Weighted means

The CS equation for the pressure is found to be the weighted mean of the pressure calculated from the virial and compressibility equations ... 

Let and be the fractions of states with odd and even total spins. Sj =0,1,2,.. ., 2s. When the 2s + 1 spin-states. Sj are iimesolved, the appropriate combination of syimnetric and antisyimnetric cross sections is the weighted mean... 

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

When the constitution point lies in a two-phase region the alloy breaks up into two phases which do not have the same composition as the alloy (though a properly weighted mean of the two compositions must equal that of the alloy). 

To gather information which will enable selection of appropriate control equipment. If a source test determines that the emission is 3000 mg of particulate per cubic meter and that it has a weight mean size of 5 p.m, a control device must be chosen which will collect enough particulate to meet some required standard, such as 200 mg per cubic meter. (4) To determine the efficiency of control equipment installed to reduce emissions. If a manufacturer supplies a device guaranteed to be 95% efficient for removal of particulate with a weight mean size of 5 /rm, the effluent stream must be sampled at the inlet and outlet of the device to determine if the guarantee has been met. 

The molecular weight (mean relative molecular mass) was obtained by determination of density but, in order to determine that the gas was monatomic and its atomic and molecular weights identical, it was necessary to measure the velocity of sound in the gas and to derive from this the ratio of its specific heats kinetic theory predicts that Cp/C = 1.67 for a monatomic and 1.40 for a diatomic gas. 

For condensing problems, determine whether apparent weighted mean temperature difference is used, and which is applicable. 

Lower molecular weight means the oil is more difficult to crack... 

Start up/load charge weighted mean iron mg/kg Fe 0.1 max. 

Fig. 2 Time-series of annual mean water temperature in the San Reservoir (Spain) and air temperature in the Ter River watershed. The series start in 1964, after the first filling of the reservoir. Annual means are based on monthly measures of the volume weighted mean temperature. Only years with at least 10 temperature profiles were included in the figure. The air temperatures are annual means for the whole Ter River watershed, calculated from data collected in several meteorological stations in the basin, and weighted according to their area of influence...

Figure 9.3. Percentage of non-detectable amino acids in collagen extracts from archaeological human skeletons. Numbers on top of the columns indicate number of carbon atoms per amino acid. XW = weighted mean of % loss (cf. text). Only high-carbon amino acids are more frequently lost than the average.

Table of double-closed data Z, with weighted means, weighted sums of squares and weight coefficients added in the margins, from Table 32.4... 

Weight coefficients can be used to define weighted measures of location and spread. In particular, we define the weighted mean m of a vector x by means of ... 

In the case of an nxp matrix X we can define two sets of weighted measures of location and spread, one for each of the two dual spaces and in terms of weighted means and weighted variances ... 

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