Twin symmetrical

Twins are commonly found or formed in all types of crystals. Their boundaries are of two general types coherent and incoherent. The coherent boundaries are usually also symmetric, so they offer little resistance to dislocation motion. However, the incoherent ones are not symmetric and may resist dislocation motion considerably. 

Some trivia Gabriele Veneziano, in the late 1960s, worked on string theories. However, interest in his particular version of the theory faded when other physicists showed they would only work in twenty-six dimensions. Also, some researchers believe that all known elementary particles have unseen symmetric twins called sparticles. 

A twin peak due to symmetric and antisymmetric N—H stretches means an NH group. By putting the pieces together we find that the compound is benzamide,... 

Opposed-flow configurations can be used to establish strained premixed flames. Like the diffusion-flame situation, there are several ways to create the opposed flow, including opposed porous plates [197] or opposed contraction nozzles [349]. As illustrated in Fig. 17.8, two opposed contraction nozzles form a symmetric flow. When the mixture stoichiometry, temperature, and flow rates are equal in both nozzles, twin flames are stabilized near the center. 

Pseudosymmetry creates some of the most difficult problems in crystal structure work. The pseudo-symmetric crystal may be a true single crystal with small deviations from a higher symmetry (case 1) or (case 2) a twin producing a symmetrized structure (3) with a simulated higher symmetry. In both cases, the true structure of low symmetry [H-structure (3, 11)] may give the same reflections with only slight intensity variations (a), or additional reflections (b) exist which are weak, so... 

To calculate the WAXS fiber pattern of PTFE phase I, we assumed that the CF2 units are equally distributed around the chain axis due to the high mobility of twin reversals in the high-temperature phase. In other words, the electron density of the PTFE chains is cylindrically symmetric in space average. Thus we are able to calculate the mean molecular structure amplitude according to Eq. (26). 

Oxometalloporphyrins were taken as models of intermediates in the catalytic cycle of cytochrome P-450 and peroxidases. The oxygen transfer from iodosyl aromatics to sulfides with metalloporphyrins Fe(III) or Mn(III) as catalysts is very clean, giving sulfoxides, The first examples of asymmetric oxidation of sulfides to sulfoxides with significant enantioselectivity were published in 1990 by Naruta et al, who used chiral twin coronet iron porphyrin 27 as the catalyst (Figure 6C.2) [79], This C2 symmetric complex efficiently catalyzed the oxidation... 

Despite the quantitative difference between aromatics and antiaromatics, the qualitative picture is the same The combination of a, T-distortive ground state and a -attractive excited state along the Kekule modes is manifested in soft potentials in the ground state and steep ones in the twin excited state. This in turn is expressed as exalted frequencies and symmetrized geometries in the twin excited state. 

The device can be designed as a single or a twin calorimeter, also called differential calorimeters. The twin calorimeter technique eliminates the perturbations due to heat loss to the surroundings, for example. They measure the difference of heat release in two symmetrically constructed alorimetric cells. 

Note also that, when a contribution due to a uniaxial magnetic anisotropy is included in the particle energy [see Eq. (4.73)], the emerging parameter h, on changing, in a natural way guides the system through the variety of oscillation situations from the absence of any symmetric potential (an isotropic particle) to a twin pair of infinitely deep wells (a magnetically hard particle). In still other... 

For example, Wakayama and coworkers discovered the formation of two oppositely orientated domains of 5,10,15,20- lclrakis(3,5-di-ferf-bulylphcnyl)-porphine deposited onto a Cu surface using low-temperature scanning tunneling microscopy [124]. It was demonstrated that the twin domains were produced by a pair of chiral conformations induced by a combination of symmetrical tilting and twisting rotation of the phenyl rings with respect to... 

The original Heitler-London calculation, being for two electrons, did not require any complicated spin and antisymmetrization considerations. It merely used the familiar rules that the spatial part of two-electron wave functions are symmetric in their coordinates for singlet states and antisymmetric for triplet states. Within a short time, however, Slater[10] had invented his determinantal method, and two approaches arose to deal with the twin problems of antisymmetrization and spin state generation. When one is constructing trial wave functions for variational calculations the question arises as to which of the two requirements is to be applied first, antisymmetrization or spin eigenfunction. 

Serber[15] has contributed to the analysis of symmetric group methods as an aid in dealing with the twin problems of antisymmetrization and spin state. In addition, Van Vleck espoused the use of the Dirac vector model[16] to deal with permutations. [17] Unfortunately, this becomes more difficult rapidly if permutations past binary interchanges are incorporated into the theory. Somewhat later the Japanese school involving Yamanouchi[18] and Kotani et al.[19] also published analyses of this problem using symmetric group methods. 

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