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.     

Determination of sulfamethazine in swine and cattle feed by reversed-phase liquid chromatography with post-column derivatization: pre-collaborative study

In-house validation of a liquid chromatographic method for determination of sulfamethazine in swine and cattle feed was performed to verify that the method was ready for collaborative study under AOAC INTERNATIONAL guidelines. In this method, sulfamerazine is added during the extraction procedure and is used as an internal standard to correct for variable recovery of sulfamethazine from a variety of swine and cattle feed matrixes. The determinative step involves the use of post-column derivatization with dimethylaminobenzaldehyde which reacts with the primary amine group on the sulfonamides. Detection is at 450 nm, a wavelength at which most co-extracted matrix materials and other feed additives do not absorb light. The results indicate that the method recovery, precision, and ruggedness meet normal criteria to be ready for a collaborative study. Fortification experiments over a range of sulfamethazine concentrations from 0.006 to 0.26% showed an overall recovery relative to the internal standard of 100 +/- 2%. These studies include both swine and cattle feed matrixes. The mean recovery in the analysis of 3 beef cattle experimental feeds was 98.9%. The method results agreed with the AOAC INTERNATIONAL Official Method for colorimetric analysis of swine feed. Method precision was excellent during in-house validation studies, with coefficients of variation (CVs) ranging from about 0.5 to 3%. The method ruggedness was verified with an overall CV of 3.5%.     

Reversed-phase liquid chromatographic determination of riboflavin in feeds

A method for determination of riboflavin in animal feeds using liquid chromatography (LC) was developed for feed samples fortified with riboflavin at 1 mg/lb or greater (up to 10,000 mg/lb). Feed samples were extracted in 0.1 N HCl with heating on a steam bath for 30 min, followed immediately by mechanical shaking for 30 min. Sample extracts were diluted to target volume with 2% acetic acid and filtered; riboflavin was determined by LC on a reversed-phase C18 column with 2% acetic acid-acetonitrile (85 + 15) mobile phase for separation and fluorescence detection with excitation at 460 nm and emission at 530 nm. The extraction was compared with that of the AOAC Official Method for riboflavin in food and feed premixes. The 2 method extractions were not significantly different from each other at the 95% confidence level. The developed method also had good linearity over 4 orders of magnitude, recovery of 95-99% from spiked feed samples, a limit of detection of riboflavin at 0.00034 microg/mL in solution, a limit of quantitation of 0.023 mg/lb in feed, and good ruggedness.     

Determination of sulfathiazole in type C medicated swine feed by reversed-phase liquid chromatography with post-column derivatization

A convenient method was developed for determination of sulfathiazole (STZ) in Type C medicated swine feed by reversed-phase liquid chromatography (LC) with post-column derivatization. Addition of extractant solution (0.2N HCl and 1.5% diethylamine in 25% methanol) and an internal standard (IS), sulfamethylthiazole (SMZ), to 5 g sample was followed by mechanical shaking for 1 h. The extract was clarified by chilling, centrifugation, and filtering before injection onto a C18 reversed-phase column. The mobile phase components were 2% acetic acid and 1:1 acetonitrile-methanol (83 + 17%, v/v). Run time was about 20 min. Determination and, largely, the method's selectivity were based on detection at 450 nm of the derivative formed by the post-column reaction of dimethylaminobenzaldehyde with the primary amine of the analyte and IS. The IS, SMZ, differs from STZ by a single substituent methyl group, is stable, and is readily resolved from STZ. Although SMZ is not commercially available, it can be synthesized with relative ease from purchased reagents and will be supplied by the authors to interested laboratories. In single-laboratory validation, linearity was demonstrated over the range of 0.055-550 microg/mL, well beyond the target concentration of 5.5 microg/mL. The estimated limit of detection was 0.04 microg/mL; the calculated limit of quantitation was 0.13 microg/mL (feed concentration of 2.4 g/T or 2.7 mg/kg). Wet-spiking trials with a variety of swine feed matrixes showed recovery to be 100-102% for the intended concentration range, 50-200 g/T, with coefficient of variation (CV) < 2%. The method ruggedness was verified with an overall CV of 2.9%.     

Determination of sulfamethazine in swine and cattle feed by reversed-phase liquid chromatography with post-column derivatization: collaborative study

A liquid chromatographic (LC) method for the analysis of sulfamethazine (SMT) in complete swine and cattle feed was collaboratively studied. The method uses post-column derivatization with dimethylaminobenzaldehyde and detection at 450 nm. To 5g finely ground feed, extractant (0.2N HCl + 1.5% diethylamine in 25% methanol), and internal standard solutions are added, and the SMT is extracted by shaking for 1 h. Clarified extract (high-level sample extract diluted to a target concentration of ca 5.5 microg/mL) is chromatographed on a Cla reversed-phase LC column with acetonitrile-2% acetic acid (17 + 83) mobile phase. Sulfamerazine is used as an internal, or surrogate standard to correct for variable recovery of sulfamethazine from a variety of feed matrixes. Six Youden matched-pair samples were sent to 10 collaborators in Korea, Canada, and the United States. Label claims on the commercial feeds ranged from 0.0077 to 0.22% SMT. The SMT mean recovery as determined from the 5 samples with known analyte content was 99.8%. The within-laboratory relative standard deviation (repeatability) ranged from 0.28 to 4.72%. Among-laboratory (including within-laboratory) relative standard deviation (reproducibility) ranged from 1.26 to 4.87%. The authors recommend the method for AOAC INTERNATIONAL Official First Action status.