Twists definition

Figure Al.4.4. The definition of the Euler angles (0, ( ), x) that relate the orientation of the molecule fixed (x, y, z) axes to the (X, Y, Z) axes. The origin of both axis systems is at the nuclear centre of mass O, and the node line ON is directed so that a right handed screw is driven along ON in its positive direction by twisting it from Z to z through 9 where 0 < 9 < n. ( ) and x have the ranges 0 to In. x is measured from the node line.

The three-dimensional conformation of a protein is called its tertiary structure. An a-helix can be either twisted, folded, or folded and twisted into a definite geometric pattern. These structures are stabilized by dispersion forces, hydrogen bonding, and other intermo-lecular forces. 

In summary we think that, on a superficial basis, a comparison of the effects of different nucleophilic species added covalently at the (3-nitrogen atom of an arenedi-azonium ion yields results that are almost trivial. Of more interest are unexpected results such as those of Exner and Lakomy for the substituent -N = CHC6H5. A possible explanation for the latter results emerged when the twisted structure of the substituent became known. We emphasize, however, that definitive explanations on the basis of Hammett or related substituent constants are not found very frequently. 

Fig. 3. Projection of the upper and the lower triangle of a geometry between an octahedron and a trigonal prism. Definition of the twist angle y>.

A quantitative study of the cholesteric induction and of the chiral transfer from dopant to phase requires the definition of the helical twisting power 3. This quantity expresses the ability of a chiral dopant to twist a nematic phase and can be numerically expressed in Eq. (2) where p is the cholesteric pitch, c the dopant molar fraction, and r its enantiomeric excess its sign is taken to be positive or negative for right-handed (P), or left-handed (M) cholesterics, respectively. This relation holds for molar fractions <0.01-0.05 ... 

Another basic property of solenoids is their twist. This parameter reflects the fact that successive coils are not stacked exactly above one another but with a small angular offset. Twist may be defined in relation to reference points at corresponding positions in consecutive coils (Fig. 1A). When connected, these points form a helix. The sense of the twist is given by the hand of this helix as it winds around the solenoid axis. Note that the definition of protein solenoid twist (Kobe and Kajava, 2000) differs from the usual definition of the twist in /1-sheets which is defined by the twist of /(-strands... 

Data for some 90 compounds with the general structure [9] were analysed in terms of the twist-torsion angle r and the out-of-plane bending, x- which measures the extent of pyramidalization at the carbon and nitrogen centres. [Scheme 1. For full details see the definitions in the original paper (Kaftory et al., 1990).] In all cases is small (<5-6°), so pyramidalization at carbon... 

To make cut pile carpets, two strands of BCF yarns are twisted together and heat-set with steam using a Superba heat setting machine at 135-145 °C or at 175-195 °C when heat-set with super-heated steam in a Suessen. An experimental design experiment [94] showed the higher the heat set temperature, then the lower is the bulk of the final carpet, but there is an increase in the tip definition and walk performance. The tufted carpets are then dyed with disperse dyes at atmospheric boil [95] in a continuous or a batch process. PTT carpets showed excellent resiliency in walk test experiments, equivalent to a nylon and much better than both PET and polypropylene, had lower static charge of <3.5 kV, and were resistant to coffee, mustard, betadine, red acid dyes and other stains [96],... 

In several examples including nitroanilines, the effect of twisting the chromophore from planarity decreases the absorption intensities. The reasons for the bathochromic effect as the angles of twist in the 4-aniline series increase is subject to discussion. When considering this (as well as in all attempts to obtain definitions of polarity of solvents by quantitative parameters) it is important to exclude or minimize the presence of hydrogen bonding overlapping158 other interactions. 

Fabrics are two-dimensional materials made from fibers. Their primary purpose is to cover things and they are commonly used in clothes, carpets, curtains, and upholstery. The motive for covering may be aesthetic, thermal, or acoustic. Fabrics are made out of or twisted bundles of fibers. The spinning of yams can occur in two ways staple fibers can be twisted into a thread ( spun yam ) or monofilaments can be twisted into a similar usable thread ( filament yam or continuous filament yam ). All these definitions are important in order to understand the conversation of the fiber industry. 

Finally, concentration units in soil are a combination of the above with a twist. Soil is a multiphase media, and different concentration units are applied, typically, to each phase. The interstitial space (in between the soil) is filled with water or air in most cases, and the corresponding concentration units for water or air, respectively, would be used. In addition, the concentration of a compound adsorbed to the sediment is normally given either as mass of compound/mass of solid or moles of compound/mass of solid. The mass of solid is one of the few soil parameters that can be determined definitively, so that is what is used. 

FIGURE 24-15 Linking number, Lk. Here, as usual, each blue ribbon represents one strand of a double-stranded DNA molecule. For the molecule in (a), Lk = 1. For the molecule in (b), Lk = 6. One of the strands in (b) is kept untwisted for illustrative purposes, to define the border of an imaginary surface (shaded blue). The number of times the twisting strand penetrates this surface provides a rigorous definition of linking number. 

Now, in the statistical limit for which we can treat our final manifold of closely spaced twisted triplets as an effective continuum, the sum in eq. (12-24) can be replaced by a definite integral whose weight function is taken to be the density of vibronic states, p(E). Thus we write... 

Fig. 12. Definition of solid state structural parameters for tris chelate complexes with D3 symmetry 0 is the twist angle and is the projection of the bite angle a onto the plane which is perpendicular to the C3 symmetry axis, 0 is the pitch angle and is the angle subtended by the plane of the chelate ring and the C3 symmetry axis r, d, s and h are the metal ligand distance, bite distance, triangle edge, and the distance between the triangles, respectively. From Ref.82 ...

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