Methods slope

The Newton-Raphson approach, being essentially a point-slope method, converges most rapidly for near linear objective functions. Thus it is helpful to note that tends to vary as 1/P and as exp(l/T). For bubble-point-temperature calculation, we can define an objective function... 

In order to compress the measured data through a wavelet-based technique, it is necessary to perform a series of convolutions on the data Becau.se of the finite size of the convolution filters, the data may be decomposed only after enough data has been collected so as to allow convolution and decomposition on a wavelet basis. Therefore, point-bypoint data compression as done by the boxcar or backward slope methods is not possible using wavelets. Usually, a window of data of length 2" m e Z, is collected before decomposition and selection of the appropriate... 

Table 1 Representative data evaluating data obtained from various studies for calculating the LOD and LOQ values for the extraction/analysis procedure using the 3(RMSE)/slope method to estimate the LOD/LOQ and the 799, j,seloq method to calculate the MDL and MQL...

In the dual slope method, referring to the Fig. 12.1, the support (Sp), with the thermometer (Th) and the sample (S), is heated by the heater (H) with a constant power I during the first phase of an acquisition. In this step, the sample temperature Ts rises from 1 to T2. Then, the power P is reduced to a value P to bring the sample back to a temperature T( 7, . During these phases, the temperatures rrise and TfM are both recorded. The two following equations describe the heating and the cooling phase respectively ... 

Hence, the heat capacity can be obtained with a fit from the derivatives of the temperatures. In the dual slope method, the analysis of the experimental data is quite complex, but there are two advantages the range of temperature can be wide and the explicit knowledge of G(T) is not necessary. 

In the second run, the heat capacity of the sample was measured in the 0.7-4.2 K temperature range, with the dual slope method and the conductance G made by a Cu wire. Data of heat capacity were obtained with a more complex method described in ref. [37]. 

To overcome the uncertainty of the actual onset of ionization, among several others, [80] the critical slope method has been developed. [25,81] It makes use of the fact that from theory realistic values of IE are expected at the position of the ionization efficiency curve where the slope of a semilog plot of the curve is... 

Barfield, A.F. Wahrhaftig, A.L. Determination of Appearance Potentials by the Critical Slope Method. J. Chem. Phys. 1964, 47,2947-2948. 

Effect of Acetic Acid. Addition of acetic acid (35 X 10 2 mole/ liter) to a solution containing Tetralin hydroperoxide (2.0 X 10 2 mole/ liter) and dilauryl thiodipropionate (2.5 X 10 2 mole/liter) not only eliminated the 60-minute induction period but substantially increased the rate of reaction (Figure 5). The over-all rate equation in the presence of acetic acid at 70°C., determined by the initial slopes method was... 

The dual-slope method has a number of important features. Conversion accuracy is independent of the effect of temperature or aging on the clock frequency and integrating capacitor value, since they need to remain stable only during a conversion cycle. Accuracy... 

Identification of the Parameters of a Model by the Steepest Slope Method... 

To make the calculation for the identification of parameters kg, n, k by using the highest slope method (MHSM), we must determine the function that will be minimized and the mathematical model of the process which correlates these parameters with the computed values of c and t. Because we have the dependences Ca — T and t — t we can consider for the minimization the functions below written as ... 

Figure 5.11 Representation of the displacement to the great curvature domain. A, according to the greatest slope method B, according to the regular simplex method.

Point-Slope Methods. Euler s method follows directly from the initial condition as a starting point and the differential equation as the slope (Fig. 3). Consider the simple model of a single differential Eq. (13) with one first-order rate process ... 

Several investigators have gone to great length to insure that the anisotropies be independent of the medium. Hayamizu and Yamamoto41 measured the proton anisotropy of trihalobenzenes in two liquid crystals using the slope method and found virtually identical results. Mohanty (private communication) studied the molecule acetylene in four liquid crystals at various pressures using several references. The results were a fairly reproducible anisotropy of 22 2 ppm. 

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