Statistical frequencies

A two-dimensional disorder results when rod-like polymeric molecules are mutually shifted with statistical frequency. Translational symmetry then only exists in the direction of the molecules, and not in the transverse directions. The rod is a three-dimensional object with one-dimensional translational symmetry. Its symmetry is that of a rod group. Layer groups and rod groups are subperiodic groups. They are listed in detail in International Tables for Crystallography, Volume E. 

Table 4.30. Statistical frequency distributions of electron countsa, common formulasa, and localized bonding descriptions (in terms of number of metal-centered lone pairs, 2c/2e bonds, tu bonds, and average sd hybridization) for organometallic complexes of groups 3-10...

Another important application of NMR to polymer systems is the elucidation of the stereochemical configurations of Polymer chains. Poly (methyl methacrylate) was first studied by Bovey in 1960. It is now possible to analyse for the statistical frequency of occurrence of all possible combinations of up to four successive pairs of units (dyads) capable of occurring with either the same (meso) or opposite (racemic) configurations. 

Edgeworth, F. Y. 1907. On the representation of statistical frequency by a series. J. Royal Statistical Society, Series A. 70 102-6. 

Flickering clusters water molecules that are arranged into ice-like structures, which are believed to be transient features that change in statistical frequency of occurrence as a function of temperature and pressure. 

It is emphasized that by means of the statistical frequency analysis it is possible to separate dataset in populations, even if can be difficult to select one or two general threshold to utilize as reference to identify background values. In addition, the value distributions are not sufficient to divide the dataset into different populations, because they show an overlap, and give no idea of the spatial distribution and geometry of the geochemical anomalies. This is true both at local and regional scale. 

Lima A. describes statistical methods to evaluate background values, namely, statistical frequency analysis and spatial analysis. The author illustrates the application of GeoDAS software to perform multifractal inverse distance weighted (MIDW) interpolation and a fractal filtering technique, named spatial and spectral analysis (S-A) method, to evaluate geochemical background at regional and local scale. 

Figure 5.9 An hypothetical genetic code in which all amino acids are codified by three codons. It would be the most balanced code, in the sense that all amino acids would have the same statistical frequency, but it has not been nature s choice.

Now the interpretation of probability as a measure can easily be related to the classical concept of statistical frequency. Probability measures are simply the relative frequencies of certain events which have occurred. The relationship between probability as a measure and the Bayesian viewpoint is perhaps more difficult. Here probability is a measure of a subjective degree of belief which is obtained by a system of choices between bets. This process will be explained in the next section with reference to another useful subjective measure, that of utility. 

The function 2(y) is the statistical frequency function describing the position of other resonances in a sequence relative to the A th resonance. It is discussed in Section IX. Hwang (29) used (98) for (y), the result of assuming the spacing distribution can be approximated by a chi-squared distribution with eight degrees of freedom. This is quite satisfactory and leads to an analytic result ... 

Porter and Thomas (42) have given strong theoretical arguments that the statistical frequency functions for all the partial resonance level widths should be chi-squared distributions with v degrees of freedom as given by (75). In this case, the number of degrees of freedom is the number of channels open for decay of the compound nucleus by the process to be... 

By applying Equation (7-1) to the various meteorological conditions (direction and velocity of wind as well as turbulence in the atmosphere), and including the statistical frequencies of these conditions, the expected stresses can be computed in the form of frequency distributions of the concentrations of pollutants in air for the evaluation of technical installations under normal operating conditions, yearly mean values as well as short-term values are determined. Short-term values are concentration values which arc not exceeded during 95% of h/year. Due to the use of... 

Figs. 2 and 3 show two theoretical blending bed reclaiming models. The material slices and the statistical frequency distributions of the input and output variations... 

Different molecular groups have different preferences for interacting with solvent or other chemical groups. The relative propensity for contact of each pair of amino acids is the result of a complex set of enthalpic and entropic effects. However, they can also be evaluated empirically, by observing the statistical frequency of naturally occurring interactions (by proximity) between pairs of amino acids in a population of well resolved X-ray protein structures. 

Test point no. Speed (rev/min) Torque (nm) Statistical frequency (%)... 

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