W Weight factor

Debye heat capacity equation 572-80 Einstein heat capacity equation 569-72 heat capacity from low-lying electronic levels 580-5 Schottky effect 580-5 statistical weight factors in energy levels of ideal gas molecule 513 Stirling s approximation 514, 615-16 Streett, W. B. 412... 

W = weight in kg, El = height in cm, A = age in years Energy expenditure then should be multiplied by a stress factor to estimate the total energy expenditure (TEE) ... 

Here w is a weighting factor. Asr (s) is the absorption factor (in this case for symmetrical absorption), Hz (5) and In consider the non-ideal character of the two-phase topology (cf. p. 124, Fig. 8.10) by consideration of a smooth phase transition zone and density fluctuations inside the phases. 

This is purely an average over configurational space. This equation is similar to (4.15) with a special choice for w and the additional weighting factor since... 

Here, w(xfc) is the weighting factor for any property at a given position on the fcth step xfc. For example, for a constant-temperature molecular dynamics or a Metropolis MC run, the weighting factor is unity. However, we wish to leave some flexibility in case we want to use non-Boltzmann distributions then, the weighting factor will be given by a more complicated function of the coordinates. The ergodic measure is then defined as a sum over N particles... 

Now, let us discuss the rate equations embodied in eq.(74). To do this, there is need of a statistical analysis. If the system is kept coupled to a thermostat at absolute temperature T, and assuming that w(i - >if) contains effects to all orders in perturbation theory, the rate of this unimolecular process per unit (state) reactant concentration k + is obtained after summation over the if-index is carried out with Boltzman weight factors p(if,T) ... 

Thus, p(f + 8f) is a sum of contributions with the phase factors (( >ab t)< b t)), the weight factors w t)Wb t)), and phase-space distributions Pb t) which appear with a probability Tab t). Associating M(f) with the Liouville operator 1 — the scheme becomes somewhat more involved. In addition to... 

Correction for nonconstant variance. To correct for nonconstant variance, it is necessary to weight standard measurements according to their local variance, S. For each standard concentration the variance is determined by repetitive analysis at that level, and a weighting factor, w = 1/s, is calculated. 

In expression 5, W is a weighting factor as before, aoab is the measured cross relaxation rate and (Tab is the calculated cross relaxation rate at any stage in the calculation as given by expression 3. Since a is directly proportional to 1/r, this expression reduces to expression 2 in the limit of a single rigid conformer, if W is adjusted to absorb the proportionality constants. 

In external photon beam therapy, weighting factors, W /p., are currently estimated based on the a/(i model to compensate for differences in fractionation. 

The biologically weighted dose is a quantity intended to be correlated, as closely as possible, to the relevant biological/clinical effect. However, in all radiotherapy reports, the (physical) absorbed doses D and the biological weighting factors W jp, Rhdr, II pdr> IErbe, etc.) should always be indicated separately and not just the biologically weighted doses Dajp, T>hdr, -Dpdr, -Drbe, etc.). 

The weighting factors, W, as introduced above, aim to be a pragmatic approach to harmonize prescription and reporting of radiation treatments. They are based on actual clinical practice, current techniques, and available radiobiological data. Their use should be limited to the technical treatment modality for which they were designed. They are not universally applicable factors, and they should not be multiplied or combined between each other. 

Finally, it must be stressed again that the selected weighting factors W (and thus the biologically weighted doses) are based on available radiobiological data and clinical observation, but they always imply clinical judgment and experience. 

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