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expected cost of a sum of costs is equal to the sum of the expected values for each individual cost) It is important to distinguish between the expected value and other measures of central tendency associated with a distribution, such as the median (the value that has a 50% chance of being exceeded) and the most likely value (most probable, often referred to as the best estimate ), which do not have this additive property in general For example, the cost of items A and B of Table 111 each have an expected value of (8 02) (10 05) (12 03) 102 This means that the expected cost of 1,000 such items is 10,200 ( k) The most likely costs of 10 for each item cannot be added to obtain a most likely value for more than one item.

, The Adiabatic Phase and Pancharatnem s Phase for Polarized Light, J Mod Opt, 34, 1401 1407 (1987) B Jena, J K Horber, L Wilson and P Matsudaira (Eds), Atomic Force Microscopy in Cell Biology, vol 68, Academic Press, San Diego, 2002 Bhushan B, H Fuchs, S Hosaka, Applied Scanning Probe Methods, Springer, Berlin, 2004 Biegen B and R Smythe, High Resolution Phase Measuring Laser Interferometric Microscope for Engineering Surface Metrology, Proc SPIE, 1009, 35 44 (1988) Binnig G and H Rohrer, Scanning Tunneling Microscopy, Helv Phys Acta, 55, 726 735 (1982) Binnig G and H Rohrer, The Scanning Tunneling Microscopy, Sci Amer (August, 1985) Binnig G, C F Quate, and C Gerber, Atomic Force Microscope, Phys Rev Lett, 56, 930 933 (1986) Blais F, Review of 20 Years of Range Sensors Development, Journal of Electronic Imaging, 13, 231 240 (2004) Bonnell D A.

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(Ed), Scanning Probe Microscopy and Spectroscopy: Theory, Techniques, and Applications, 2nd ed, Wiley-VCH, New York 2000 Born M and E Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th ed, University Press, Cambridge, 1999 Bosch T and M Lescure (Eds), Laser Distance Measurements, vol MS 115, SPIE Optical Engineering Press, Bellingham, 1995 Bosch T, N Servagent, and S Donati, Optical Feedback Interferometry for Sensing Application, Opt Eng, 40, 0 27 (2001) Braga P C and D Ricci, Atomic Force Microscopy: Biomedical Methods and Applications, Humana Press, Totowa, NY, 2004 Breitmeier U and R J Ahlers, Dynamically Focusing Electro-Optical Sensor System for Micropro lometry, Proc SPIE, 802, 170 173 (1987) Brodman R and W Smilga, Evaluation of a Commercial Microtopography Sensor, Proc SPIE, 802, 165 169 (1987) Browne M A, O Akinyemi, and A.

Boyde, Confocal Surface Pro ling Utilizing Chromatic Aberration, Scanning, 14, 145 153 (1992) Bruce C F and B S Thornton, Obliquity Effects in Interference Microscopes, J Sci Instrum, 34, 203 204 (1956)..

The identity matrix I in (3.145) is of order M + N M + N . The transmission matrix T relates the incident Floquet modes to the waveguide modes. This can be deduced as T = I +y

In this example, the variable values are hard-coded in the script. In a real-world application, you would of course receive these values from outside the script, such as via submitted form values in the $_POST superglobal array. Remember that, although using prepared statements and placeholders gives you some protection against SQL injection attacks, you should always check or filter user input before doing anything with it, such as storing it in a database. You can find out more about this and other security-related issues in 20.

The ions are exposed to an alternating electric eld and, when the frequency of this eld is the same as , the ions are steadily accelerated to larger and larger radii and, simultaneously, move into phase with each other. Since depends on m/z, this ratio can be determined in the analyzer for individual ions to a very high degree of accuracy. The resolution attainable with this analyzer is >1 000 000. What makes this type of detector unusual is that ions are not directly detected by impacting on the detector but rather by their effect as they pass near plates within the detector which induces a current in the plates consisting of sine waves called a free induction decay (FID). As will also be described later (Sections 6.2.1), a continuous wave function like the FID can be converted by a mathematical tool called the Fourier transform

We also know that the crossing path and the lower path are the same after they join at the secondary ampli er input and that they cancel each other up to that point, so al = ax . (6.26) Therefore, the net transfer function is a = au + ax + al = au = ax = al , (6.27)

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