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where k s = (e", cP,,) is the scattered direction. In (7.1.3), F(k", ki ) represents the N-particle collective scattering amplitude. It can be decomposed into coherent component (F(k s , ki )) and incoherent component F(k s , ki ). (7.1.4) The optical theorem can be applied to N scatterers, which can be viewed as a single object called N-scatterer. Thus, for the case of nonabsorptive scatterers we have 41f , , (7.1.5) kIm { F(k i1 ki)} = dn s [F(k s1 ki)1 2

471"

The phase function P(k s ' ki) and the scattering coefficient f'i,s are next defined to take into account the collective scattering behavior of N particles.

Figure 53 When you de ne a property or method as obsolete, any developer using the method knows that the property or method is on the obsolescence path

P(k s , ki ) =

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Cyranoski, D. (2002). Rebirth and Regeneration: Japan s Center for De velopmental Biology. Nature 415(February): 952 3. Defense Research and Development Canada. www.drdc-rddc.gc.caI. European Federation of Pharmaceutical Industries and Associations. (2002). The Year in Review 2001 2002. Brussels, Belgium. Findlay, C. and A. Watson, Eds. (1999). Food Security and Economic Re form: The Challenges Facing China s Grain Marketing System (Studies on the Chinese Economy). New York: Palgrave Macmillan. Flannery, R. (2002). Shanghai Buzz. Forbes Global(May): 48 50. Friend, S. and R. Stoughton (2002). The magic of microarrays. Scienti c American(Feb): 44 9. Hill, D. (2000). Latin America: R&D Spending Jumps in Brazil, Mexico, and Costa Rica, NSF 00-316. Arlington, VA: National Science Foun dation, Division of Science Resources Studies. Hill, D. (2002). Latin America: High-Tech Manufacturing on the Rise, but Outpaced by East Asia, NSF 02-331. Arlington, VA: National Science Foundation, Division of Science Resources Studies. Hoag, H. (2003). Transgenic salmon still out in the cold in United States. Nature 421(23): 304. Hoover s Online. hoovnews.hoovers.com. Informations Sekretariat Biotechnologie. www.i-s-b.org. Inter-American Development Bank. www.iadb.org. Japan Bioindustry Association. www.jba.or.jp. Japan Biological Information Research Center. www.jbirc.aist.go.jp. Japan Pharmaceutical Manufacturers Association (JPMA). www.jpma.or.jp. Japan-America Society. www.us-japan.org. Kroeber, A. (2002). The Hot Zone. WIRED 10(11): 200 4. Mathews, J. and C. Dong-Sung (2000). Tiger Technology: The Creation of a Semiconductor Industry in East Asia. Cambridge: Cambridge Uni versity Press. McDowell, N. (2002). Africa hungry for conventional food as biotech row drags on. Nature 418(August): 571 2. Mexico-Info.com. www.mexico-info.com. National Center for Biological Sciences (NCBS), Bangalore. www .tifr.res.in. National Institute of Advanced Industrial Science and Technology. unit.aist.go.jp. Organization of Pharmaceutical Producers of India (OPPI). www .indiaoppi.com. Overby, S. (2002). A Buyer s Guide to Offshore Outsourcing. CIO(November): 69 72. Pharmaceutical Research and Manufacturers of America (2002). 2002 In dustry Pro le. Washington, DC: PhRMA.

(IF(k s , ki)1

(7.1.6)

(7.1.7) The limit in (7.1.6) is taken for fixed no, where no = N/V is the number of particles per unit volume. Thus the definition of (7.1.6) and (7.1.7) contains collective scattering effects. The results of (7.1.6) and (7.1.7) should also be independent of the shape of elemental test volume V. On the other hand, the coherent N-particle scattering amplitude (F) as given by the coherent wave is dependent on the shape of the elemental volume V. Thu~ the phase function in (7.1.6) only includes the incoherent wave. The phase function and the scattering coefficient defined in (7.1.6) and (7.1.7) are per unit volume quantities in the limit of large volume. Note that the limit with large N and large V is taken for convergence. The coherent field is excluded from the equations defining the extinction coefficient and the phase function. The absorption coefficient is

(7.1.8)

5

where Pa is the power absorbed by the N particles in volume V that includes coherent wave interaction among the particles. Thus, the absorption coefficient is the absorption cross section per unit volume in the limit of large V. The extinction coefficient is (7.1.9) Once the phase matrix and the extinction coefficient are calculated, the radiative transfer equation assumes the following standard form

I(r, s)

dO' P(S, s')I(r, s')

(7.1.10)

De ne a standard obsolescence plan for your application This plan de nes when properties and methods are made obsolete, how long they should be obsolete in a warning mode, and at what point they should be marked with a compile-time error This provides a phased approach to modifying your application

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