Degrees of symmetry

Measurements of local volume dux distributions may be used to estabHsh the degree of symmetry of a spray. Flux values must be integrated across the measurement planes and verified against the Hquid dow rate of the atomizer. 

Symmetrie-achse, /. axis of symmetry, -ebene, /. plane of symmetry, -grad, m. degree of symmetry. 

Substances whose structures have a high degree of symmetry generally have higher melting points than closely related compounds that lack this symmetry. There are striking examples of this... 

For practical purposes two different approaches have been used. If the nuclear framework has a center with high degree of symmetry, it may be convenient to expand the Hartree-Fock functions fk(r) in terms of spherical harmonics Ylm(6, q>) around this center ... 

In summary, using work collected from forward and backward paths greatly improves the accuracy of the estimates, and for the symmetric system studied here eliminates the bias. In our particular example, the cumulant estimators using forward and backward work data produce the most precise free energy estimates, followed by Bennett s optimal estimator. However, this somewhat poorer performance of the optimal estimator is caused in part by the high degree of symmetry of the system studied. 

Cycloheptatrienylium bromide, instead of having the properties of a typical covalent organic halide, melts at 203°, is strongly deliquescent, miscible with water, and insoluble in the less polar organic solvents. The infrared spectrum is a simple one consistent with the high degree of symmetry postulated for the ion. 

In some aromatic molecules that have a high degree of symmetry, i.e. with a minimum D2h symmetry (e.g. benzene, triphenylene, naphthalene, pyrene, coronene), the first singlet absorption (So —> Si) may be symmetry forbidden61 and the corresponding oscillator strength is weak. The intensities of the various forbidden vibronic bands are highly sensitive to solvent polarity (Ham effect). In polar solvents, the intensity of the 0-0 band increases at the expense of the others. 

An indication of such a morphological transition is a pronounced enhancement of oxide film roughness at a thickness of 11 nm, observed by AFM, as shown in Fig. 5.5. The appearance of this surface ripple corresponds to the first potential peak in Fig. 5.4. An investigation using differential IR spectroscopy revealed that the peak position, width and degree of symmetry of the Si-O absorption bands... 

The conclusions to be drawn so far about what is needed in a design to induce a native-like fold are therefore that the sequences should either show a high degree of symmetry and be based on the heptad repeat [6], or they should have a hydrophobic core that is shape complementary and at least partly aromatic [1,2,5,9]. 

The near monodispersity typically associated with dendrimers prepared by both the divergent or convergent growth approaches presents a number of interesting characterization traits when compared to traditional narrow polydisper-sity linear polymers. These features are further enhanced by the high degree of symmetry normally associated with dendritic macromolecules and permit an unprecedented amount of structural information to be obtained using standard characterization techniques. 

Fig. E.l. Relations among plane groups. In this figure, the plane groups are shown in their degrees of symmetry, as indicated by the order of the factor groups. A plane group with high symmetry always has one or several subgroup(s). The chart shows such relations within the same lattice.

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