Propagation factor

Forward Analysis In this type of analysis, we are interested in the propagation of initial perturbations Sxq along the flow of (1), i.e., in the growth of the perturbations 5x t xo) = (xo -h Sxq) — xq. The condition number K,(t) may be defined as the worst case error propagation factor (cf. textbook [4]), so that, in first order perturbation analysis and with a suitable norm j ... 

Propagating events or propagating factors allow the accident sequence to continue, developing consequences that are subsequently more severe. Examples are failures of release-detection systems or the presence of ignition sources. 

Figure 10.4 shows normalized Ba/K and Sr/K distributions between sanidine and a hydrothermal solution (liyama, 1972), Li/K between muscovite and a hydrothermal solution (Voltinger, 1970), and Rb/Na between nepheline and a hydrothermal solution (Roux, 1971b), interpreted through the local lattice distortion model, by an appropriate choice of the Nernst s law mass distribution constant K and the lattice distortion propagation factor r. 

Measured s values (helix propagation factor values) obtained by various groups110,12,24-311 for all the amino acids are listed in Table 1. Chakrabartty and Baldwin1281 have also compared free-energy changes and determined rank orders of helix propensities of all the amino acids as measured in various experimental peptide systems. 

Helix initiation (represented by the helix nucleation parameter a) in a random coil conformation is the slowest and energetically least favored step, whereas subsequent growth of the helix nucleus (represented by the helix propagation factor, s) is rapid and relatively favored. 83 ... 

It is seen that is an amplification or propagation factor, and the object of the exercise is now to find out under what conditions its magnitude is less than unity, which is the stability condition. 

Using Equations 2.48, 2.55, and 2.59, changes in the complex propagation factor y are related to this complex power transfer [4],... 

A preliminary step to dielectric measurement by wave-transmission techniques is to relate the basic wave parameter, called the propagation factor, 7 of the material, to permittivity. In terms of the propagation factor the equations for the electric and magnetic fields of a plane wave travelling in the x-direction in a uniform, infinite material are ... 

If we represent each vertex by a dot and each G° propagator by a line, the series can be represented diagramatically and is shown in Fig. 7.3. We have written the series in /-space, since the propagators factor. In the diagrams, t increases from right to left. This sequence of collision events... 

There is a theoretical optimum for spiking samples to achieve the best precision for the ratio measurements. The error propagated by this measurement factor alters as one moves away from the theoretical optimum. This error propagation factor can be calculated from the isotope system being measured and is dependent on the isotopic abundances in the natural sample and the isotopically enriched (spike) material. The error propagation factor is therefore the theoretical factor influencing the precision of the ratio measurements, as a function of the closeness to the calculated optimum spike. 

A number of error propagation plots have been calculated to illustrate how the error propagation factor may be minimised by adjustment of the amounts of the analyte and spike isotopes. Details of the chosen isotope systems and their lUPAC abundances are given in Table 4 with the spike isotope listed first). 

Using the Cd Cd system as an example, the optimum ratio in the spiked solution to minimise the error propagation factor is ... 

The amplitude of the SAW is dependent upon time t and propagation path x. The dependency is assumed as exp (i(o)t - /3x)). A complex propagating factor 3 is defined by the wave number k and attenuation a as... 

The variation of the complex propagating factor for constant frequency is derived as... 

Substituting Equation 4.32 into Equation 4.9 gives the change in the complex propagating factor ... 

The latter approach does have its uses, however, particularly if one is interested in the sequence of multiple reflections in the sample which are, so to speak, concealed in the propagation factor f(Z) of admittance formulas. 

In these circumstances the path integral propagator factorizes as ... 

Ikegami, E, Yoshida, S., Takeuchi, T., and Umeriha, M. 1984. Propagation factors controlling mean field strength on urban streets. IEEE Trans. Antennas and Propagation AP-32(8) 822-829. 

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