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The above transmitted field can be decomposed into lcp and rcp components: lcp + j rcp j Etr = Vtr + Vtr 2 2 Comparing (9.21) and (9.22) we obtain

1 1 1 0 0 0 0 0

where a is the element spacing of the array, Vs represents the modal voltage of the aperture source, and es x is the modal vector of the source field, which is assumed to be a real function of x. For instance, if the source is an array of waveguide apertures, then es x will be equal to the modal electric field vector [1] of a waveguide. The above array of apertures will produce an incident wave to the scatterers at an angle with the z-axis, where is given by = k0 a sin (4.2)

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Fama and French (1996) gave a more comprehensive study of the factors mentioned by the authors cited above They found that by observing the returns of corporations that stocks with higher betas did, indeed, yield a higher return on average but that beta only explained a small fraction of the differences in returns between stocks There were, however, other factors noted above that aided the CAPM in explaining excess returns Fama and French thus theorized that these items must be additional risk factors based on their empirical evidence that (242) provided a good t to the data Size Factor Fama-French factors try to pick up sources of risk not represented by the market portfolio The size factor, for instance, could proxy for the ability of a rm to rebound in a down market.

(6.23)

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Observe that the array factor is now represented by a polynomial of z, known as Schelkunoff s polynomial. For a real value of sin z = 1, which represents a unit circle in the complex z-plane, known as Schelkunoff s unit circle (Figure 1.18). On the circumference of the unit circle, a segment exists where sin < 1. This segment is known as the visible region and any point lying outside the segment,

It has long been known that small rms give a higher stock return on average than large rms with the same beta The Fama-French model uses this to imply that perhaps access to credit, reserves of resources, and the like, make being a small rm inherently more risky While large rms may be able to weather a storm, small rms are more easily blown away The same intuition applies to the book-to-market equity value of a rm or BE/ME ratio As we saw in 1, the stock value of a healthy rm is the present value of all future earnings This number should be in excess of the price paid for the assets of a company if the company is productive.

Like the other authors, Evans and Twyman (1999) add security checks to Java programs using bytecode rewriting. With their system, the security policy author speci es events and

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