Intrinsic shape

It is also clear from Eq. (2.5.1) that the linewidth of the observed NMR resonance, limited by 1/T2, is significantly broadened at high flow rates. The NMR line not only broadens as the flow rate increases, but its intrinsic shape also changes. Whereas for stopped-flow the line shape is ideally a pure Lorentzian, as the flow rate increases the line shape is best described by a Voigt function, defined as the convolution of Gaussian and Lorentzian functions. Quantitative NMR measurements under flow conditions must take into account these line shape modifications. 

Nuckolls and Katz have synthesized discotic liquid crystalline molecules in which the core is a helix in its own right.37 Nonracemic helicene 33 was found to assemble into a columnar mesophase in which the helicenes stack on top of each other. CD spectroscopy showed a strong increase of the Cotton effect upon going from the molecularly dissolved state to the aggregated state, exhibiting an amplification of chirality. These helical columns give rise to a strong expression of chirality because the intrinsic shape of the helicenes... 

The question now is whether it is observable or not. This signal has to be above the systematics (that depends on what you use to do the measurements) and above the (white) noise due to the intrinsic shape fluctuations of the source galaxies. In practice the measurement is made in the following way. Galaxy ellipticity,25000 e, are measured and a "super" pixel (say of the order of a few arcmin size) and averaged out. In the weak lensing regime we have,... 

Jones C. E., Basu S., and Dubinski J. (2001) Intrinsic shapes of molecular cloud cores. Astrophys. J. 551, 387-393. 

For all fuzzy sets, including three-dimensional functions of electron density-like continua provided with suitable membership functions, the differences between the corresponding fuzzy sets can be expressed by a metric based on a generalization of the Hausdorff distance. The basic idea is to take the ordinary Hausdorff distances h a) for the a-cuts of the fuzzy sets for all relevant a values, scale the Hausdorff distance h)a according to the a value, and from the family of the scaled Hausdorff distances, the supremum determines the fuzzy metric distance f A,B) between the fuzzy sets A and B. If, in addition, the relative positions of the fuzzy sets A and B are allowed to change, then the infimum of the f(A, B) values obtained for the various positionings determines a fuzzy metric of the dissimilarities of the intrinsic shapes of the two fuzzy sets. 

Handedness is intrinsic (to the asymmetric object). Therefore, enantiomorphy is also intrinsic because any rigid motion by definition changes only external relations but leaves intrinsic shape unaltered. On this view, enantiomorphy and asymmetry are necessarily coextensive. Handedness, however, is a further property because being asymmetric does not determine whether an object is right or left handed. 

Insertion of a carbonyl between two methylene groups transforms an n-alkane into an alkanone. Since the group volume and bond angle to neighboring carbon atoms of a carbonyl are only c. 15% and c, 4° larger, respectively, than those of a methylene [37-40], the intrinsic shapes and sizes of alkanes and alkanones with the same number of carbon atoms are very similar. On that basis, they should form similar solid phase structures differences may be attributable to the opposite... 

As the SCC of LCE depended on the size of the LC domains, which was usually in the micrometer range, it was researched whether SCC could be realized for nanoscale shaped bodies [144]. In MCLP nanoparticles based on the nematic main chain polyether l-(4-hydroxy-4 -biphenyl)-2-(4-hydroxyphenyl)butaneandin other LC main-chain moieties a shape change between ellipsoids and spheres could be observed. This effect was only observed if the particle size in these polymer systems was below a critical size. This size related effect resulted from an quasi-equilibrium between the intrinsic shape of the entangled MCLP and the thermodynamically most stable form in the isotropic phase, the sphere [144]. 

Repulsive electronic tension drives the quantum mechanical electronic diffusion. Kinetic energy density T defines the intrinsic shape of atoms and molecules... 

A piece of monophonic music is made of a temporal succession of specific sounds endowed with various characteristics, represented in a musical score by note symbols distributed around a stave made of a few parallel lines. The characteristics of a note are its pitch, represented by its position on the frame (the sharper the sound, the upper the note) and possibly a side symbol altering it to slightly sharper or flatter its duration, represented by its intrinsic shape (from a full note or more to a sixteenth or less) its strength (from fortissimo to pianissimo), and its tone, which makes the same note played by various voices or instruments sound different. Another characteristic of a piece of music is its tempo, which tells how long it takes to play some subdivision of the note a tempo of 72 means there are 72 durations of the chosen note in a minute (about as many as heart beats) training musicians use a metronome (like the clock of a processor) to feel the tempo. In polyphonic music there is a harmonious superposition of melodic patterns played by several performers, usually lead by a chief... 

Their synthesis has motivated experimental progress in understanding the intrinsic shape-dependent properties of metal and semi-conductor nanocrystals. 

We present preliminary results on the intrinsic shapes of s[nral galaxy disks, based on a K -band imaging surrey. The sample galaxies were selected to be face-on on the basis of their HI linewidths and their luminosities. We fit two-dimensional bulge-disk modds that minimize the impact of spiral structure on the apparent shape. We find that for the majority of galaxies the intrinsic disk ellipticity at a few scale lengths is 0.35 and briefly discuss implications for the diape of the dark matter halos and for the intrinsic scatter in the TuUy-Fisher relation. 

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