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Maximization of rectangles

Maximization of rectangles applied to find the optimum intermediate conversion and optimum sizes of two CSTR s in series. (Adapted from... [Pg.284]

Maximization of Rectangles. In Fig. 6.10, construct a rectangle between the x-y axes and touching the arbitrary curve at point M x, y). The area of the rectangle is then... [Pg.133]

Part (b) Solution. Drawing slopes and diagonals according to the method of maximization of rectangles we end up with Fig. E6.36. [Pg.146]

To minimize the amount of catalyst needed Chapter 6 says use the method of maximization of rectangles, so tabulate versus l/(- A)opt... [Pg.441]

And use the method of maximization of rectangles as shown in Fig. E19.2fo. Then from the performance equation... [Pg.441]

Figure 8.13 Maximization of rectangles applied to find the optimum intermediate conversion and optimum sizes of two CSTRs in a cascade configuration. (Adapted from O. Levenspiel, Chemical Reaction Engineering, 2nd ed. Copyright 1972. Reprinted by permission of John WUey Sons, Inc.)... Figure 8.13 Maximization of rectangles applied to find the optimum intermediate conversion and optimum sizes of two CSTRs in a cascade configuration. (Adapted from O. Levenspiel, Chemical Reaction Engineering, 2nd ed. Copyright 1972. Reprinted by permission of John WUey Sons, Inc.)...
We will use this method of maximizing a rectangle in later chapters. But let us return to our problem. [Pg.134]

Suppose that the initial state is confined to a rectangle R = (i,nin> max) x (i where imin and max are the minimal and maximal i coordinates of the region containing nonzero sites and j in and jmax are the minimal and maximal j coordinates of that same region. Then according to corollary 1, the transient length T2d majority is bounded by... [Pg.283]

Figure 6.9 shows that the total reactor volume is as small as possible (total shaded area is minimized) when the rectangle KLMN is as large as possible. This brings us to the problem of choosing (or point M on the curve) so as to maximize the area of this rectangle. Consider this general problem. [Pg.133]

Figure 6.10 Graphical procedure for maximizing the area of a rectangle. Figure 6.10 Graphical procedure for maximizing the area of a rectangle.
In words, this condition means that the area is maximized when M is at that point where the slope of the curve equals the slope of the diagonal NL of the rectangle. Depending on the shape of the curve, there may be more than one or there may be no best point. However, for /ith-order kinetics, n > 0, there always is just one best point. [Pg.134]

Let us stick to response geometrical interpretation of black box with two input factors. A simple graphic system with x-y coordinates is sufficient for this. One may insert values of variation levels of one factor on one axis, and those of the other factor on another axis. Each black box status will have a corresponding point in the surface. As has been said in Sect. 2.1.3, factors are defined by their domains. This means that each factor is defined by its minimal and maximal values where it may be changed continuously or discontinuously. If the factors are concordant then those limits in the plane form a rectangle within which are the points that coincide with black box statuses. Dashed lines in Fig. 2.28 mark the limit values of the domain of factors and full lines the limits of concordant domain of factors. To present graphically the response values, we use the third axis of the coordinate system, so that the response surface has the shape given in Fig. 2.29. [Pg.262]

A wide variety of problems can be solved by finding maximum or minimum values of functions. For example, suppose it is desired to maximize the area of a rectangle inscribed in a semicircle. The area of the rectangle is given by A = 2xy. The semicircle is given by x + y = r, for y > 0, where r is the radius. To simplify the mathematics, note that A and A are both maximum for the same values of x and y, which occurs when the comer of the rectangle intersects the semicircle, that is, when y = r - x. Thus, we must find a maximum value of the function A = 4x (r -x ) = 4r x - 4x". The required condition... [Pg.262]

Restored A restored window is one that can be used interactively and is identical in function to a maximized window, with the simple difference that it does not necessarily take up the entire screen. Restored windows can be very small, or they can take up almost as much space as maximized windows. Generally, how large the restored window becomes is the user s choice. Restored windows display a restore box (the middle button in the upper-right corner) with a single rectangle in it this is used to maximize the window. Restored windows have a border. Figure 12.19 shows an example of Notepad in a restored state. [Pg.491]

