Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

Equivalence of Visual Immunoprecipitate Assay (VIP) for Salmonella for the detection of motile and nonmotile Salmonella in all foods to AOAC culture method: collaborative study

Six foods representative of a wide variety of processed, dried powder processed, and raw food types were analyzed by the Visual Immunoprecipitate Assay (VIP) for Salmonella and AOAC INTERNATIONAL culture method. Paired samples of each food type were simultaneously analyzed; one sample by the VIP method and one by the AOAC culture method. A total of 24 laboratories representing federal government agencies and private industry, in the United States and Canada, participated in this collaborative study. Food types were inoculated with species of Salmonella with the exception of raw ground chicken, which was naturally contaminated. No statistical differences (p < 0.05) were observed between VIP for Salmonella interpretation and the AOAC culture method for any inoculation level of any food type or naturally contaminated food. The method was adopted Official First Action status by AOAC INTERNATIONAL.     

Equivalence of assurance Gold Enzyme Immunoassay for visual or instrumental detection of motile and nonmotile Salmonella in all foods to AOAC culture method: collaborative study

Six foods representative of a wide variety of processed, dried powder processed, and raw food types were analyzed by the Assurance Gold Salmonella Enzyme Immunoassay (EIA) and AOAC INTERNATIONAL culture method. Paired samples of each food type were simultaneously analyzed; one sample by the Assurance method and one by the AOAC culture method. The results for Assurance method were read visually and instrumentally with a microplate reader. A total of 24 laboratories representing federal government agencies and private industry, in the United States and Canada, participated in this collaborative study. Food types were inoculated with species of Salmonella with the exception of raw ground chicken, which was naturally contaminated. No statistical differences (p < 0.05) were observed between Assurance Gold Salmonella EIA with either visual or instrumental interpretation and the AOAC culture method for any inoculation level of any food type or naturally contaminated food. The Assurance visual and instrumental options of reading sample reactions produced the same results for 1277 of the 1296 sample and controls analyzed.