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[xt xt] F(r),

(3.184) where x is the three-dimensional column vector whose components are the unit vectors of whatever right-handed Cartesian axes we happen to be using for our threedimensional space (3.185)

Numbers don t lie, but they can certainly obscure. For example, high salaries and reported pro ts can hide a sickly debt-to-equity ratio. You can identify unpro table activities, departments, and ventures by tracking income and expenses by class. Ratios enable you to interpret the information reported on the Balance Sheet and Income Statement to determine a company s capability to expand, its ability to meet its obligations, and its pro tability. If your sole proprietorship or subchapter S corporation shows a tax loss for three out of ve consecutive years, the IRS may limit deductibility of losses by reclassifying the venture as a hobby.

This way both E and 13 will be ordinary vectors rather than column-matrix vectors. Substituting (3.181) in (3.184), we find that (see Problem 3.9)

E(r) =

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The challenge in assessing biotech computing as a separate market is in dis tinguishing it from the overall computing industry. One reason for the dif culty in identifying the segment of the computing industry that is most closely associated with biotech is that the general industry trends of com puting and biotech are highly correlated. For example, as shown in Figure 4.7, the performance of the biotech and computer industry stocks from

y now, you know that your Balance Sheet provides a snapshot of what the company is worth to its owners: Assets Liabilities = Owner s Equity. This chapter goes beyond the Balance Sheet basics to explore some of the more complicated transactions involving assets and liabilities. Acquiring or selling a xed asset, accounting for borrowed funds, and recording capital contributions and distributions are all events that are unrelated to the normal income-producing activities of the business. This chapter discusses the correct method for recording them and analyzes their impact on the Balance Sheet.

ip r . /

n, (3.186)

B(r) =

Depreciation Selling a xed asset Accounting for borrowed funds Recording capital contributions Recording distributions to owners

900 800 700

u>.(p)e ip .r / \ (3.187)

where u>.(p) ->.xt u>.(p) is the ordinary vectorform of ->.u>.(p). Except for the use of the Schr<>dinger picture with momentum and helicity rather than the Heisenberg picture with wave vector and linear polarization, (3.186) and (3.187) are completely equivalent to (2.146) and (2.147). The helicity basis u>.(p) corresponds to circular polarization and the wavefunction of the photon to the mode functions of the field.

As you may recall from 4, assets are classi ed as either current or xed. Classi cation is based on whether the assets are expected to be converted to cash within the current business cycle. Current assets are cash equivalents and assets expected to be converted to cash within one year. Fixed assets

Feynman's 1986 Dirac Memorial Lecture at Cambridge University [207] gives an insightful account on why there must be antiparticles and on the spinstatistics theorem. 2 and Appendix 3 of the book by Pike and Sarkar [492] will give you a good idea of what the group theory approach to photon localization is about. Jordan's papers [331-336] on this subject are also quite readable as well as the pedagogical paper by Han and Kim on the little group for photons [270]. The key original references are the 1948 paper by Pryce [501], 1949 paper by Newton (no, this is not Isaac!) and Wigner [464], and Wightman's imprimitivity reformulation [643]. Also related to this group theory approach are [32], [645], [647], [648], and the references mentioned in [464]. For those wishing to study group theory in depth, there are many books on the subject. I find the following books particularly useful: [330], [639], [396], and [650].

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