Fig. 3. Maximal ELC force error AF o as a function of the particle -coordinate for a simulation box of size 10 x 10 x 5 and a periodicity of = 10. The cutoffs were R = 0 [rectangles), R = 0.1 [circles), and R = 0.3 [triangles). As 3d-method P M was used, tuned for an rms force error of 10 ". For R = 0.3, the P M error dominates... Fig. 3. Maximal ELC force error AF o as a function of the particle -coordinate for a simulation box of size 10 x 10 x 5 and a periodicity of = 10. The cutoffs were R = 0 [rectangles), R = 0.1 [circles), and R = 0.3 [triangles). As 3d-method P M was used, tuned for an rms force error of 10 ". For R = 0.3, the P M error dominates...
Theorem 5 is the basis of the Rectangle Partition algorithm that reduces mask decomposition to two classical graph-theoretical problems computing the number of connected components in a graph (to compute a and w) and computing the size of maximal independent set in the bipartite graph. [Pg.17]

Standard bond lengths [Kaliszan, Lamparczyk et al, 1979 Radecki, Lamparczyk et al, 1979 Kaliszan, 1987]. It was used to model GC retention indices. A slightly different shape parameter is the length-to-breadth ratio L/B that is defined as the ratio of the longest to the shortest side of the rectangle that envelopes a molecular structure and at the same time maximizes L/B ratio [Janini, Johnston et al., 1975 Wise, Bonnett et al., 1981]. [Pg.686]

Fig. 17 Example of application of 4D HNCACO technique, (a) Pulse sequence. Evolution for CO is in the real-time mode, and for N and CA in semi-constant-time mode (a, = (/, -l- A)/2, 6, = t,(l-A/Wi)/2, C = A(l- 6Amaxi)/2) or constant-time mode (a,- = (A -I- /,)/2, 6,- = 0, c,- = (A—/,)/ 2), where A stands for An ca and Aca-co. respectively, t, is the evolution time in ith dimension and imaxi is the maximal length of evolution time delay. Delays were set as follows An h = 5.4 ms An-ca = 22 ms Aca-co = 6.8 ms. (b) Coherence transfer in the peptide chain. Amide nitrogen and proton frequencies (filled colored rectangles) are fixed during Fourier transformation. Each plane contains CO-CA peak for i and i—1 residue, (c) 2D spectral planes for CsPin protein obtained by SMFT procedure performed on the 4D HNCACO randomly sampled signal (Poisson disk sampling) with fixed Hn and N frequencies obtained from 3D HNCO peak list (d) 2D spectral planes for MBP obtained in the same manner. Reprinted with permission from [81]... Fig. 17 Example of application of 4D HNCACO technique, (a) Pulse sequence. Evolution for CO is in the real-time mode, and for N and CA in semi-constant-time mode (a, = (/, -l- A)/2, 6, = t,(l-A/Wi)/2, C = A(l- 6Amaxi)/2) or constant-time mode (a,- = (A -I- /,)/2, 6,- = 0, c,- = (A—/,)/ 2), where A stands for An ca and Aca-co. respectively, t, is the evolution time in ith dimension and imaxi is the maximal length of evolution time delay. Delays were set as follows An h = 5.4 ms An-ca = 22 ms Aca-co = 6.8 ms. (b) Coherence transfer in the peptide chain. Amide nitrogen and proton frequencies (filled colored rectangles) are fixed during Fourier transformation. Each plane contains CO-CA peak for i and i—1 residue, (c) 2D spectral planes for CsPin protein obtained by SMFT procedure performed on the 4D HNCACO randomly sampled signal (Poisson disk sampling) with fixed Hn and N frequencies obtained from 3D HNCO peak list (d) 2D spectral planes for MBP obtained in the same manner. Reprinted with permission from [81]...

See other pages where Maximization of rectangles is mentioned: [Pg.157]    [Pg.162]    [Pg.432]    [Pg.409]    [Pg.8]    [Pg.157]    [Pg.162]    [Pg.432]    [Pg.409]    [Pg.8]    [Pg.284]    [Pg.72]    [Pg.14]    [Pg.244]    [Pg.166]    [Pg.273]    [Pg.218]    [Pg.23]    [Pg.86]    [Pg.137]    [Pg.491]    [Pg.391]    [Pg.334]    [Pg.12]    [Pg.12]    [Pg.12]    [Pg.13]    [Pg.13]    [Pg.14]    [Pg.16]   
See also in sourсe #XX -- [ Pg.133 ]




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