Vice-versa

For the case of a double-D coil we multiply each matrix element with an element shifted by a constant distance of the same line. This is done in x- and y-direction. The distance between the two elements is the correlation length X for filtering in x-direction and a second correlation length for the movement in y-direction. Thus one gets two new matrices Ax and Ax for the filtering from the left to the right (positiv x-direction) and vice versa (negativ x-direction). 

Side drilled holes are widely used as reference reflectors, especially when angle beam probes are used (e.g. for weld testing). However, the distance law of side drilled holes is different to that of a flat bottomed hole. In the literature [2] a conversion formula is given which allows to convert the diameter of a side drilled hole into the diameter of a flat bottomed hole and vice versa, valid in the far field only, and for diameters greater than 1.5 times the wave length. In practical application this formula can be used down to approximately one nearfield length, without making big mistakes. Fig. 2 shows curves recorded from real flat bottomed holes, and the uncorrected and corrected DGS curves. 

If a surface, typically a metal surface, is irradiated with a probe beam of photons, electrons, or ions (usually positive ions), one generally finds that photons, electrons, and ions are produced in various combinations. A particular method consists of using a particular type of probe beam and detecting a particular type of produced species. The method becomes a spectroscopic one if the intensity or efficiency of the phenomenon is studied as a function of the energy of the produced species at constant probe beam energy, or vice versa. Quite a few combinations are possible, as is evident from the listing in Table VIII-1, and only a few are considered here. 

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]. 

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. 

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. 

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... 

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... 

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),... 

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. 

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. 

In order to obtain appreciable conductivities, semiconductors must be doped witli small amounts of selected impurities. It is possible to switch tire doping type from n to p type, or vice versa, eitlier during tire growtli of a crystal or by tire selective introduction of impurities after tire growtli. The boundary region between tire p type and n type regions is... 

The question of determination of the phase of a field (classical or quantal, as of a wave function) from the modulus (absolute value) of the field along a real parameter (for which alone experimental determination is possible) is known as the phase problem [28]. (True also in crystallography.) The reciprocal relations derived in Section III represent a formal scheme for the determination of phase given the modulus, and vice versa. The physical basis of these singular integral relations was described in [147] and in several companion articles in that volume a more recent account can be found in [148]. Thus, the reciprocal relations in the time domain provide, under certain conditions of analyticity, solutions to the phase problem. For electromagnetic fields, these were derived in [120,149,150] and reviewed in [28,148]. Matter or Schrodinger waves were... 

Finally, and probably most importantly, the relations show that changes (of a nonhivial type) in the phase imply necessarily a change in the occupation number of the state components and vice versa. This means that for time-reversal-invariant situations, there is (at least) one partner state with which the phase-varying state communicates. 

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.)... 

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. 

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. 

The invariant measure corresponding to Aj = 1 has already been shown in Fig. 6. Next, we discuss the information provided by the eigenmeasure U2 corresponding to A2. The box coverings in the two parts of Fig. 7 approximate two sets Bi and B2, where the discrete density of 1 2 is positive resp. negative. We observe, that for 7 > 4.5 in (15) the energy E = 4.5 of the system would not be sufficient to move from Bi to B2 or vice versa. That is, in this case Bi and B2 would be invariant sets. Thus, we are exactly in the situation illustrated in our Gedankenexperiment in Section 3.1. 

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]. 

While the trivial and trade nomenclature in most cases has accidental character, the lUPAC Commission has worked out a series of rules [4] which allow the great majority of structures to be represented uniformly, though there still exists some ambiguity within this nomenclature. Thus, many structures can have more than one name. It is important that the rules of some dialects of the lUPAC systematic nomenclature are transformed into a program code. Thus, programs for generating the names from chemical structures, and vice versa (structures from names) have been created [5] (see Chapter II, Section 2 in the Handbook). 

The MEP at the molecular surface has been used for many QSAR and QSPR applications. Quantum mechanically calculated MEPs are more detailed and accurate at the important areas of the surface than those derived from net atomic charges and are therefore usually preferable [Ij. However, any of the techniques based on MEPs calculated from net atomic charges can be used for full quantum mechanical calculations, and vice versa. The best-known descriptors based on the statistics of the MEP at the molecular surface are those introduced by Murray and Politzer [44]. These were originally formulated for DFT calculations using an isodensity surface. They have also been used very extensively with semi-empirical MO techniques and solvent-accessible surfaces [1, 2]. The charged polar surface area (CPSA) descriptors proposed by Stanton and Jurs [45] are also based on charges derived from semi-empirical MO calculations. 

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. 

For the so-called one-point crossover a position within the chromosomes is randomly picked at the same position in both parents and the chromosomes are both cut at this position. Then the first part of chromosome 1 is concatenated with the second part of chromosome 2, and vice versa. This procedure is shown in Figure 9-29. 

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... 

It is always possible to convert internal to Cartesian coordinates and vice versa. However, one coordinate system is usually preferred for a given application. Internal coordinates can usefully describe the relationship between the atoms in a single molecule, but Cartesian coordinates may be more appropriate when describing a collection of discrete molecules. Internal coordinates are commonly used as input to quantum mechanics programs, whereas calculations using molecular mechanics are usually done in Cartesian coordinates. The total number of coordinates that must be specified in the internal coordinate system is six fewer... 

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). 

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