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Consider an incident wave impinging upon a volume of dense media consisting of spheres of moderate sizes and size distribution (Fig. 6.4.1). The incident wave direction is ki and polarization directions are Vi and h'i' ki

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When you do, a parenthetical sum will follow each watch list and portfolio name (Figure 14.8, with arrows added for emphasis) so you can con rm that your portfolio s contents in a given watch list are in synch with the actual holdings you have entered into MarketMatrix. In this instance, there are 34 items in the Current Trust watch list and 34 items in the Trust portfolio, so they appear to be in synch. Keep in mind that the information in My Watch Lists and the information in My Portfolios are intended to provide different kinds of information. The watch list shows simply the company name (or symbol, if you have elected that style of display) contained within each list. The portfolio shows the raw symbol followed by the quantity owned as well as the entry price (Figure 14.9). Watch lists are typically created and managed within ProphetCharts, whereas portfolios are typically created and managed either in MarketMatrix or on the Portfolio page of the Investor Toolbox.

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(6.4.1) (6.4.2)

(6.4.3)

We want to caIeulate the extinction and the phase matrix using the results in the previous sections. This requires a transformation of coordinates. To do that we assume a body frame of the medium such that Zb points in the negative ki direction (Fig. 6.4.1):

Zb = For the body frame we further let,

(6.4.4) (6.4.5)

, , ,

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(6.4.7) (6.4.8)

In the body frame the wave is "normally" impinging upon the dense medium. The averaged exciting field coefficients obey the homogeneous system of equations of (6.3.16) and (6.3.17). Setting the determinant equal to zero provides a solution for the effective propagation K with

FIGURE 14.9 The watch lists show just the company names of the watch list contents, whereas the portfolio lists display the basic information about the positions being held.

K = K' + iK"

(6.4.9)

The determination of the real part K' from (6.3.16) and (6.3.17) presents no numerical difficulty. However, the determination of the imaginary part K" from (6.3.16) and (6.3.17) can be difficult numerically because

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the set of equations in (6.3.16) and (6.3.17) to determine both real and imaginary parts together may cause accuracy problem for the imaginary part. (ii) The imaginary part Kif is strongly dependent on the pair distribution function. The function Sp(k, KIR sjs /) includes an integration of the pair distribution function in the spatial domain. We note that the pair distribution function can have sharp spikes particularly for sticky particles. This further complicates the accuracy of K". Thus we use (6.3.16) and (6.3.17) to determine only the real part K'. As for the imaginary part Kif, we note that it is related to the extinction coefficient by lie = 2K". As shown later, we perform angular integrations of the phase functions to obtain the scattering coefficient lis. Absorption coefficient K a is next determined. Then the extinction coefficient is obtained as lie = lin + K,s. After solving the determinantal equation, the exciting field coefficients ~~sJ(M) and ~~sJ)(N) are determined to within a single arbitrary constant. That is, the ratios of the ~~sj)(M) and ~}sj)(N) to each other are determined by solving (6.3.16) and (6.3.17). The one single constant is determined by the generalilled Ewald-Oseen extinction theorem.

(A) Vertical Polarization Incidence in the Body Frame E i = Vi = -Vib. The arbitrary constant is determined by the generalized Ewald-Oseen extinction theorem. In the body frame, the incident and transmitted angles are normal. Thus replacing ()i = ()t = 0 in (6.3.24), we have

8/=1

The rehabilitations of the two buildings were different in that Watauga Hall was a university project administered in part by the North Carolina Department of Administration with no oversight by federal of cials. The Montague Building was a privately owned building restored by a developer with oversight by the United States Department of the Interior acting through the state preservation of ce (SHPO).

+ T(s,)(N)y(S/)(N)(V)]

(6.4.10)

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