problem_set5 - 10.34 Fall 2006 Homework #5 Due Date:...

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10.34 – Fall 2006 Homework #5 Due Date: Wednesday, Oct. 11 th , 2006 – 9 AM Problem 1: Singular Value Decomposition The composition of a mixture of chemicals is usually determined by putting the mixture in a spectrometer or chromatograph. The signal coming out of an analytical-chemistry instrument for a mixture is typically a linear combination of the signals one would have obtained if the sample was pure. For example, using a spectrometer: S mix () λ n = x S i i n Where S( ) is the signal measured of a mixture with mole fractions { x i }, and S i ( ) is the signal that would have been measured if the mixture had been pure, i.e. if x i =1 and all other x ’s had been zero. The spectrum S is a continuous function of the wavelength , but the spectrometer only records the spectrum at N discrete set of wavelengths n . Very often, the composition x of a mixture changes, either with time (e.g. when we are measuring batch kinetics) or as a function of some knob being turned in a chemical plant.
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 10.302 taught by Professor Clarkcolton during the Fall '04 term at MIT.

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problem_set5 - 10.34 Fall 2006 Homework #5 Due Date:...

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