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lio from long and short positions rather than achieving neutrality via a derivatives contract based on an underlying index. Jacobs: This re ects the fact that long-only portfolios are generally constrained by the weights of the names in the underlying index, whereas market neutral long-short portfolios, if properly constructed, are free of index weights. This is most noticeable when you look at stock underweights. Given that the market capitalization for the median stock in the U.S. equity universe is 0.01% of the market s capitalization, a portfolio that cannot short can achieve, at most, a 0.01% underweight in the average stock; this underweight is obtained by excluding the stock from the portfolio. The manager may have a very negative view of the company, but the portfolio s ability to re ect that insight is extremely limited. The manager that can sell short, however, can underweight this stock by as much as investment insights (and risk considerations) dictate. Levy: It s important to note that the market neutral long-short portfolio also has greater leeway to overweight stocks, because the manager can use offsetting long and short positions to control portfolio risk. Whereas a long-only portfolio may have to limit the size of the position it takes in any one stock or stock sector, in order to control the portfolio s risk relative to the underlying benchmark index, the market neutral long-short portfolio manager is not circumscribed by having to converge to benchmark weights to control risk. The freedom from benchmark constraints gives market neutral long-short portfolios greater leeway in the pursuit of return and control of risk a bene t that translates into an advantage over market neutral portfolios constructed without shorting.

When the sizes of the diffracting apertures are less than the wavelength, scalar diffraction theory yields nonnegligible errors, and other numerical methods such as the nite difference time domain (FDTD) method and the nite element method (FEM) may become necessary to use [Kunz, 1993; Ta ove and Hagness, 2005] However, these methods are not practical with large scale simulations as compared with methods utilizing the FFT With diffracting aperture sizes of the order of the wavelength used and in the near eld, the ASM has been found to give satisfactory results [Mellin and Nordin, 2001] With the ASM, one disadvantage is that the input and output plane sizes are the same.

Case reports and reports of case series have an important role in the progression of our knowledge.

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The output plane size is usually desired to be considerably larger than the input plane size in most applications, and this can be done with the ASM only by repeatedly using the ASM in short distances and additionally using ltering schemes to make the output size progressively larger The Fresnel, Fraunhofer approximations, and the ASM can be considered to be valid in practice at small angles of diffraction It is desirable to have approximate methods that are valid at wide angles of diffraction in the near eld as well as the far eld and also based on the Fourier integral to be implemented with the FFT so that.

In the present case, j(xi , yi ) is the phase shift caused by the wave propagation from the origin of the reference wave front at (xc ; yc ; zc ) to the hologram aperture at (xi , yi ); kroi is the phase shift caused by the wave propagation from the aperture at (xi , yi ) on hologram to an object point located at (xo , yo , zo ). The radial distance roi is given by roi q xo xi 2 yo yi 2 z2 o 15:10-2

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