Gauss curve

Multiplication with a scalar height then defines the amplitude of the peak. This is shown in the example Gauss Curve. m below ... 

Then, comparing the moments (24) with the moments of Gauss curve (p(Q),... 

The magnetic field (about 16,000 gauss) curves the ion beam, the radius... 

Often forgotten is the fact that there may be a clinically significant drug response difference between two populations even if the average response differences are small, perhaps not even statistically significant (39). If population data are represented by a normal distribution (Gauss) curve, the persons with abnormal responses may be represented by one of the edges of the curve. 

This equation is unidimensional, and the concentration N. x, t) in it is expressed as mole m k Besides, in substance it is adequate with normal distribution density function (Gauss curve) ... 

ESR lines in solution can almost always be approximated by a Lorentz function. In the solid state the line-shape can in general be reproduced by a Gauss curve. In some instances a so-called Voigt profile can give a better approximation to the experimental line-shape. A Voigt line is a convolution of a Lorentz and a Gauss line. The shape is determined by the ratio ABi/ABg of the respective line-widths. The shapes of the 1st derivative lines of these types are given in Fig. 9.1. 

Fig. 9.14 Homogeneous (a) and inhomogeneous (b) ESR lines. The spin-spin relaxation time T2 = 1/(y-ABl) is obtained from the line-width ABl measured at half height of the absorption amplitude of the Lorentz line (a). The inhomogeneous line (b) is an envelope of overlapping homogeneous line. The shape of the envelope approaches a Gauss curve...

The variation of the cumulative residence time distribution function is represented by a Gauss curve, indicating the concentration variation C t) as a function of time according to Figure 14.5 ... 

The overlaid peaks of the simulation were separated with the vertical separation method for area integration. For comparison, the overlaid peaks of the simulation were separated with the recommended curve fitting by Mr Westerberg (deconvolution) using the Gauss curve model. 

Note that Laplace (not Gauss) first derived the equation for the Gaussian (normal) error curves, which need not be normal in the sense that they normally apply to errors encountered in practice (text above). 

Kinetic curves were analyzed and the further correlations were determined with a nonlinear least-square-method PC program, working with the Gauss-Newton method. 

The most effective spectrophotometric procedures for pKa determination are based on the processing of whole absorption curves over a broad range of wavelengths, with data collected over a suitable range of pH. Most of the approaches are based on mass balance equations incorporating absorbance data (of solutions adjusted to various pH values) as dependent variables and equilibrium constants as parameters, refined by nonlinear least-squares refinement, using Gauss-Newton, Marquardt, or Simplex procedures [120-126,226],... 

In this problem the Gram-Charlier will be compared with the Gamma Gauss distributions for an impulse response curve with the equation... 

Figure 8.13 Dispersion of an instantaneous point source [equation (8.5.1)]. A quantity of the diffusing species equivalent to the surface of whatever curve on the diagram is deposited initially at x = 0. The curves are Gauss functions.

The following function gauss. m creates a Gaussian curve with a given width and centre and a peak maximum of one, which is more convenient for our purposes. 

The best-fitting set of parameters can be found by minimization of the objective function (Section 13.2.8.2). This can be performed only by iterative procedures. For this purpose several minimization algorithms can be applied, for example, Simplex, Gauss-Newton, and the Marquardt methods. It is not the aim of this chapter to deal with non-linear curve-fitting extensively. For further reference, excellent papers and books are available [18]. 

The normal distribution and the statistical tools linked with it are the most important statistical tools in analytical chemistry. The normal distribution was first studied by the German mathematician Carl Friedrich Gauss as a curve for the distributions of errors. 

G. K.-L. Chan, M. Ka llay, and J. Gauss, State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. J. Chem. Phys. 121, 6110 (2004). 

The Gauss integral is an integer number Ny that can be calculated by considering the field B, along the curve C, ... 

Adding the proton-free solvent carbon tetrachloride to polystyrene, one observes the relationship between line width and temperature as shown in Figures 5a and 5b. For the system polystyrene with 21.5% carbon tetrachloride the absorption curves for various temperatures are plotted against the field strength (2) in gauss. As the temperature decreases, the line broadens, as shown more clearly in... 

Integrate this identity over the region Q of the valley enclosed by the curve L along the top of the ridge, using Gauss theorem in two dimensions,... 

The line widths recorded are the distances, in gauss, between the two maxima of the differential curve and thus represented the width of the absorption curve at the level of maximum slope. For a curve of Lorentzian shape, this width is equal to 0.577/T2, where T2 is the spin-spin or transverse relaxation time (12). Since the curves were not strictly Lorentzian (though they were so to well below the region of maximum slope) and in any case were not of identical shape, the recorded line widths do not have this exact theoretical significance, and small differences in width between two samples could be caused by shape differences rather than variations in relaxation phenomena. Nevertheless, since the conclusions drawn later from the observed line widths depend on major differences in level rather than subtle differences in numerical value, they should be perfectly valid. 

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