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(b) Write a MATLAB routine to simulate the system represented by (10.P.4) using the explicit Euler method [which will produce x n = [xn yn ]T such that xn x(tn ) and yn y(tn )]. Assume that h = 0.05 and the initial condition is x 0 = [1 0]T . Plot x n and (x(t), y(t)) (via (10.P.5)) on the (x, y) plane. (c) Write a MATLAB routine to simulate the system represented by (10.P.4) using Heun s method [which will produce x n = [xn yn ]T such that xn x(tn ) and yn y(tn )]. Assume that h = 0.05 and the initial condition is x 0 = [1 0]T . Plot x n , and (x(t), y(t)) [via (10.P.5)] on the (x, y) plane. Make reasonable choices about the number of time steps in the simulation. 10.18. In the previous problem the step size is h = 0.05. (a) Determine whether the simulation using the explicit Euler method is stable for this choice of step size. (Hint: Recall that one must consider the eigenvalues of I + hA.)

There is another eld of study that produces mathematical models that are, at times, closely related to chromatic adaptation models. This is the eld of computational color constancy. The objective in this approach is to take limited color information available in a typically trichromatic representation of a scene and produce color-constant estimates of the objects. Essentially this reduces to an attempt to estimate signals that depend only on the spectral re ectances of objects and not on the illumination. On the other hand, chromatic adaptation models aim to predict the failure of color constancy actually observed in humans. It is simple to prove that precise color constancy is not possible, or desirable, for the human visual system. The examples of metameric object color pairs that cannot both be color constant and the need to include illuminants in practical colorimetry suf ce to make this point. All this means is that striving for the most color-constant model is not necessarily a good way to model the human visual system. There are, however, applications in

Figure 14.26 shows numerical simulations using de Groot s (1996) method for various algorithms presented in section 14.7. Two types of general improved behavior under vibration conditions can be observed. They are the algorithms in the upper chart in Figure 14.26; narrow the peaks and atten the valleys for the odd harmonics of the ratio of the sampling frequency to the vibrations frequency. There are also those algorithms that show reduced sensiti ty at the odd harmonics but introduce sidelobes between the even and odd harmonics. There are signi cant differences between the two types of algorithms here, particularly at frequencies below the actual sampling frequency as shown in Figure 14.27.

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In GoLive, floating boxes are as simple to place as any other object you add to your page; just drag the floating box icon from the Objects palette. To place a floating box on your page, follow these steps: 1. Drag the floating box icon from the Basic tab of the Objects palette into place on your page. The top-left corner is the best place. The floating box works differently from other page objects. Although you are placing the floating box, the object actually dragged and placed is a very small SB marker that comes along with the actual floating box. Rather than place it exactly where you want the box to be on your page, place the SB box inline (in a line of text) at the top of your page. Although the SB box displaces your line of text by one line while in layout mode, it s invisible within a browser. The position of the SB doesn t affect the box s position in any way.

Next, a component that performs addition can be written as the OpAdd class:

public class CreateAlbumController extends SimpleFormController { private String[] labels; protected Map referenceData(HttpServletRequest request) throws Exception { return new ModelMap( labels , labels); } public void setLocales(String[] labels) { this.labels = labels; } }

Figure 5.48 Taylor tapering functions for sidelobe levels from 20 dB to 45 dB. [Source: Meikle, H.D., Modern Radar Systems, Artech House, Norwood, Massachusetts, 2001.] Table 5.17