Histograms, using

Histograms - used to reveal the variation of characteristics or frequency distribution obtained from measurement... 

Precise thickness measurements by TEM require sections transverse to the basal lamellar surface. Conversely, only lamellae that can be identified as untilted "edge-on" or "flat-on" in AFM images are suitable for thickness analysis. The average thickness obtained by these techniques is based on sampling microscopic areas and will only be correct if the morphology is uniform in the sample. Micrographs taken from different areas of the specimen are usually studied, and statistical analysis of histograms used for quantitative analysis [255,256]. 

For the moment estimates, we have seen that the composition PDF, /, (delta functions (i.e., the empirical PDF in (6.210)). However, it should be intuitively apparent that this representation is unsatisfactory for understanding the behavior of fyiir) as a function of fj. In practice, the delta-function representation is replaced by a histogram using finite-sized bins in composition space (see Fig. 6.5). The histogram h, (k) for the /ctli cell in composition space is defined by... 

Figure 3.17. Interatomic distances in CsCI. The distances are given for the CsCI compound (cubic, cP2-CsCl type, a = 411.3 pm) with Cs and Cl in the representative positions 0, 0, 0, and A, A, A respectively, white and black atoms in Fig. 3.8. In the tables the first two groups of distances (in pm) are given as positions of each atom around the reference atom. Notice that not only atoms in the reference cell but also those in the adjacent cells must be considered (see Figs. 3.8 (d)-(f)). At the right side, the corresponding histograms using the reduced distances d/dmm are shown the first two bars summarize the data contained in the table.

Fig. 9. Flow analysis of apoptotic human peripheral blood lymphocytes using direct TUNEL assay. Human peripheral blood lymphocytes (1 x 10 ) treated (A) without or (B) with dexamethasone (0.1 ijlM) for 16 h were transferred to a 15-ml tube. Paraformaldehyde (2%) was added to cells with shaking and incubated for 10-15 min in ice with occasional shaking. Cells were washed with PBS with 1% BSA and 3-4 ml cold acetone was then added to cells. After 2-3 min incubation on ice with occasional shaking, cells were washed twice and TUNEL reaction mixture including enzyme TdT and fluorescein-labeled anti-dUTP antibody was added to cells (H). For the negative control group, only label solution without TdT was added to cells ( ). Cells without any addition of reaction or label solution were used for assessment of the autofluorescence ( ). The cell mixture was incubated 1 h at 37°C in the dark. The result of the apoptosis after flow analysis was expressed as a histogram using software CellQuest (Becton Dickinson). In Fig. 9A Ml (nonapoptotic cells), 86% M2 (apoptotic cells), 14%. In Fig. 9B Ml (nonapoptotic cells), 78% M2 (apoptotic cells), 22% (our unpublished data).

Comparison of color histograms does not necessarily have to be done in RGB space. Histograms can also be computed for a variety of color spaces or certain subspaces. Swain and Ballard computed the histograms using three opponent color axes red-green (RG), blue-yellow (BY), and black-white (BW). Let c = [cr, cg, cb]T be the color of the input pixel, then the transformed pixel coordinates c = [crg, Cby, q,w]r are given as... 

However, the RDF(CM) is not appropriate when the solute is an elongated molecule, as it was discussed before, for the case of (3-carotene in several solvents [47] and benzophenone in water [50], In these cases of elongated solutes, an appropriate function is the minimum-distance distribution function (MDDF), where the histogram used to calculate the distribution function is not the distance between the CMs of solute-solvent, but the minimum distance between them. The MDDF is defined as... 

Figure 11.54 The bimodal growth of Ag nanoprisms. a) TEM image of a sample of Ag nanoprisms formed using single-beam excitation (550 20 nm) inset, histograms used to charactaize the size distribution as bimodal. b, c) TEM images of nanoprism stacks showing that nanoprisms have nearly identical thicknesses (9.8 1.0 nm). d) Schematic diagram of the proposed light-induced fusion growth of Ag nanoprisms. Reprinted by permission from Macmillan Publishers Ltd Nature [109] C> (2003).

Figure 18.11 Frequency distribution of denitrification measurements from a variety of estuarine ecosystems. The inset is a frequency histogram using denitrification measurements from all aquatic systems. Both figures used data from the denitrification summary developed by Greene...

Other useful types of distributions are the simple adding distributions . Examples are the cumulative frequency distribution and the histograms. Herber and Pieters (1982) made an adding distribution and histogram using not only the data of the analysis, but also the precision of the determination. This may lead to a better insight into the real character of the distribution. Fig. 2 gives an example. 

If those equations are not suitable for analysis of the histogram or the cumulative histogram, use the extended equations. 

Results A standard set of descriptive statistics was generated for each scenario based on the set of 50 Monte Carlo runs. The temporal performance data were also plotted as a histogram using a bin size of 10 seconds, illustrated in Figure 25. 

Each histogram used in the calculation has typically other features (another dispersion, other number of data...). Then, it might not be a good and feasible solution to divide the histogram into same classes/intervals. Each histogram can have a different value, (Ax)a, and a different number of classes, . ... 

Figure 7. Amplitude distribution curves and height histograms used for surface texture parameters determinations for Epiclon-derived Pis. Each insert shows corresponding 3x3 pm bidimensional topographical image...

The muon lifetime of 2.2 ps sets a natural limit of 0.45 MHz on the widths of, aSR lines. The nominal frequency resolution is given by the inverse length of the histogram. Using pulsed machines it is not uncommon to observe the FID over a time window of 20 ps, which leads to a nominal resolution of 0.05 MHz. 

Tests for normality Tests for normality are statistical methods (Descriptive Statistics, Histograms) used to determine if the data collected is normal or abnormal so as to be properly analyzed by other tools. Correlation/regression analysis These tools help to identify the relationship between inputs and outputs or the correlation between two different sets of variables. 

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