surfaces, the eigenvalue problem for a is reduced to finding a nontrival solution of Eq. (12-199), subject to the six boundary conditions, (12-200), (12-203), and (12-204). In particular, let us suppose that we specify Pr, Gr, and a2 (the wave number of the normal model of perturbation). There is then a single eigenvalue for a such that / / 0. If Real(er) < 0 for all a, the system is stable to infinitesimal disturbances. On the other hand, if Real(er) > 0 for any a, it is unconditionally unstable. Stated in another way, the preceding statements imply that for any Pr there will be a certain value of Gr such that all disturbances of any a decay. The largest such value of Gr is called the critical value for linear stability. 

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