Reciprocal bases

An automated procedure to measure peak widths for peak capacity measurements has been proposed.35 Since peak width varies through the separation, the peak capacity as conventionally measured depends on the sampling procedure. The integral of reciprocal base peak width vs. retention time provides a peak capacity independent of retention time, but requires an accurate calculation of peak width. Peak overlap complicates automation of calculation. Use of the second derivative in the magnitude-concavity method gives an accurate value of the standard deviation of the peak, from which the base peak width can be calculated. 

Since a, af = S0, or in tensor notation, a, aj = S, the reciprocal axes are contravariant and are written as a . As the Miller indices are the coordinates in the reciprocal base system, they must be covariant and are written as ht. Thus, the Miller indices transform like the direct axes, both being covariant. 

The length of the reciprocal base vectors is defined according to ... 

The direct base vectors and the reciprocal coordinates h, k, I transform in a covariant manner. The reciprocal base vectors and the direct coordinates u, v, w transform in a contravariant manner. 

The reciprocal coordinate system was defined above (1.2). If a, b, c are the reciprocal base vectors of the vectors a,b,c, the vector r = Ha + Kh + Lc (H, K, L being coprime integers) represents the normal to the plane Hu + Kv-h Lw-= 1. Its norm is r = l/(d//KL) where is the distance of the plane from the origin, and hence the distance between consecutive planes in the same family. The reciprocal lattice is the set of vectors... 

Fig. 13. Injection molding machine A, hydiaulic motoi foi turning the screw B, hydraulic cylinder and piston allowing the screw to reciprocate about three diameters C, hopper D, injection cylinder (a single-screw extmder) E, no22le F, fixed platen G, tie rods H, mold I, movable platen , hydraulic cylinder and piston used to move the movable platen and supply the force needed to keep the mold closed and K, machine base.

A guarded hot-plate method, ASTM D1518, is used to measure the rate of heat transfer over time from a warm metal plate. The fabric is placed on the constant temperature plate and covered by a second metal plate. After the temperature of the second plate has been allowed to equiUbrate, the thermal transmittance is calculated based on the temperature difference between the two plates and the energy required to maintain the temperature of the bottom plate. The units for thermal transmittance are W/m -K. Thermal resistance is the reciprocal of thermal conductivity (or transmittance). Thermal resistance is often reported as a do value, defined as the insulation required to keep a resting person comfortable at 21°C with air movement of 0.1 m/s. Thermal resistance in m -K/W can be converted to do by multiplying by 0.1548 (121). 

In synthetic fibers the number of ionic groups or dye sites is relatively small, and may have been introduced dehberately to make the base polymer dyeable. The restrictions on dye absorption are therefore very great the dye molecule must find an available specific site from among the limited number of sites in the fiber. This situation follows a Langmuir isotherm, where the reciprocal of dye in fiber 1 /DF is direcdy proportional to the reciprocal of dye in the dyebath 1 /HT. A plot of 1/against 1/H therefore gives a straight line. 

The reservoir is the lube oil storage tank. In some of the packaged compressors, it is built into the package base, and, in some standardized compressors, it is built into the compressor frame. In a reciprocating... 

Fig, 10. Activation entropy requireinents by reacting position as affected by previous substitutions based on Zavitsas [80], As the activation entropy becomes more negative, steric demands on the transition state are more stringent. The effect of previous or/ho-substitution on reaction at the para position is hard to explain, in light of both the reciprocal effect of para substitution on ortho and the effect seen with the d -oriho pre-substitution. 

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