Subrange

Fig. 3. Charge distributions of the BPTI structures sampled from the indicated subranges of the MD trajectory for the BPTI X-ray structure from ref. [34]...

Example of the use of subrange precision control charts for samples that span a range of analyte concentrations. The precision control charts are used for... 

The deviation function AW Too) is obtained as a function of r90 for various temperature intervals by calibration of the platinum resistance thermometer, using specified fixed points from Table A2.1. The form of the AW(Too) function is dependent on the temperature range in which the thermometer is being calibrated. For example, in the temperature subrange from 234.3156 to 302.9146 K, the form of the deviation function is... 

Table A2.4 Temperature subranges, deviation functions, and calibration points over the temperature range covered by platinum... 

Table A2.4 is a tabulation of subranges in the temperature region 13.8033 to 1234.93 K, together with the form of the deviation equation that applies to each, and the calibration points from which the coefficients in the deviation equation are to be obtained.

Note that the Kolmogorov power spectrum is unphysical at low frequencies— the variance is infinite at k = 0. In fact the turbulence is only homogeneous within a finite range—the inertial subrange. The modified von Karman spectral model includes effects of finite inner and outer scales. 

Rorabacher, D. B., Statistical Treatment for Rejection of Deviant Values Critical Values of Dixon s Q Parameter tind Related Subrange Ratios at the 95% Confidence Level, A a/. Chem. 63, 1991, 139-146. 

For freely suspended bioparticles the most likely flow stresses are perceived to be either shear or normal (elongation) stresses caused by the local turbulent flow. In each case, there are a number of ways of describing mathematically the interactions between turbulent eddies and the suspended particles. Most methods however predict the same functional relationship between the prevailing turbulent flow stresses, material properties and equipment parameters, the only difference between them being the constant of proportionality in the equations. Typically, in the viscous dissipation subrange, theory suggests the following relationship for the mean stress [85] ... 

The simplest and fastest techniques for grouping molecules are partitioning methods. Every molecule is represented by a point in an n-dimensional space, the axes of which are defined by the n components of the descriptor vector. The range of values for each component is then subdivided into a set of subranges (or bins). As a result, the entire multidimensional space is partitioned into a number of hypercubes (or cells) of fixed size, and every molecule (represented as a point in this space) falls into one of these cells [57]. 

Step 2. Separate the total range of temperature, AT, into, v subranges each of size AT/s. Form 5 subsets of data corresponding to these temperature subranges. 

The area under the curve, lying between the limits of each of the subranges, is approximately equal to the frequency of occurrence of that subrange. 

Chasnov, J. R. (1991). Simulation of inertial-conductive subrange. Physics of Fluids A Fluid Dynamics 3, 188-200. 

The viscous-convective subrange in nonstationary turbulence. Physics of Fluids 10, 1191-1205. 

Tennekes, H. (1979). The exponential Lagrangian correlation function and turbulent diffusion in the inertial subrange. Atmos. Environ. 13, 1565-1567. 

Both from deposition studies and force balances it can be derived that the optimum (aerodynamic) particle size lies between 0.5 and 7.5 pm. Within this approximate range many different subranges have been presented as most favourable, e.g. 0.1 to 5 pm [24], 0.5 to 8.0 pm [25], 2 to 7 pm [26] and 1-5 pm [27-29]. Particles of 7.5 pm and larger mainly deposit in the oropharynx [30] whereas most particles smaller than 0.5 pm are exhaled again [31]. All inhalation systems for drug delivery to the respiratory tract produce polydisperse aerosols which can be characterized by their mass median aerodynamic diameter (MMAD) and geometric standard deviation (oq). The MMAD is the particle diameter at 50% of the cumulative mass curve. 

Concept (b) is less useful, except in rare cases where the energy spectrum has been measured. It is common to assume that the turbulence is homogeneous and isotropic and that the eddies in question are in the inertial ( — 5/3 power) subrange. This assumption is unlikely to be valid in an overall sense though it may be reasonable locally (GIO) or for the high wavenumber (small) eddies which are of primary interest. For an example of the application of the theory, see Middleman (Ml3). 

According to Kolmogorov s (1941) inertial subrange theory of turbulence, the exponent in Eq. 1 is m = 3. Inserting into Eq. 4 ... 

Most correlations show that di2 is proportional to the Weber number raised to the power of -0.6, which is consistent with the theory of drop breakup by turbulent shear forces. Strictly, these correlations should be applied only where the drop size is in the inertial subrange of turbulence, i.e.,... 

However, checks should be made that flow is fully turbulent at both scales and that the drop size remains within the inertial subrange of turbulence [Eq. (46)]. As a minimum, residence time should be maintained, i.e.,... 

Rorabacher, D.B., Statistical method for rejection of deviant values Critical values of Dixon s Q parameter and related subrange ratio of the 95% confidence level. Anal. Chem., 63, 139-146, 1991. 

The various density ranges form a hierarchy [2], indicated by boldface, underlining, and italics, as well as indentation within the list below. If a subrange in the hierarchy happens to coincide with a range, then its name is given in parentheses after the name of the range. 

The ITS-90 scale extends from 0.65 K to the highest temperature measurable with the Planck radiation law (—6000 K). Several defining ranges and subranges are used, and some of these overlap. Below —25 K, the measurements are based on vapor pressure or gas thermometry. Between 13.8 K and 1235 K, Tg is determined with a platinum resistance thermometer, and this is by far the most important standard thermometer used in physical chemistry. Above 1235 K, an optical pyrometer is the standard measrrremerrt instmment. The procedtrres used for different ranges are sttmmarized below. 

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