Gaussian distribution half-width

LiC/cm. A Gaussian distribution about the draw direction characterises the chain axis reorientation in the stretched samples. The PVDF (draw ratio 3) has a Gaussian distribution of width 220 (half-width at e of maximum). Angular dependence of the magnetisation for the poled PVDF homopolymer films was not expected due to the low remanent polarisation of the samples. 

Fig. 3.31. Distributions (i)/(Ee) dEe of electron energy (E ) for a low-pressure HF-plasma (suffix pi, Maxwellian with temperature = 80000 K) and an electron beam (suffix eb, simplified to Gaussian shape with 40 eV half-width) (ii) rTx (Ej) ofthe Ej dependent electron impact ionization cross-section for X=Ti...

Half-Height Method. For an ideal Gaussian distribution the peak width Wb at the half of the maximal height is 2.355 or. If the width at the half-height is inserted in Eq. (1), we get... 

In certain applications it is of interest to express the width of the Gaussian distribution at half its value at the maximum. Thus, as the maximum value is /(0) = y/ct jn, the value of z at half of this value is y/ln 2/a and the width at half-height is given by... 

FIGURE 9.1 Linewidth versus standard deviation. A gaussian distribution of unit amplitude is plotted on an x-axis scale in units of the standard deviation (or sigma). At 3.15x0 the unit intensity has dropped to 0.1%. The linewidth in simulations is usually expressed as the halfwidth at half height (HWHH), which is equal to circa 1.17x0, or as twice this value that is, the full width at half height (FWHH). 

Because it is often difficult to measure the base width (W) accurately, it is probably better to use the peak width at half peak height, which is known to equal 2.355Gaussian distribution. Hence ... 

A Gaussian curve is characterised by peak position, peak height and peak width. Commonly, the half width is used, i.e. the width at half peak height. We accommodate this convention. In statistics, the Gaussian distribution is usually normalised to unit integral, however, this is not useful in the present context. 

The formation of a boundary between the dextran solution and the dextran solution containing PVP 360 (concentration 5 kg m 3) yields an apparently normal Gaussian distribution of the material detected by Schlieren optics. The various apparent diffusion coefficients obtained by an analysis of the Schlieren curves, which include diffusion coefficients obtained by the reduced height-area ratio method, the reduced second-moment and the width-at-half-height method, show the same qualitative behavior although quantitative differences do exist. This is seen in Fig. 7 where the... 

Thermal motion induces different displacement speeds for the molecules and thus different transition probabilities. These change from one molecule to another and from one population of molecules to another. In this case, the spectral distribution will be Gaussian. The full width at half maximum of a Gaussian spectrum is greater than that of a Lorenzian spectrum. 

We take a Gaussian distribution of chain lengths with a full-width half maximum AL and peaking at Lp to account for the expected disorder in the liquid phase at room temperature. 

The small random crystal strains can be quantified and this is also given in Table 5. It was found that the sttain can be described by a Gaussian distribution characterised by a mean value, 8, of zero and a half width of 8a = 2cm . The analysis also differed from that of previous workers in both the hyperfine values and the requirement of a nuclear quadrupole term. The transitions within the lowest excited singlet could also be observed directly [31]. It can be concluded that the Cu(ll)/MgO system can be described as an almost pure dynamic Jahn-Teller case. 

The exponential term leads to a Gaussian distribution around the distance r j with a half-peak width depending on the smoothing parameter B. 

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