Gaussian shape

The Derivative of Gaussian (DroG) operator is a classical example of a compound edge gradient. It combines a Gaussian shaped smoothing with a following differentiation and is described in [5]. 

When a chromatographic peak has a Gaussian shape, its width at the baseline, w, is four times its standard deviation, T. 

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...

The chromatogram of the test sample for plate number determination normally is not a Gaussian-shaped peak, which means that all three equations result in different N values. Therefore, it is important to specify which method is used for the calculation of plate number. If the method used deviates from the normal practice, it must be justified. This is especially true for a column manufacturer. 

At each temperature one can determine the equilibrium lattice constant aQ for the minimum of F. This leads to the thermal expansion of the alloy lattice. At equilibrium the probability f(.p,6=0) of finding an atom away from the reference lattice point is of a Gaussian shape, as shown in Fig. 1. In Fig.2, we present the temperature dependence of lattice constants of pure 2D square and FCC crystals, calculated by the present continuous displacement treatment of CVM. One can see in Fig.2 that the lattice expansion coefficient of 2D lattice is much larger than that of FCC lattice, with the use of the identical Lennard-Lones (LJ) potential. It is understood that the close packing makes thermal expansion smaller. 

Although there was some skewing towards low molecular weights particularly for the narrowest distribution, these curves were generally well fit by a Gaussian shape. Furthermore, the same was found for the copolymer fractions shown in Figure 16. Results are summarized in Table V. 

In order to properly take into account the instrumental broadening, the function describing the peak shape must be considered. In the case of Lorentzian shape it is Psize = Pexp - instr while for Gaussian shape p = Pl -Pl tr- In the case of pseudo-Voigt function, Gaussian and Lorentzian contributions must be treated separately [39]. 

Fig. 2.7 Dependence of the experimental line width Cexp on the effective absorber thickness t for Lorentzian lines and inhomogenously broadened lines with quasi-Gaussian shape (from [9])...

Gaussian shape the mean-squared displacement of spins or molecules follows the same Gaussian evolution as the concentration of a pointlike source. It has the shape... 

Gaussian-shaped depth profiles of P with three parameters of maximum concentration (Cmax), projected range (Rp) and range straggling (ARp). The energy loss (dE/dx) and energy straggling ( 2 square root of the variance) of the a beam in the Si layer were taken into account ... 

Fig. 20 Chain sliding diffusion model of primary nucleation. Polymer chains are rearranged from Gaussian shape within the melt into a nucleus through chain sliding diffusion within the nucleus and disentanglement within the interface. Bottom graph indicates change in free energy of the nucleus against N...

Frequency-selective REDOR (fsREDOR) is a very powerful technique developed for the study of 13C and 15N uniformly labeled peptides or proteins [92]. The basic idea of this technique is to combine REDOR and soft n pulses to recouple a selected 13C-15N dipole-dipole interaction in a multiple-spin system. Usually one could use Gaussian shaped pulses to achieve the required selective n inversions. Other band selective shaped pulses have been developed for a more uniform excitation profile [93]. In its original implementation, fsREDOR was used to extract the intemuclear distances of several model crystalline compounds [92], In the past few years, this technique has proven to be very useful for the study of amyloid fibrils as well. For the Ure2p10 39 fibril samples containing 13C and 15N uniformly... 

Efficiency, N, for column separations is related to retention time and peak width measured in terms of the standard deviation, assuming an ideally Gaussian-shaped peak (p. 16), i.e. 

For a stationary spray without scanning, a Gaussian shaped mass distribution typically develops with an annular-jet or discrete-jet atomizer. The radial mass distribution in the spray can be formulated in terms of mass flux)632]... 

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