In this paper an alternating trilinear decomposition (ATLD) algorithm that is an improvement of the traditional PARAFAC algorithm without any constraints is described as an alternative algorithm for decomposition of three‐way data arrays. It is based on an alternating least squares principle and an improved iterative procedure that, in a real trilinear sense, uses the Moore–Penrose generalized inverse with singular value decomposition. Its performance is compared with that of the traditional PARAFAC algorithm by a series of Monte Carlo simulations with different noise levels. It was found that the ATLD algorithm has a capability to converge faster than the traditional PARAFAC algorithm. The ATLD‐based second‐order calibration retains the second‐order advantage that calibration in the presence of unknown interferents can be performed to provide satisfactory concentration estimates. Both algorithms have been used for simultaneous determination of overlapped chlorinated aromatic hydrocarbons measured by means of a high‐performance liquid chromatograph with a diode array detector. © 1998 John Wiley & Sons, Ltd.

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The development of ultrasensitive and rapid methods for the detection of dipicolinic acid (DPA), a biomarker for bacterial spores including Bacillus anthracis, is increasingly important. This paper reports the results of an investigation of surface enhanced Raman spectroscopy (SERS) based ultrasensitive detection of DPA using a gold nanoparticle/polyvinylpyrrolidone/gold substrate (AuNPs/PVP/Au). The strong SERS effect of this substrate exploits the particle-particle and particle-substrate plasmonic coupling, which is optimized by manipulating the diameter of the nanoparticles (50-70 nm). The correlation between the SERS intensity of the diagnostic band and the DPA concentration (0.1 ppb to 100 ppm) was shown to exhibit two linear regions, i.e., the low- (<0.01 ppm) and high-concentration (>1 ppm) regions, with an intermediate region in between. The presence of a linear relationship in the low-concentration region was observed for the first time in SERS detection of DPA. A detection limit of 0.1 ppb was obtained from the substrates with 60 nm sized Au NPs, which is, to our knowledge, the lowest detection limit reported for DPA using this type of SERS substrate. This finding was also supported by the estimated enhancement factor (approximately 10(6)) and a large adsorption equilibrium constant for the low-concentration region (1.7 x 10(7) M(-1)). The adsorption characteristics of DPA on the SERS substrates were analyzed in terms of monolayer and multilayer adsorption isotherms to gain insights into the correlation between the SERS intensity and the DPA concentration. The observed transition from the low- to high-concentration linear regions was found to correspond to the transition from a monolayer to multilayer adsorption isotherm, which was in agreement with the estimated minimum DPA concentration for a monolayer coverage (approximately 0.01 ppm).