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By Nicholas Chako, Robert P. Bauman, Edward J. Lofgren (auth.), Robert M. Besançon (eds.)

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The analytical equations may be expressed in matrix form, A = KC, where A is a column matrix of measured absorbance values at the several analytical frequencies, C is a column matrix of the (unknown) concentrations of the species present, and K is a rectangular matrix of calibration values, one measured value (ab) at each analytical frequency for each species. Multiplication of each side on the left by the transpose of K gives KA =A' = KKC = K'C, where A' has the same dimension as C and K' is a square matrix.

Refinements in the design of segmented accelerating tubes and the use of shells at intermediate potentials between the grounded pressure tank and the high voltage terminal have been the main factors leading to reliable operation of Van de Graaff accelerators at over 10 MeV. More than twice that voltage is achieved in the tandem design in which negative ions are accelerated from ground potential to a positive terminal where they are stripped of electrons to form positive ions and then further accelerated to ground potential.

These were in operation by 1961. In a few years the BNL linac was replaced by an updated 200-MeV machine which is still in operation in 1982. A similar linac was built at the newly formed Fermi National Laboratory in Batavia, Illinois to be the injector for the second stage of the 200-500-GeV proton synchrotron. A 20-MeV proton linac is in operation at the KeK Laboratory in Japan where it is the injector for the 12 GeV synchrotron. This machine's KeK Laboratory in Japan where it is the injector for the 12 Ge V synchrotron.

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