Statistical dispersion

In this scheme, digital particles are still wandering localized clusters of informa-tionl but (conventional) variables such as space, time, velocity and so on become statistical quantities. Given that no experimental measurement to date has yet detected any statistical dispersion in the velocity of light, the sites of a hypothetical discrete underlying lattice can be no further apart than about 10 cm. 

Statistical Dispersion of Capacitance, ESR, and Parallel Resistance Values... 

Figure 32.1 shows the permeability obtained for aU the nonirradiated samples. The average value of aU these samples is /vav = 21.6 L/m h. The highest value of the statistical dispersion is yvav + 2(r=38.8 L/m h, and the lowest value is av 2other hand. Figures 32.2 and 32.3 show the permeability of the gamma- and electron-irradiated samples, respectively. As it can be seen, in both cases the dispersion values of permeabUity are within the limit values of the nonirradiated dispersion, proving that the variabUity in the results is not the consequence of radiation, but of membrane nonhomogeneity. 

Results verification is totally different from results validation. Results validation (point 4.7.5. and 5.9. of NBN-EN-ISO-CEI 17025 standard) shows, each year, or when it is judged necessary, that a given laboratory has the capacity to apply a particular method, repetitively, in respect of obtained data during initial validation. Trueness and statistical dispersion of results are the basis of the definition of the uncertainty of the standard of measurement [16] and, in some cases, the basis for the definition of the limit of detection and quantification. Management of data from validation results, as control card, could permit the detection and control of eventual deviation. Validation of results is the internal quality control procedure which verifies the stability of performance of the methods for which accreditation is sought, in the limited-scope procedural context. 

On the other hand, lanthanide ions are well known for their unique optical properties. These properties are extensively used in numerous fields such as laser amplifiers (Adam, 2002 Kuriki et al., 2002) or electroluminescent materials (Kido and Okamoto, 2002) for instance. Coordination polymers could be veiy interesting as far as optical properties are concerned. Indeed they are transparent and the rare earth ions distribution can be perfectly controlled by an appropriate choice of the ligand while in plastic or glasses they are generally statistically dispersed. The prerequisites of such coordination polymers exhibiting optical properties are obviously the following the material must be thermally rather stable, solvent molecules must be avoided and the inter-metallic distances must be carefully adjusted in order to allow the best efficiency for the targeted application. 

The natural heulandite samples were exchanged with 1 M AgNOs solution and treated at 160 °C and 210 °C, respectively [80B1, 81B1]. From the determined composition AgT sAh 28128 8072 18 H2O, by XRD analyses, only 56 % of Ag was located. The additional silver was suggested to be statistically dispersed within stmctural voids. 

The variance is a measure of the statistical dispersion, indicating how the possible values are spread around the expected value. The variance of a random variable Xis, = E X — /u.) with the expected value E X) = f X dP. 

For the discussion of the chaotic behavior statistical methods will be used. The relative cumulative frequency or the probability, respectively, is shown in Figure 7 for four velocity classes, see Table 3. From these data the relative frequency or probability density, respectively, is obtained, see Figure 8. It turns out that the frequency distribution is completely non-Gaussian, and the range characterizing the statistical dispersion is increasing with the relative velocity of the impact, while midrange point and mean value coincide fairly well, see Table 4. 

This simply assumes that axial dispersion (D m. s ) is superimposed onto plug flow. Axial dispersion may be caused by a velocity profile in the radial direction or statistical dispersion in a packing or turbulent diffusion or by any physicochemical process which delayes some particles with respect to others. The model parameter is the axial PECLET number, Pe = uL/D, or its reciprocal, the dispersion number, D /uL. Depending on the boundary conditions assumed at the reactor inlet and outlet (which are different from those of the simple assumptions above), a lot of mathematical formulae can be found in the literature for the RTD [3]. This is often academic as in the range of usefulness of the model (small deviation from plug flow, say Pe > 20) all conditions lead to res-... 

