Fixed identities

The gain used for the amplification of the two sensor signal outputs is not exactly identical. This is because of the fact that the gain of each amplifier is regulated by a potentiometer whose resistance is varied using a manual setscrew. Thus it is virtually impossible to fix identical gain for the two amplifiers. 

Figure Bl.6.12 Ionization-energy spectrum of carbonyl sulphide obtained by dipole (e, 2e) spectroscopy [18], The incident-electron energy was 3.5 keV, the scattered incident electron was detected in the forward direction and the ejected (ionized) electron detected in coincidence at 54.7° (angular anisotropies cancel at this magic angle ). The energy of the two outgoing electrons was scaimed keeping the net energy loss fixed at 40 eV so that the spectrum is essentially identical to the 40 eV photoabsorption spectrum. Peaks are identified with ionization of valence electrons from the indicated molecular orbitals.

Equation (Bl.8.6) assumes that all unit cells really are identical and that the atoms are fixed hi their equilibrium positions. In real crystals at finite temperatures, however, atoms oscillate about their mean positions and also may be displaced from their average positions because of, for example, chemical inlioniogeneity. The effect of this is, to a first approximation, to modify the atomic scattering factor by a convolution of p(r) with a trivariate Gaussian density function, resulting in the multiplication ofy ([Pg.1366]

In all of these stmctures the atomic positions are fixed by the space group syimnetry and it is only necessary to detennine which of a small set of choices of positions best fits the data. According to the theory of space groups, all stmctures composed of identical unit cells repeated hi three dimensions must confomi to one of 230 groups tliat are fomied by coinbinmg one of 14 distinct Bmvais lattices with other syimnetry operations. 

It turns out that the permutations P ean be allowed either to aet on the "names" or labels of the eleetrons, keeping the order of the spin-orbitals fixed, or to aet on the spin-orbitals, keeping the order and identity of the eleetrons labels fixed. The resultant wavefunetion, whieh eontains N terms, is exaetly the same regardless of how one allows the permutations to aet. Beeause we wish to use the above eonvention in whieh the order of the eleetronie labels remains fixed as 1,2, 3,... N, we ehoose to think of the permutations aeting on the names of the spin-orbitals. 

It is sufficient, as Sing has pointed out, merely to replace as normalizing factor by the amount adsorbed at some fixed relative pressure (p/p ), in practice taken as (p/p°), = 0-4. The normalized adsorption n/ o (= j). obtained from the isotherm on a reference sample of the solid, is then plotted against p/p°, to obtain a standard a,-curve rather than a t-curve. The a,-curve can then be used to construct an a,-plot from the isotherm of a test sample of the solid, just as the t-curve can be used to produce a t-plot. If a straight line through the origin results, one may infer that the isotherm under test is identical in shape with the standard the slope b, of the linear branch of the j-plot will be equal totio 4 Just as the slope b, of the t-plot was equal to nja (cf. Equation (2.34)). 

Let X G 2 be an arbitrary fixed element. Using the Galerkin method (see, for instance, Mikhailov, 1976), we can prove that there is a unique function 9 G Si satisfying the identity... 

Cost Calculation. The main elements determining production cost are identical for fine chemicals and commodities (see Economic evaluation), a breakdown of production cost is given in Table 2. In multipurpose plants, where different fine chemicals occupying the equipment to different extents are produced during the year, a fair allocation of costs is a more difficult task. The allocation of the product-related costs, such as raw material and utiHties, is relatively easy. It is much more difficult to allocate for capital cost, labor, and maintenance. A simplistic approach is to define a daily rent by dividing the total yearly fixed cost of the plant by the number of production days. But that approach penalizes the simple products using only part of the equipment. 

Solubility. Sohd—Hquid equihbrium, or the solubiHty of a chemical compound in a solvent, refers to the amount of solute that can be dissolved at constant temperature, pressure, and system composition in other words, the maximum concentration of the solute in the solvent at static conditions. In a system consisting of a solute and a solvent, specifying system temperature and pressure fixes ah. other intensive variables. In particular, the composition of each of the two phases is fixed, and solubiHty diagrams of the type shown for a hypothetical mixture of R and S in Figure 2 can be constmcted. Such a system is said to form an eutectic, ie, there is a condition at which both R and S crystallize into a soHd phase at a fixed ratio that is identical to their ratio in solution. Consequently, there is no change in the composition of residual Hquor as a result of crystallization. 

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