The above equation enables us to calculate the equilibrium constant for any value of AG or vice versa, and we readily see that for a reaction to go to completion , i.e. for K to be large, AG needs to be large and negative. [Pg.66]

Very finely divided minerals may be difficult to purify by flotation since the particles may a ere to larger, undesired minerals—or vice versa, the fines may be an impurity to be removed. The latter is the case with Ii02 (anatase) impurity in kaolin clay [87]. In carrier flotation, a coarser, separable mineral is added that will selectively pick up the fines [88,89]. The added mineral may be in the form of a floe (ferric hydroxide), and the process is called adsorbing colloid flotation [90]. The fines may be aggregated to reduce their loss, as in the addition of oil to agglomerate coal fines [91]. [Pg.477]

In tlie case of mutual AB exchange this matrix can be simplified. The equilibrium constant must be 1, so /r k . Also, is equal to Mg and vice versa, and the couplmg constant is the same. For instance, if L is the Liouville matrix for one site, then the Liouville matrix for the other site is P LP, where P is the matrix describing the pemuitation. [Pg.2102]

A structure drawn by a molecular editor such as ISIS Draw) can be translated by the data conversion program AutoNom into a lUPAC name, and vice versa, by exchanging structure information through a ROSDAL string [18, 19]. [Pg.26]

An advantage of PCA is its ability to cope with almost any kind of data matrix, e.g., it can also deal with matrices with many rows and few columns or vice versa. [Pg.448]

In the presence of charcoal, chlorine and hydrogen combine rapidly, but without explosion, in the dark. A jet of hydrogen will bum in chlorine with a silvery flame and vice versa. [Pg.321]

Figure 9-29. Crossover the parent chroinosoines are both cut at the crossover position, and the first part of chromosoine 1 is concatenated with the second part of chromosoine 2, and vice versa. |

Ac this point It is important to emphasize that, by changing a and p, it is not possible to pass to the limit of viscous flow without simultaneously passing to the limit of bulk diffusion control, and vice versa, since physical estimates of the relative magnitudes of the factors and B [Pg.39]

Once again, these fluxes are not all independent and some care must be taken to rewrite everything so that syimnetry is preserved [12]. Wlien this is done, the Curie principle decouples the vectorial forces from the scalar fluxes and vice versa [9]. Nevertheless, the reaction temis lead to additional reciprocal relations because [Pg.702]

As for CIDNP, the polarization pattern is multiplet (E/A or A/E) for each radical if Ag is smaller than the hyperfme coupling constants. In the case where Ag is large compared with the hyperfmes, net polarization (one radical A and the other E or vice versa) is observed. A set of mles similar to those for CIDNP have been developed for both multiplet and net RPM in CIDEP (equation (B1.16.8) and equation (B1.16.9)) [36]. In both expressions, p is postitive for triplet precursors and negative for singlet precursors. J is always negative for neutral RPs, but there is evidence for positive J values in radical ion reactions [37]. In equation (B 1.16.8), [Pg.1607]

Intrinsic defects (or native or simply defects ) are imperfections in tire crystal itself, such as a vacancy (a missing host atom), a self-interstitial (an extra host atom in an otherwise perfect crystalline environment), an anti-site defect (in an AB compound, tliis means an atom of type A at a B site or vice versa) or any combination of such defects. Extrinsic defects (or impurities) are atoms different from host atoms, trapped in tire crystal. Some impurities are intentionally introduced because tliey provide charge carriers, reduce tlieir lifetime, prevent tire propagation of dislocations or are otlierwise needed or useful, but most impurities and defects are not desired and must be eliminated or at least controlled. [Pg.2884]

The linear response of a system is detemiined by the lowest order effect of a perturbation on a dynamical system. Fomially, this effect can be computed either classically or quantum mechanically in essentially the same way. The connection is made by converting quantum mechanical conmuitators into classical Poisson brackets, or vice versa. Suppose tliat the system is described by Hamiltonian where denotes an [Pg.708]

The crossover operator is applied to the selected pairs of parents with a probability a typical value being 0.8 (i.e. there is an 80% chance that any of the p/2 pairs will actually undergo this type of recombination). Following the crossover phase mutation is appUed to all individuals in the population. Here, each bit may be inverted (0 to 1 and vice versa) with a probability P. The mutation operator is usually assigned a low probability (e.g. 0.01). [Pg.497]

The paradox involved here ean be made more understandable by introdueing the eoneept of entropy ereation. Unlike the energy, the volume or the number of moles, the entropy is not eonserved. The entropy of a system (in the example, subsystems a or P) may ehange in two ways first, by the transport of entropy aeross the boundary (in this ease, from a to P or vice versa) when energy is transferred in the fomi of heat, and seeond. [Pg.339]

Defining order in an amorphous solid is problematic at best. There are several qualitative concepts that can be used to describe disorder [7]. In figure Al.3.28 a perfect crystal is illustrated. A simple fonn of disorder involves crystals containing more than one type of atom. Suppose one considers an alloy consisting of two different atoms (A and B). In an ordered crystal one might consider each A surrounded by B and vice versa. [Pg.130]

The topological (or Berry) phase [9,11,78] has been discussed in previous sections. The physical picture for it is that when a periodic force, slowly (adiabatically) varying in time, is applied to the system then, upon a full periodic evolution, the phase of the wave function may have a part that is independent of the amplitude of the force. This part exists in addition to that part of the phase that depends on the amplitude of the force and that contributes to the usual, dynamic phase. We shall now discuss whether a relativistic electron can have a Berry phase when this is absent in the framework of the Schrddinger equation, and vice versa. (We restrict the present discussion to the nearly nonrelativistic limit, when particle velocities are much smaller than c.) [Pg.166]

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