Gradient of straight line

Figure 7.2. (A) The greased-gap technique for recording depolarizations of the rat isolated vagus nerve. (B) The effect of ondansetron on depolarizations of the rat isolated vagus nerve induced by 5-HT. Symbols indicate controls (9) or in the presence of ondansetron at I x 10 M (O), 3 X 70" M (M), I X 10 M (O) or 3 x 10 M (A). Results are the mean + S.E.M. of at least four determinations. Experiments were performed as described by Ireland and Tyers [21J. (C) Data from the experiments illustrated in B plotted according to Arunlakshana and Schild [22]. Each point is the result from a separate tissue. The gradient of straight line (95 Vo confidence limits) was determined using linear regression analysis.

Figure 23 shows typical stress-strain curves for plastics and explains the various types of curves. In particular, the linear elastic region (Hooke s line) is clearly defined for the materials with a very high modulus of elasticity (gradient of straight line through origin) such as ceramics, cast iron, steel, Cu, Al, and PMMA (brittle). 

This method of optimization is known as the generalized reduced-gradient (GRG) method. The objective function and the constraints are linearized ia a piecewise fashioa so that a series of straight-line segments are used to approximate them. Many computer codes are available for these methods. Two widely used ones are GRGA code (49) and GRG2 code (50). 

If this type of behaviour occurs, a plot of apparent fluidity against l/dj at constant tw will be a straight line. The gradient of the line is equal to 8C3 for the corresponding value of tw. Hence, vs can be calculated from equation 3.74 and then the corrected flow rate as before. 

A-F This straight line represents the ESPVR. If a ventricle is taken and filled to volume a , it will generate pressure A at the end of systole. When filled to volume b it will generate pressure B and so on. Each ventricle will have a curve specific to its overall function but a standard example is shown below. Changes in contractility can alter the gradient of the line, a-f This curve represents the ED PVR. When the ventricle is filled to volume a it will, by definition, have an end-diastolic pressure a . When filled to volume b it will have a pressure b and so on. The line offers some information about diastolic function and is altered by changes in compliance, distensibility and relaxation of the ventricle. 

The gradient of the line, m, can also be equated to the differential coefficient (written as dy/dx)) and can be said in turn to be the result of differentiating y with respect to x. The intercept on the y-axis (the ordinate) when x = 0 is c, another constant (subject to the caveat above), m can also be determined from the coordinates, (xi, yi) and (xj, yi) of two arbitrary points (best separated as far apart as is possible to improve the accuracy of this calculation of gradient) on the straight line. 

Clearly, this gives a straight line when 6/7m is plotted against 8/7m- Note that the gradient of the line is a 6/8 ratio, but it is that of neither A or B, and lies between the two. The proportion of each type of Pb in any mixture is indicated by the position of the mixture on the line joining the composition of each constituent. The complete isotopic composition of each component of the mixture needs to be taken into consideration if the atomic ratio of the two components is required. 

We thus obtain a femily of straight line (Fig. 9.5a). Other lines in the family would be parallel lines with a gradient 2. 

Hofstee plot A graphical method used in enzyme kinetics to obtain a straight line fiom experimental data. It involves forming aplotofV/SversusVinwhichSis the substrate concentration at which the velocity v is observed. The gradient of the line is equal to -K and the intercept on the y-axis is equal to the maximum velocity V. Also known as the Eadie-Hofstee plot, it is named after Canadian biochemist George Sharp Eadie (1895-1976) and B. H. J. Hofstee who developed the plot in 1942 and 1959, respectively. See michaelis-MENTEN KINETICS. 

By plotting InCp po) against x the damping coefficient a is the gradient of the resulting straight line. To separate the elements oq and Ota in a it is possible to measure the backscattering acoustic wave pressure Ps. 

A plot of Tm l) against 1/7 would give a straight line with an intercept Tra(0, p) given by the Flory-Vrij equation and a gradient having a different interpretation than that from Eq. (2.17). 

The relationship between film thickness of hexadecane with the addition of cholesteryl LCs and rolling speed under different pressures is shown in Fig. 25 [50], where the straight line is the theoretic film thickness calculated from the Hamrock-Dowson formula based on the bulk viscosity under the pressure of 0.174 GPa. It can be seen that for all lubricants, when speed is high, it is in the EHL regime and a speed index 4> about 0.67 is produced. When the rolling speed decreases and the film thickness falls to about 30 nm, the static adsorption film and ordered fluid film cannot be negligible, and the gradient reduces to less than 0.67 and the transition from EHL to TFL occurs. For pure hexadecane, due to the weak interaction between hexadecane molecules and metal surfaces, the static and ordered films are very thin. EHL... 

Since the second member on the right-hand side is essentially constant for the solid and liquids considered, we should expect a plot of log[cos Go cos G((/)] versus log U to give straight lines of gradient n that are directly superposable, irrespective of liquid viscosity. 

The intensities of the echoes (signal intensities) are than plotted as a function of delays. This yields a straight line whose gradient is — l/Tj. The decay in the intensities of echoes (i.e., of the succession of signals which follow the FID), is determined solely by T2. 

If one does not use the short gradient pulse (SGP) approximation, the term A has to be substituted with (A 8/3). In the case of a mono-disperse system, the plot of ln(E) versus y2g282A is a straight line having the absolute value of the slope equal to the self-diffusion coefficient. For polydisperse sample, the signal intensity decay can be interpreted in terms of a distribution of diffusing species ... 

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