Four-point region

This curve is used to represent the spectrum between the two center points in this region. Cubic equations are computed for every four-point region of the spectrum, so that the entire range of interest is covered. This method is used by some manufacturers of FT-IR spectrometers to produce a smooth spectrum on a screen or on... 

Diffusivities of various elements ate determined experimentally. Dopant profiles can be determined. The junction depth can be measured by chemically staining an angle-lapped sample with an HE/HNO mixture. The -type region of the junction stains darker than the n-ty e region. The sheet resistivity can also be measured using a four-point probe measurement. These two techniques ate used for process monitoring. 

Fig. 10,3 The four points - (0,0), (1,0), (0,1), (1,1) - corresponding to the input vectors for the XOR problem (see table 10.2). Note how the line r = wixi + 11)2x2 divides the plane into only two regions and is thu.s unable to isolate the points (0,0) and (1,1) from the points (0,1) and (1,0).

Identify the major species in solution by assigning each of the points to one of the four characteristic regions of the titration curve. In the titration reaction, hydroxide ions react with molecules of weak acid ... 

In this case the operability region can be visualized as a rectangular prism in the 3-dimensional xo rD-cF - space as seen in Figure 12.6. A grid of four points in each variable has been used. 

Miller and Bada (1988) and Miller et al. (1989) attempted to answer the question as to whether biogenesis processes can occur at hydrothermal vents in regions of the deep sea. Miller states clearly that biomolecules could not have been formed under such conditions. Holm (1992) sums up Miller s arguments in the following four points ... 

To illustrate the first stage in the search procedure, examine the four points in Figure 5.4 for stage 1. We want to reduce the initial interval [xv jc3]. By examining the values of f(x) [with the assumptions that/(x) is unimodal and has a minimum], we can discard the interval from xx to jc2 and use the region (x2, x3) as the new interval. The new interval contains three points, (jc2, x9 x3) that can be introduced into Equation (5.12) to estimate a, and so on. In general, you evaluate/(jt ) and discard from the set xl9 x2, jc3 the point that corresponds to the greatest value of/(jt), unless... 

The phase diagram features four phase regions, three phase boundaries, and two points of particular interest the triple point (TP) and the supercritical point (CP). Values for TP and CP from The International Association for the Properties of Water and Steam6 (IAPWS) are 273.16 K and 611.657 Pa (IAPWS, 2002) and 647.096 K and 22.064 MPa (IAPWS, 2002), respectively. Three of the phases (solid, liquid, and gas) are bounded by equilibrium... 

Next, consider the case with p = 0.02014. The traverse across Fig. 12.6(a) as r is varied now also cuts the region of multi stability. It passes above the cusp point C (see Fig. 12.5), giving rise to two turning points in the stationary-state locus, but below the double-zero eigenvalue point M. There are still four intersections with the Hopf curve, so there are four points of Hopf bifurcation. The Hopf point at highest r is now a subcritical bifurcation. The dependence of the reaction rate on r for this system is shown in Fig. 12.6(d). 

Figure 3.16 illustrates a flow field with a specific region highlighted. Based on the spreadsheet representation of the flow field (CVD SolutionAlone. xls), the objective is to determine mass flow into and out of the highlighted region and relate the analysis to the stream function. The coordinates of the four points that define the comers of the region are ... 

According to this equation the maximum number of phases that can be in equilibrium in a binary system is = 4 (F= 0) and maximum number of degrees of freedom needed to describe the system = 3 (n=l). This means that all phase equilibria can be represented in a three-dimensional P,T,x-space. At equilibrium every phase participating in a phase equilibrium has the same P and T, but in principle a different composition x. This means that a four-phase-equilibrium (F=0) is given by four points in P, 7, x-space, a three-phase equilibrium (P=l) by three curves, a two-phase equilibrium (F=2) by two planes and a one phase state (F= 3) by a region. The critical state and the azeotropic state are represented by one curve. 

Fig. 27. Impedance diagrams measured at four points of the polarization curve of Fe in 1 MH2SO4, in the so-called passivation region. The numbers indicate frequency in Hz. From ref. 94.

Returning to the example of Figure 8.16, we see that the four points, namely a, b, c, and d, are positioned symmetrically within the experimental region. If we suppose that the region E is constrained in the following manner... 

Figure 21-19. Region of complete separation (solid line) in the (mj/mm) plane for a feed concentration of 25 g racemate/L calculated with the parameter of the MDM adsorption isotherms and for the given lab-scale SMB unit (12 columns each 100-mm X 16-mm i.d., 3 in each zone). The four points mentioned illustrate the following scenarios 1, robust conditions to obtain pure enantiomers 2, less robust system with highest productivity 3, area of pure extract and impure raffinate 4, area of pure raffinate and impure extract. 1-A 2-0 3-D 4-0. (From reference 124, with permission.)...

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