Literatur

Ohne Zusammenfassung     

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.     

Comparison of different methods for combining phase-contrast images obtained with multiple coils

The ability to determine coil sensitivities implies that a method optimized in terms of maximized signal-to-noise ratio (SNR) can be applied to the combination of multiple coil images. An optimization of SNR subsequently results in a minimized variance in quantitative velocity measurements using phase-contrast imaging. When coil sensitivities are unknown, the weighted mean method, utilizing the square of the signal magnitude as weights, is suitable for combination of multiple phase images. In this study, the optimized method using estimated coil sensitivities was compared to the weighted mean method both theoretically and experimentally. It is shown that absence of noise correlation between the different coil images implies no difference between the methods regarding the variance of the phase. In the practical situation, noise correlation does exist, implying an opportunity for further reduction of phase variance using the optimized method. In vitro and in vivo studies showed, however, no significant difference between the two methods studied.     

Alternative anaerobic enrichments to the bacteriological analytical manual culture method for isolation of Shigella sonnei from selected types of fresh produce

Alternative methods of reducing oxygen during anaerobic enrichment in the Bacteriological Analytical Manual (BAM) Shigella culture method were evaluated and compared to the current and less practical GasPak method. The alternative anaerobic methods included the use of reducing agents in Shigella broth and reducing culture container headspace volume to minimize atmospheric effects on oxygen concentration in Shigella broth during enrichment. The reducing agents evaluated were sodium thioglycollate, L-cystine, L-cysteine, titanium(III) citrate, and dithiothreitol, each at concentrations of 0.1, 0.05, and 0.01%. The use of Oxyrase for Broth with the enrichment medium (Shigella broth) was evaluated at concentrations of 10, 20 and 30 microL/mL. Recoveries of chill- and freeze-stressed S. sonnei strains 357 and 20143 were determined with each anaerobic method, including the GasPak method, using inoculation levels ranging from 10(0)to 10(3) cells. For each anaerobic method, strain, inoculation level, and stress type, 5 replicate enrichments were evaluated by streaking to MacConkey agar for isolation. The numbers of cultures with each method from which S. sonnei was isolated were used to compare the alternative anaerobic methods to the GasPak method. The alternative anaerobic method with which chill- and freeze-stressed S. sonnei strains 357 and 20143 were isolated most consistently was the use of Oxyrase for Broth in Shigella broth at a concentration of 20 microL/mL. This method was compared to the GasPak anaerobic method in evaluations on the recovery of S. sonnei strains 357 and 20143 from artificially contaminated test portions of parsley, cilantro, green onions, strawberries, carrots, and celery. A third anaerobic method included the use of 0.5 cm mineral oil overlay on cultures containing Oxyrase for Broth at concentrations of 20 microL/mL. Recovery rates of strain 357 were significantly greater (p < 0.05) with the GasPak method than with Oxyrase for Broth, with and without the 0.5 cm mineral oil overlay, for test portions of parsley, cilantro, and celery. When Oxyrase for Broth was used with Shigella broth, strain 357 was isolated at higher rates from all produce types, except cilantro, when 0.5 cm mineral oil overlay was applied to enrichment cultures. The use of mineral oil overlay with Oxyrase for Broth also improved recovery of strain 20143 from test portions of all produce types except green onion and strawberries. These differences were significant (p < 0.05) with parsley, carrots, and cilantro (1 of 2 evaluations). No statistically significant differences (p > 0.05) between the GasPak and Oxyrase for Broth anaerobic methods occurred when mineral oil overlay was used with Oxyrase for Broth. The use of Oxyrase for Broth with a 0.5 cm mineral oil overlay is a practical alternative for anaerobic enrichment with the BAM method in the analysis of some produce types. Differences in recovery among the different produce types and methods occurred between S. sonnei strains 357 and 20143, emphasizing the need for additional S. sonnei strains in future evaluations.     

Success-factors in transition to university mathematics

This study examines different factors' relative importance for students' performance in the transition to university mathematics. Students' characteristics (motivation, actions and beliefs) were measured when entering the university and at the end of the first year. Principal component analysis revealed four important constructs: Self-efficacy, Motivation type, Study habits and Views of mathematics. Subsequently, orthogonal partial least squares (OPLS) analysis was used for measuring the constructs' ability to predict students' university mathematics grades. No individual constructs measured at the time of entrance predicted more than 5% of the variation. On the other hand, jointly they predicted 14%, which is almost in pair with upper secondary grades predicting 17%. Constructs measured at the end of the first year were stronger predictors, jointly predicting 37% of the variation in university grades, with Self-efficacy (21%) and Motivation (12%) being the two strongest individual predictors. In general, Study habits were not important for predicting university achievement. However, for students with low upper secondary grades, the textbook and interaction with peers, rather than internet-based resources, contributed positively to achievement. The association between Views of mathematics and performance was weak for all groups and non-existing for students with low grades.