The Intuitive Explanation of

The dislocation image lies to one side of the dislocation, in agreement with the intuitive explanation of the origin of dislocation contrast given in Section 5.1. 

Anyway, the interpretation of the interactions as a polarization consequence allows the intuitive explanation of a set of experimental observations. Thus, CaC03 - variety of calcite with the same stmcture such as MgCOj - decomposes to an higher temperature (the decomposition starts about 500°C while MgCOj decomposes at 300°C). 

How can we predict whether a given cycloaddition reaction will occur with suprafacial or with antarafacial geometry According to frontier orbital theory, a cycloaddition reaction takes place when a bonding interaction occurs between the HOMO of one reactant and the LUMO of the other. An intuitive explanation of this rule is to imagine that one reactant donates electrons to the other. As with elec-trocyclic reactions, it s the electrons in the HOMO of the first reactant that are least tightly held and most likely to be donated. But when the second reactant accepts those electrons, they must go into a vacant, unoccupied orbital—the LUMO. 

An intuitive explanation of biofilm drug resistance is that antimicrobial compounds are physically excluded from the community by the barrier properties of the glycocalyx. Such intuition however envisages that the glycocalyx functions as a biocide-impermeable umbrella, but since it generally possesses a diffusivity approximating that... 

On the plus side, the integration of the error allows us to detect and eliminate very small errors. To make a simple explanation of why integral control can eliminate offsets, refer back to our intuitive explanation of offset with only a proportional controller. If we desire e = 0 at steady state, and to shift controller output p away from the previous bias ps, we must have a nonzero term. Here, it is provided by the integral in Eq. (5-5). That is, as time progresses, the integral term takes on a final nonzero value, thus permitting the steady state error to stay at zero. 

We have already discussed the physical reason for the effect of the parameters h and K on the indirect correlation (Section 4.5) or, equivalently, on the induced conformational changes. But we still need an intuitive explanation of the effect of q. Why does q = 1 mean no communication between the sites Why does q < 1 result in positive indirect cooperativity or, equivalently, induces conformational change in the second subunit in the same direction as in the first subunit And why does q > 1 have the opposite effect ... 

Intuitive Explanation of Passionate Mistakes 225 Figure 7.1 The Effect of Appetite in an Exponentially Discounted Model... 

FIGURE 7.4 Intuitive explanation of the spontaneous formation of emulsion droplets from a SEDDS. 

This chapter continues with a description of a few basic numerical methods and their underlying principles. However, a solid first course in numerical analysis cannot be replaced by the concise intuitive explanations of numerical methods and phenomena that follow below. 

This mesomeric picture gives an intuitive explanation of the higher s character of the C-H equatorial bond, as it indicates a measure of sp2 hybridization in this case. One should then be tempted to draw a mesomeric picture showing similar delocalization in axial C 1—H and 05—H bonds, and moreover to extend such representations to ordinary ethers. However calculations for methanol and dimethyl ether in the staggered conformation predict that the effect should be much smaller for these compounds. In this respect, we may mention that the practical significance of the interaction of the oxygen p-type lone pair with the antiperiplanar OH bond in methanol has been recently questioned (20). So the effect discussed in this section may be restricted to the pyranose-like, acetal or mixed acetal type of compounds. 

Although the intuitive model of disordered interfaces between nanocrystals has provided an explanation of the reported high diffusion coefficients in these samples, it will be seen later that this is unrealistic. The nature of the interfaces depends on the method of sample preparation, and these can be highly ordered, akin to grain boundaries in bulk samples. Thus, other explanations must be sought and, in the case of ionic materials, these have been based on surface space-charge and surface texture approaches. 

Obviously the Lewis theory of valence is unable to provide any satisfactory explanation of the stability and the physical origin of the chemical bond. Moreover, Lewis did not really understand the mechanism of the pairing of electrons. However, as shown below, quantum mechanics confirms very nicely most of the intuitive ideas of Lewis and consequently the essential features of its chemical formulas. 

