Vertical thinking

For most of our education we are taught to think in a logical manner. This is called vertical thinking because the process involves proceeding directly from one state of information to another, and in this sense is continuous. Lateral thinking is a discontinuous process and depends on the ability to escape form the rules of vertical... 

If we think in terms of the particulate nature of light (wave-particle duality), the number of particles of light or other electi omagnetic radiation (photons) in a unit of frequency space constitutes a number density. The blackbody radiation curve in Fig. 1-1, a plot of radiation energy density p on the vertical axis as a function of frequency v on the horizontal axis, is essentially a plot of the number densities of light particles in small intervals of frequency space. 

Schaar That is interesting, because in normal epithelium vertical divisions usually occur. Would you think that there could be some sort of epistasis that would put Pins closer to being able to anchor these astral microtubules from the spindle Have you tried to mislocalize Pins ... 

Each dipole is pinned down at its midpoint, but can rotate freely in the plane of the paper around that point. The GA will be used to determine the set of angles made by the dipoles with the vertical axis that yields the lowest total energy. It is not hard to think of a low-energy arrangement, but this problem forms a convenient platform through which to follow the workings of the GA. 

We can refine, or zoom into, objects, splitting any of the vertical bars on the diagram into several. Thinking about it in more detail, we realize that the vendor company has different departments that deal with different parts of the business. Also, the customer organization will have users as well as a site manager who establishes a liaison with the vendor (see Figure 6.10). 

Although it is easy to think of a solution to this problem without the need to introduce computers, it is nevertheless instructive to observe how the genetic algorithm works its way toward this solution. Potential solutions, constructed as vectors, can easily be prepared by specifying the angle that each dipole makes with the vertical axis. A typical string would then be written as an ordered list of these angles, for example ... 

In this geometry, you need to think of the carbon atom of methane as occupying a position in the center of the tetrahedron and the four hydrogen atoms as occupying the four vertices. Here is a baU-and-stick representation of a methane molecule ... 

Yes, I said. I think sier Zorzi is not admitting how much he is worried about his wife— there is stress in those vertical strokes. But he obviously loves her very much, and his son also. And the first letter... ... 

In terms of the gradient of the stationary-state locus, the condition expressed by eqn (7.55) locates a singular point as dx/drres - 0/0. Loosely, we can think of the locus simultaneously having turning points both horizontally and vertically, as indicated in Fig. 7.7. This corresponds to situations such as (a) an isolated point or (b) the transcritical touching of two branches. 

Coordination polyhedron. It is standard practice to think of the lignnd atoms that are directly attached to the central atom as defining, i coordination polyhedron (or polygon) about the central atom. Thus Co(NH,)h]J+ is an octahedral ion and [PtCIJ2- is a square planar ion. In this way the coordination number may equal the number of vertices in (he coordination polyhedron. Exceptions are common among orgunonietnlhtf compounds. 

In anisotropic materials, the electronic bonds may have different polarizabilities for different directions (you may think of different, orientation-dependent spring constants for the electronic harmonic oscillator). Remembering that only the E-vector of the light interacts with the electrons, we may use polarized light to test the polarizability of the material in different directions, lno is one of the most important electro-optic materials and we use it as an example. The common notations are shown in Figure 4.7. If the E-vector is in plane with the surface of the crystal, the wave is called a te wave. In this example, the te wave would experience the ordinary index na of LiNbOs (nG 2.20). If we rotate the polarization by 90°, the E-ve ctor will be vertical to the surface and the wave is called tm. In lno, it will experience the extraordinary index ne 2.29. Therefore these two differently polarized waves will propagate with different phase velocities v c/n. In the example of Figure 4.7, the te mode is faster than the tm mode. 

The high heat of formation of the N3 cation ( 350 kcal/mol) makes it very attractive as a component of high energy density materials (HEDMs). However, its large vertical electron affinity (vEA) of 6.1 eV poses a problem So far, the preparation of only NsAsFg, N ShF, and NjSb2Fu has been reported. The oxidation of Br2 (IP 10.5 eV) by N SbFj shows that N3 is also susceptible to nucleophilic attack by Lewis bases. Calculations on NjNj show that such a crystal may exist, but nucleophilic attach of the anion is a likely side-reaction. We think that less electronegative derivatives of N3 may be less sensitive to both reduction and nucleophilic attack. 

We can think of two limiting sorts of transitions one in which the transition always occurs at the same temperature independent of pressure, the other where it is always at the same pressure independent of temperature. These would correspond to vertical and horizontal lines respectively in Fig. XI-3. In Clapeyron s equation dP/dT = L/TAV, these correspond to the case dP/dT = oo or 0 respectively. Thus in the first case we must have AV = 0, or the two phases have the same volume, in which case pressure does not affect the transition. And in the second case L = 0, or AS = 0, there is no latent heat, or the two phases have the same entropy, in which case temperature does not affect the transition. Put differently, increase of pressure tends to favor the phase of small volume, increase of temperature favors the phase of large entropy. 

Effect of 11 of the 12 symmetry operators (all except identity) of point group D3h (6m2) on a triangular bipyramid (think of the molecule PCI5), with five marked vertices A, B, C, D, and E (the chlorine atoms). 

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