First kind limit

Electrodes of the first kind have only limited application to titration in non-aqueous media a well-known example is the use of a silver electrode in the determination of sulphides and/or mercaptans in petroleum products by titration in methanol-benzene (1 1) with methanolic silver nitrate as titrant. As an indicator electrode of the second kind the antimony pH electrode (or antimony/antimony trioxide electrode) may be mentioned its standard potential value depends on proton solvation in the titration medium chosen cf., the equilibrium reaction on p. 46). 

A first kind of these insurance products are called "catastrophe bonds" and consist in securitizing environmental risks in bonds, which could be sold to high-yield investors. The catastrophe bonds are able to transfer risk to investors that receive coupons that are normally a reference rate plus an appropriate risk premium. By these products, insurance companies limit risk exposure transferring natural catastrophe risk into the capital markets. In this way, with the involvement of the financial markets, their global size offers enormous potential for insurers to diversify risks. 

If an analytical test results in a lower value x, < x0, then the customer may reject the product as to be defective. Due to the variation in the results of analyses and their evaluation by means of statistical tests, however, a product of good quality may be rejected or a defective product may be approved according to the facts shown in Table 4.2 (see Sect. 4.3.1). Therefore, manufacturer and customer have to agree upon statistical limits (critical values) which minimize false-negative decisions (errors of the first kind which characterize the manufacturer risk) and false-positive decisions (errors of the second kind which represent the customer risk) as well as test expenditure. In principle, analytical precision and statistical security can be increased almost to an unlimited extent but this would be reflected by high costs for both manufacturers and customers. 

As can be seen from the distribution function B in Fig. 7.8, an analytical value Xacv produces only in 50% of all cases signals y > yc. Whereas the error of the first kind (classifying a blank erroneously as real measurement value) by the choice of k = 2... 3 can be aimed at a 0.05, the error of the second kind (classifying a real measured value erroneously as blank) amounts /) 0.5. Therefore, this analytical value -which sometimes, promoted by the early publications of Kaiser [1965, 1966], plays a certain role in analytical detection - do not have any significance as a reporting limit in case of y < yc, when no relevant signal have been found. For this purpose, the limit of detection, Xio, has to be used. 

The first kind of simplification exclusively concerns the size of the basis set used in the linear combination of one center orbitals. Variational principle is still fulfilled by this type of "ab initio SCF calculation, but the number of functions applied is not as large as necessary to come close to the H. F. limit of the total energy. Most calculations of medium-sized structures consisting for example of some hydrogens and a few second row atoms, are characterized by this deficiency. Although these calculations belong to the class of "ab initio" investigations of molecular structure, basis set effects were shown to be important 54> and unfortunately the number of artificial results due to a limited basis is not too small. 

For example, if two means are being compared, and we want to limit the error of the first kind to a= 0 05, and we have 15 degrees of freedom in the data. 

The solution of the first kind is stable and arises as the limit, t —> oo, of the non-stationary kinetic equations. Contrary, the solution of the second kind is unstable, i.e., the solution of non-stationary kinetic equations oscillates periodically in time. The joint density of similar particles remains monotonously increasing with coordinate r, unlike that for dissimilar particles. The autowave motion observed could be classified as the non-linear standing waves. Note however, that by nature these waves are not standing waves of concentrations in a real 3d space, but these are more the waves of the joint correlation functions, whose oscillation period does not coincide with that for concentrations. Speaking of the auto-oscillatory regime, we mean first of all the asymptotic solution, as t —> oo. For small t the transient regime holds depending on the initial conditions. 

There is currently no air quality regulation in Europe or any other part of the world to control the ambient concentrations of particles on a number basis. However, particle numbers are currently being regulated at vehicle tailpipe exhausts through Euro-5 and Euro-6 emission standards [103]. These are the first ever limits of this kind, though only applicable in Europe, to control the emissions of particle numbers at source. These standards include a lower size limit of 23 nm for minimising the... 

Remember a confidence limit of a mean one mistake can be to exclude a value which in fact belongs to the interval around the mean, i.e. to exclude a correct value, another mistake would be to include a wrong value. Hence we have two kinds of error a type I error associated with a probability, a, of an error of the first kind, and a type II error with a probability, / , of an error of the second kind. The relationship between H0 and these errors are explained in Tab. 2-1. 

Conventional testing tables for correlation coefficients, as described in Section 2.4.2, can be used to test the significance of autocorrelation or cross-correlation coefficients in terms of their dependence on the degrees of freedom. In the following figures, these critical values for a 5% risk of an error of the first kind are called significance limits. 

