Transformers fittings

From Eq. (14.8), we wish to evaluate the Fourier integral transform (FIT)... 

Model correlation functions. Certain model correlation functions have been found that model the intracollisional process fairly closely. These satisfy a number of physical and mathematical requirements and their Fourier transforms provide a simple analytical model of the spectral profile. The model functions depend on the choice of two or three parameters which may be related to the physics (i.e., the spectral moments) of the system. Sears [363, 362] expanded the classical correlation function as a series in powers of time squared, assuming an exponential overlap-induced dipole moment as in Eq. 4.1. The series was truncated at the second term and the parameters of the dipole model were related to the spectral moments [79]. The spectral model profile was obtained by Fourier transform. Levine and Birnbaum [232] developed a classical line shape, assuming straight trajectories and a Gaussian dipole function. The model was successful in reproducing measured He-Ar [232] and other [189, 245] spectra. Moreover, the quantum effect associated with the straight path approximation could also be estimated. We will be interested in such three-parameter model correlation functions below whose Fourier transforms fit measured spectra and the computed quantum profiles closely see Section 5.10. Intracollisional model correlation functions were discussed by Birnbaum et a/., (1982). 

The r-gon has r — 2 interior vertices. All those transformations fit together around those vertices. So, they yield an isohedral (r, 4)-polycycle. ... 

In the case of the Ai-E optical transition one can present H and V as the sum of the independent terms belonging to diflFerent representations. In this case the Fourier transform Fit) is the product of the multipliers belonging to these representations. We are interested in the multiplier, which describes the contribution of the e-vibrations. Here we consider the case of strong Jahn-Teller effect. ZPL in this case is described by the optical transitions for configurational coordinates qi and q2 in the vicinity of the AP minima. This means that one can use equation (4) with V given by equation (3). In this approximation the configurational coordinates q and q2 contribute to F(t) independently. Later we consider a contribution of one of these coordinates and omit the index of the line of the representation. 

Jandanklang, P., Maeder, M., and Whitson, A.C., Target transform fitting a new method for the non-linear fitting of multivariate data with separable parameters, J. Chemom., 2001, 15, 511-522. 

Here, % = (B—Bq) measures the spectral position as the deviation of the magnetic field B from the field Bq at the center of the spectrum, which corresponds to the position x = 0, because the field gradient B maps x onto %, as given by = B x. The determination of C(, t) from the two spectra Ig(, t) and lo( ) is a straightforward calculation through Fourier transformation. Fitting the C(, t) profile to the diffusion equation gives the diffusion rate. 

General estimates for the 100a and 100(1 - a) percentiles and their 0.90 confidence intervals can be determined by the following method, provided that data (original or transformed) fit the Gaussian distribution ... 

Resolution and sensitivity are essential to the collection of analytical chemical data with accuracy and precision. It is well known that mathematical transformation techniques enhance the resolution and sensitivity of spectroscopic methods. Fourier transform (FT), cross correlation (CC), and Fladamard transform (FIT) techniques allow for high resolution and high sensitivity of infrared spectroscopy (IR), fiuorometry, nuclear magnetic resonance... 

The gas accumulates in a special chamber which is fitted with two float switches, and these operate alarms and trips when the gas accumulates slowly or rushes in during internal explosions. This system is called a Buchholz relay, and is normally used only on transformers fitted with conservator tanks. Transformers below about 1600 kVA are often sealed type liquid-immersed units. Internal explosions are released by using a special blow-off valve. Often the space above the liquid level in this type of unit is filled with an inert gas such as nitrogen. 

To quantitatively describe the change in Ny upon stretching, Kuhn and Mark [3,4] assumed (and that may be partially verified) that the affine transformation fit. This affine assumption states that the components of the displacement vectors in the bulk sample change in the same ratio as do the external dimensions of the rubber, that is. 

However, they can be put in linear form by data transformation. Fitting these functions by least squares is not necessarily straightforward, but fortunately there are user-friendly curve fitting software utilities included with most major spreadsheets and statistical packages that will find the best fit for these and other functions. 

This transformation fits the definition of a photocatalytic reaction, whereby a thermally active catalyst is photogenerated. This situation differs from that observed with a photoassisted reaction, which is a photolytic reaction that ceases when the light source is removed. In photocatalytic systems the reaction is catalytic in the number of incident photons, and therefore the quantum yield 0 > 1. In photoassisted reactions where continuous irradiation is required to obtain the product, the quantum yield (j> <... 

Measurements of curves of compressibility in a die press and roll press were carried out for three materials such as potash, salt and fertilizer. Fig.3 shows measured curve of compressibility as well as fitted curves according to particular equations (2,6,9,11) in die press (d =25 mm) for potash. One can conclude that all equations fit well the measured values but eq. (11) derived from power modulus of volume transformation fits them best (according to visual observation as well as statistical characteristic z )-... 

Fig. 4 and fig. 5 show the same kind of information as fig. 3 does with exception that fig. 4 is for fertiliser and fig. 5 is for salt. The equation of compressibility (11) derived from power modulus of volume transformation fits the measured data best for both materials. 

After discussing the MCTDH equations of motion, a practicable scheme has to be developed which facilitates the numerical evaluation of these equations. The single-particle functions have to be represented by a finite set of numbers. This is most conveniently achieved by employing a collocation scheme of the fast Fourier transform (FIT) or of the discrete variable representation (DVR) type. The single-particle functions of the /fth degree of freedom are then represented by their values on a set of grid points. 

---