Several intuitive explanations of IZE seen in Fig. 26 are at hand. From the point of view of constructive and destructive interference one can say that since the linear coupling effectively changes the phase relations among interacting modes, the destructive interference of subsequent pump photon decays caused by phase mismatch is suppressed in the same way as the constructive interference has been suppressed in the case of perfectly matched interaction. 

Although the physical basis of TS imbalance is not well understood, one intuitive explanation of the current case is that in 4 the ring oxygen is a good 7r-bond donor because of its lone pair electrons but Cl is a very poor 7r-bond acceptor because it is maintained in an sp -hybridized state by its bond to Nl. There is not a concomitant increase in ici-04 as the Cl - Nl bond is broken because Cl remains a poor 7r-bond acceptor in the continued presence of the Cl -Nl bond. It is only as the Cl -Nl bond becomes almost completely broken that Cl becomes a good 7r-bond acceptor and ci-o4 increases sharply (Fig. 8). 

In the introduction to this chapter we gave an intuitive explanation of the origin of nonlinear optical effects and stressed the key role played by high power lasers and coherent light beams. These two concepts are defined here. We will describe one specific characteristic of laser light, namely the absorption saturation, and finally we will discuss susceptibility and frequency conversion of light. 

The fortuitous near-degeneracy of the levels poses severe difficulties to a complete quantitative description of the process in the too-many level small-molecule limit, and even in the small-molecule limit itself. The interaction potentials are poorly known. It is still unclear why collisional processes proceed on a much more rapid time scale in electronically excited states than in ground electronic states. The intuitive explanation, that the excited states are larger, is insufficient. An analysis of the excited potential energy surfaces should prove enlightening in this regard. 

The following section presents an intuitive explanation of the B-S model, in terms of the normal distribution of asset price returns. 

We first provide an intuitive explanation of the logic and then define its formal syntax and semantics. 

This recaptured much of the intuitive picture of bonding because now atomic orbitals could be sketched and bonds drawn where these orbitals overlapped. The device offered an explanation for bonding in many molecules, and where it failed— as in the tetrahedral bonding of carbon—Pauling showed that a hybrid atomic orbital system sufficed Just as two ripples on a pond can come together to form a differently shaped wave, one s and three p orbitals can mix to form four hybrid orbitals extended tetrahedrally in four directions in space. 

Property 2 of Kadanoff s transformation requires including additional terms F as a part of new scaled interactions. These terms have interaction points from different interaction lines with the contour length less than a. An intuitive explanation of the terms V results from consideration of polymer conformations corresponding to the diagrams shown in Figures 5.8 and 5.9 (see section 2.6). The latter one compares different types of diagrams used in polymer theory and the theoretical field approach. Higher orders are... 

Conditional probability, and the related topic of independence, give probability a unique character. As aheady mentioned, mathematical probability can be presented as a topic in measure theory and general integration. The idea of conditional probabihty distinguishes it from the rest of mathematical analysis. Logically, independence is a consequence of conditional probability, but the exposition to follow attempts an intuitive explanation of independence before introducing conditional events. 

An intuitive explanation of the oscillatory volume variations is given by Yoshida in Ref [8] it is based on hydrophobic effects that induce a difference of swelling rate between the oxidized and the reduced states of the catalyst. For a small piece of gel, the oscillations occur homogeneously [39]. But when the chemical wavelength is smaller than the system size, some inhomogeneous behavior in the form of waves may arise [8]. 

The intuitive notion of reductive explanation has been contrasted with a conception of mechanistic explanation. In order to arrive at a cognate of the notion of reduction, we have to abstract away from three features of the notion of mechanistic explanation we neglect teleology, we do not only focus on how -questions, and we do not only focus on events as the targets of the explanandum. The concept of kind-reduction has been characterized as follows (the explanation in (i) is non-conceptual in nature) ... 

---