Weight Distributions

To conclude this sub-section, we note that the Cl form of the wave function (2.2) leads, via the mapping (2.6) from the coefficients c, to the charge distribution weights wm, to a computationally advantageous matrix formulation of the free energy of the solute plus solvent system, which we present next. 

Figure 4-64. The result of the %2-Tit (left) and sum-of-squares fit (right). Note the uniformly distributed weighted residuals for the %2 fit.

A particle distribution weighting function p y y,y, At) represents the mean time a particle resides at a position y during its move from y to y in a time step At, and it is given by... 

Nasal Sprays Clarity, microbial bioburden, pH, particulate matter, unit spray medication content uniformity, droplet and/or particle size distribution, weight loss, pump delivery, microscopic evaluation of suspensions, particulate matter, extractables, leachables from plastic and elastomeric components of container closure and pump. 

The extent to which any chosen sampling distribution (weight function) meets our requirements is reflected most directly in the M-distribution it implies. One can estimate that distribution from a histogram H(M) of the macrostates visited in the course of a set of MC observations. One can then use this information to refine the sampling distribution to be used in the next set of MC observations. The simplest update algorithm is of the form [122]... 

The particle size distribution, X(s), above is, unfortunately, not in a form which is useful for most applications. This is because it is a scattered intensity weighted distribution (for brevity, intensity distribution ) rather than a size distribution based on the volume (weight) or number of particles. The difference between distributions weighted in different ways can be most easily explained by relating the various distributions to a number distribution. 

Metered-Dose Inhalation Aerosols Quantity of delivered dose, total number of acceptable doses delivered, color, solvate formation with propellant, particle size distribution, weight loss of canister (i.e., loss of propellant), pressure, valve corrosion, and storage in both upright and inverted positions. 

The size distributions of the sulfur- and metal-containing molecules were determined by summing the individual cut size distributions weighted by the fraction of total sulfur (or metal) in that cut. Equation 4 defines the mean size for the distribution where x is sulfur, nickel, or vanadium. 

Summing such distributions, weighted by the Boltzmann factor for vibrational excitation, over all vibrational states yields the distribution of Ffni- The average... 

Figure 3. Molecular weight distribution (weight fraction) of polypropylene at initial and two subsequent stages of degradation...

Particle size distribution Weight mean diameter 50 < dp < 70 jum + 80 jum, 5-20 wt. % -40 /tm, 10-30 wt.% Improved fluidity Good fluidization Decreased catalyst loss and attrition Se vere erosion if particles are coarse Difficulty in recovering particles <10 /am Installation of internals Multistage fluid bed with horizontal baffles... 

In most cases d 2 (the volume/surface average or Sauter mean) is used, while the width of the size distribution can be given as the variation coefficient. The latter is the standard deviation of the distribution weighted with d divided by the corresponding average d. Generally C2 will be used which corresponds to d 2 An alternative way to describe the emulsion quahty is to use the specific surface area A (the surface area of all emulsion droplets per unit volume of emulsion). 

Then, distributions for the occurrences of the various molecular properties in two sets of molecules, one of active molecules and the other of inactive molecules, are evaluated. From these frequency distributions, weights are calculated using one of the two weighting schemes, each of which seeks to quantify the differential occurrences of the defined ranges of property values in active (AC) and inactive (IN) molecules ... 

Zip Termination length initial molecuhr weight distribution Weight loss rate Order Dependence of initial rate on molecular weight... 

Fig. 10. A comparison of the product distributions (weight percent) over a Ni(IOO) catalyst observed during CO hydrogenation over clean (solid bars) and K-doped (cross-hatched bars) catalysts at T = 500 K, H2 CO = 4 1, and a total pressure of 120 torr. Potassium coverage = 0.10 monolayers (ML). From Ref. 127.

Sedimentary rock type Mass (10,9kg) Distribution (%) Weight percent Mass (1019 kg) Distribution (%) Weight percent Mass (10,9kg) Distribution (%)... 

The current definition of collection rate is based on the sold and distributed weight of batteries and their service life. However, the service life of the batteries related to appliances should be regarded as very long when hoarded batteries are taken into consideration. In order to make collectable quantity clarified and also to make the collection effort properly evaluated, the hoarding rate of the batteries should be taken into account. 

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