Gauss maximum value

Here the time o is the standard deviation of the Gauss bell-shaped curve, see Fig. 9.8-4. The maximum value of this curve or the maximum concentration of the band leaving the last vessel is... 

As the line shape function f v), a Gauss, Lorentz or Voigt function can be chosen. The mathematical expressions for these functions have v as the variable and have two parameters the band center Vq (wavenumber at which the function reaches its maximum value) and the curve width r (half width at half height). Sometimes A (half width at height 1/e) is used instead of F. The relation between both quantities is A = (In F. All these line shape functions are symmetric around the band center vo- The expressions for the functions are ... 

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. 

The foregoing discussion makes it clear that the vertical energy difference -I p) forms an electronic energy coordinate axis with a characteristic reference point, "(Ox/Red), which is experimentally accessible. This means that the probability functions can be used directly in models for electrochemical electron transfer between a solid and a simple redox system (see Sections 4.8 and 4.9). In the literature, the electronic energy coordinate axis has been denoted as E, and the characteristic points as /z°(Ox/Red) (or Fp), and and E denoted the energies corresponding to the maximum Wox E) and IERed( ) values, respectively. For quantitative purposes (see Sections 4.8 and 4.9), the probability functions are expressed as normalized Gauss functions ... 

The resulting numerical values of 204 gauss for a single-layer and 218 gauss for a doublelayer coil are much smaller than the observed maximum field strengths. It is suggested that equation (3), on which the models of Montgomery and Chandrasekhar and Hulm are based, cannot be used in the manner assumed p]. 

The line-shape of an experimental spectrum can in principle be determined by the procedure illustrated in Fig, 9.2. The 2nd derivative of the resonance line is then recorded. For a Gauss line the ratio hi/h2 between the minimum and maximum amplitudes of the 2nd derivative (Fig. 9.2(a)) equals 2.24 [18], while for a Lorentz shape it approaches the value 4. The hi/h2 ratio for a Voigt profile varies... 

Calculate the maximum splitting of the P3/2 State of the hydrogen atom due to Earth s magnetic field, which you can take as having a value of 0.6 gauss. 

Table D.2 Conversion factors for common quantities [132, 206]. These allow simple conversions from Gaussian cgs units into standard SI units and vice-versa, c == 2.998 X 10 represents the numerical value of the speed of light in SI units. The abbreviations used are poise (P), gauss (G), oersted (Oe), newton (N), pascal second (Pa s), tesla (T), ampere (A), volt (V), coulomb (C), joule (J). This quantity was formerly known as specific gravity it is the density of the material divided by the (maximum) density of water (given by 1 g cm , equivalent to 1000 kg m ).

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