Spreading range

In the transition range, spreading with the stirrer speed appears, and indeed all the more strongly, the higher the rotation speed. There is a satisfactory explanation for this circumstance, after Rautenbach and BoUenrath [451] calculated the temperature profile for a stirred tank with a low wall clearance for the laminar flow range according to their modified penetration theory. This theory assumes, that a parallel layered flow exists between the tank wall and the stirrer (similar to Couette flow), but that the liquid occluded by the stirrer is ideally mixed. For the temperature profile this means, that the layer near to the wall is at rest, but the layer near the stirrer at every stirrer blade pass is included and is mixed with the liquid bulk and acquires its temperature. After a certain number of stirrer blade passes a steady-state temperature profile is realized. 

For normal-incidence projectiles, the range spreading is equal to the transverse projected range. 

Fortunately, most of the PSD instrumentation in use today employ computer-generated data to display the particle size. Furthermore, the particle-range spread be measured can be adjusted to suit the material at hand. Thus, we ean use the histogram if we so desire, especially if it has certain advantages over the other methods of displaying PSD. 

Polynomial regression models often use data that are ill-conditioned, in that the matrix [X X] is unstable and error-prone. This usually results in the variance (MSe) that is huge. We discussed aspects of this situation in Chapter 6. When the model y = bQ + b Xi + b2xi is used, xf and Xi will be highly correlated because xf is the square of xj. If it is not serious due to excessive range spread, for example, in the selection of the x, values, it may not be a problem, but it should be evaluated. 

The researcher concluded that the days beyond 10 would be dropped for they held no benefit in interpreting the study. Also, because the range of y is so great, 0-7009, most statisticians would have performed a centering transformation on the data (xf = x,- — x) to reduce the range spread, but this researcher wanted to retain the data in the original scale. The researcher also removed days prior to day 2, hoping to make a better polynomial predictor. The statistical model that was iteratively fit was... 

There are three measures of variability. These measures indicate the spread of the data and are the range, variance, and standard deviation (Hays 1998, 171-76). Measures of variability provide the safety manager with an indication of how much the obtained results are spread out. For example, suppose a safety manager collects information on the number of lost days for three employees. The days lost are 1,1, and 2 (that is, they range from 1 to 2 days). The measures of variability would be small compared to three employees who lost 1,10, and 50 days (a range spread from 1 to 50 days). For various statistical procedures, the degree of variation in the data can impact the decision as to whether the results are significant or not. 

As experimental designs improve and explored spectral ranges spread higher, more bugs will certainly be detected, giving supplementary information. 

Natural fractals, such as clouds, polymers, aerogels, porous media, dendrites, cracks, solid fracture surfaces and so on, possess only statistical self-similarity, which takes place only in the restricted range of the spatial scales [1-3, 14]. For solid-like polymers it has been experimentally shown [20] that such a range spreads from several angstroms up to several tens of angstroms. 

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

The generally low chemical, mechanical and thennal stability of LB films hinders their use in a wide range of applications. Two approaches have been studied to solve this problem. One is to spread a polymerizable monomer on the subphase and to polymerize it either before or following transfer to the substrate. The second is to employ prefonned polymers containing hydrophilic and hydrophobic groups. 

The biasing function is applied to spread the range of configurations sampled such that the trajectory contains configurations appropriate to both the initial and final states. For the creation or deletion of atoms a softcore interaction function may be used. The standard Lennard-Jones (LJ) function used to model van der Waals interactions between atoms is strongly repulsive at short distances and contains a singularity at r = 0. This precludes two atoms from occupying the same position. A so-called softcore potential in contrast approaches a finite value at short distances. This removes the sin-... 

Pig. 2. By replacing the methyl group in p-methlyphenol with a series of softcore iiitcTaction sites it is possible to spread the range of configurations sampled to include configurations with and without a cavity in the para position. 

Several ways may be used to characterize the spread or dispersion in the originai data. The range is the difference between the iargest vaiue and the smaiiest vaiue in a set of observations. However, aimost aiways the most efficient quantity for characterizing variabiiity is the standard deviation (aiso caiied the root mean square). 

Grating Equation. The light incident on each groove is diffracted or spread out over a range of angles, and in certain directions reinforcement or constructive interference occurs, as stated in the grating formula ... 

Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories repeatability and reproducibility. Repeatability is the precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a single analyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability. 

The data we collect are characterized by their central tendency (where the values are clustered), and their spread (the variation of individual values around the central value). Central tendency is reported by stating the mean or median. The range, standard deviation, or variance may be used to report the data s spread. Data also are characterized by their errors, which include determinate errors... 

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