Variance n One of the most used descriptive measures of a probability distribution, population or sample. It is equal to the square of the standard deviation. It is a measure of deviation from the expectation value or mean. It is a measure of statistical dispersion which quantifies the deviations from the expectation value as the mean of the squares of the distance from the mean. The variance of a random variable is defined as the second central moment of the random variable and is often denoted by cr and sometimes by Var(X), defined on a probability space, S, is given by ... 

Ates, H., Kasap, E., Tomutsa, L., and Gao, H.W. 1996. Use of Statistical Dispersion Model to Study Polymer Clogging in Sandstone Samples. Paper SPE 35473 presented at the SPE/DOE Improved Oil Recovery Symposium, Tulsa, 21-24 April. DPI 10.2118/35473-MS. 

According to equation (3.1) the probability P to form exactly m nuclei within a fixed time interval [0 ] depends on a single parameter - the average number of nuclei N(f), which coincides with the statistical dispersion of the random quantity m Therefore UNif) is found by a sufficiently large... 

At first, it is statistical standard of the undefective section. Such standard is created, introducing certain lower threshold and using measured data. Under the classical variant of the shadow USD method it is measured fluctuations of accepted signal on the undefective product and installed in each of 512 direction its threshold in proportion to corresponding dispersions of US signal in all 128 sections. After introducting of threshold signal is transformed in the binary form. Thereby, adaptive threshold is one of the particularities of the offered USCT IT. 

The main sources of error which define the accuracy are counting statistics in tracer concentration measurements, the dispersion of the tracer cloud in the flare gas stream, and the stationarity of the flow during measurements. 

The next part of the procedure involves risk assessment. This includes a deterrnination of the accident probabiUty and the consequence of the accident and is done for each of the scenarios identified in the previous step. The probabiUty is deterrnined using a number of statistical models generally used to represent failures. The consequence is deterrnined using mostiy fundamentally based models, called source models, to describe how material is ejected from process equipment. These source models are coupled with a suitable dispersion model and/or an explosion model to estimate the area affected and predict the damage. The consequence is thus determined. 

Method of Moments The first step in the analysis of chromatographic systems is often a characterization of the column response to sm l pulse injections of a solute under trace conditions in the Henry s law limit. For such conditions, the statistical moments of the response peak are used to characterize the chromatographic behavior. Such an approach is generally preferable to other descriptions of peak properties which are specific to Gaussian behavior, since the statisfical moments are directly correlated to eqmlibrium and dispersion parameters. Useful references are Schneider and Smith [AJChP J., 14, 762 (1968)], Suzuki and Smith [Chem. Eng. ScL, 26, 221 (1971)], and Carbonell et al. [Chem. Eng. Sci., 9, 115 (1975) 16, 221 (1978)]. 

Hay and Pasquill (5) and Cramer (6, 7) have suggested the use of fluctuation statistics from fixed wind systems to estimate the dispersion taking place within pollutant plumes over finite release times. The equation used for calculating the variance of the bearings (azimuth) from the point of release of the particles, cTp, at a particular downwind location is... 

The Offshore and Coastal Dispersion (OCD) model (26) was developed to simulate plume dispersion and transport from offshore point sources to receptors on land or water. The model estimates the overwater dispersion by use of wind fluctuation statistics in the horizontal and the vertical measured at the overwater point of release. Lacking these measurements the model can make overwater estimates of dispersion using the temperature difference between water and air. Changes taking place in the dispersion are considered at the shoreline and at any points where elevated terrain is encountered. 

London [11] was the first to describe dispersion forces, which were originally termed London s dispersion forces. Subsequently, London s name has been eschewed and replaced by the simpler term dispersion forces. Dispersion forces ensue from charge fluctuations that occur throughout a molecule that arise from electron/nuclei vibrations. They are random in nature and are basically a statistical effect and, because of this, a little difficult to understand. Some years ago Glasstone [12] proffered a simple description of dispersion forces that is as informative now as it was then. He proposed that,... 

Gifford, F. A, 1984, Statistical Properties of a Fluctuating Plume Dispersion Model Advances in Geophysics 6 Academic Press, NY, p 117. 

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