There are three classes of instruments for the measurement of VCD. The first is based on a dispersive grating monochromator as the source of wavelength discrimination. This was the first kind of VCD instrument to be built and this design was used in the discovery of VCD in 1974 [1]. The early versions of these instruments have been described in detail [3,4,44-47], The low-frequency limit was initially 1900 cm"l, the cut-off of the InSb detector. Using a PbSnTe detector the low-frequency limit was extended to 1550 cm l [46], and subsequently using HgCdTe detectors the limit was lowered to 1250 cm l[48] and then 900 cm l [49], and finally using a Si As detector it was lowered to 650 cm l [50]. 

This is the original Christoffel-Darboux formula that includes only the polynomials of the first kind [47,48]. The formula (151) with mixed polynomials Pn and Qm has no meaning at u = u. However, this is not so in the case of Eq. (152), which is well defined in the limit u —> u. The indeterminate expression 0/0 is regularized by the THopital rule which gives ... 

Gas-stream cryostats. These were the first kind of setup available. Their advantage is that they are cheap and that no shields or windows are required (no absorption, no parasitic scattering). The device is fixed while the crystal rotates in the cold gas stream. With nitrogen the limit temperature is about 100 K helium is rarely used since it cannot be recuperated easily in such an arrangement. The reliability is not particularly good. Icing... 

This discussion has shown that the diffraction pattern can reveal three types of disorder, as discussed fully by several authors (Wiener and White, 1991a Blaurock, 1982 Hosemann and Bagchi, 1962). Thermal disorder is generally referred to as disorder of the first kind and lattice disorder as disorder of the second kind. The disorder due to the mosaic nature of the sample is referred to as orientational disorder. Thermal disorder and small amounts of orientational disorder are not particularly troublesome in the diffraction experiment. Lattice disorder, on the other hand, can be extremely problematic because one can never achieve a fully resolved image of the stmcture since there are too few stmcture factors available to obtain a faithful model. Thermal disorder simply means that the position of the atoms are .smeared in some fashion, determined by the equation of state of the molecules. If the lattice is excellent so that all of the stmcture factors observable within the limits of the... 

Jacobi polynomials depends on the particular problem at hand. If one is concerned with physical insight into an isotope eflEect, the expansion should be carried out using the minimum number of terms. That is, a set of polynomials which make the expansion for the system converge as rapidly as possible should be chosen. On the other hand, if the expansion is being used to evaluate thermodynamic quantities numerically, the limitation on the number of terms carried in the expansion is not as critical. For efficiency of computation, one would still like to have reasonably rapid convergence, and as has been demonstrated in the previous sections, this can be achieved by use of a single Jacobi polynomial, such as the shifted Chebyshev of the first kind, for the entire range of i/-values. 

We shall consider two extreme kinds of systems. In the first kind, the system is a conductor and by application of a voltage between two electrodes (for the sake of simplicity the two electrodes will be taken parallel) a current flows from one electrode to another. The failure occurs when the current density becomes larger than a threshold value. Consequently, the system becomes nonconducting. The system behaves exactly as a fuse which is destroyed when the current is too large. We shall call this failure the fuse failure. In the second case, the system is a perfect insulator and a voltage is applied between the two electrodes. Again, beyond a definite (threshold) value of the electric field, the system breaks down and becomes conducting. This phenomenon is well-known in the physics of dielectrics, since it limits the application of dielectrics as insulators. We shall talk about the dielectric problem for this kind of failure. 

The mixed crystals of the first kind which we shall call a crystals, are isomorphous with crystals of pure mercury they are deposited within liquid mixtures containing a proportion of cadmium less than a certain limit if we attribute the index 1 to mercury and the index 2 to cadmium, and if we keep the notation... 

In particular, for the conjugate acid-base pair Ax/Bx, which is located on the acidity scale over the acid-base range of the solvent L of the first kind (see Fig. 1.1.1), the complete transformation into conjugate acid with the formation of the equivalent concentration of the base of the solvent will be observed. It should be added that the acid formed would possess no acidic properties in the said solvent. Similarly, the conjugate pair A2/B2 is completely transformed into the conjugate base, which shows no basicity in the solvent. Hence, the acid-base ranges in solvents of the first kind are limited on two sides. 

Consequently, solvents of the first kind may be characterized by the limit of the levelling of acidic properties, equal to pA = pKa, by the neutrality point located at pA = pKa + 1/2 pKs, where Ks is the constant of the intrinsic acid-base dissociation, and by the limit of the strength of bases... 

Therefore, melts-solvents of the first kind are of interest in the following scientific aspects determination of the acid-base product of the ionic solvent and estimation of the upper limit of acidity of these solvents (such as nitrates, sulfates). The decrease of stability of the solvent acid can be used for the stepwise decomposition of acidic solutions of cations and synthesis of complex oxide compounds and composites by coprecipitation [53-56], It is possible to obtain complex oxides containing alkali metals by precipitation of multivalent metal oxides with the alkali metal oxide as a strong Lux base, as was reported by Hong et al., who used 0.59LiNO3-0.41LiOH mixed melt to obtain electrochemically active lithium cobaltate, LiCo02 [57]. 

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