A new profile likelihood confidence interval for the mean probability of detection in collaborative studies of binary test methods

A confidence interval for the probability of detection across laboratories (LPOD) for qualitative methods, described in the AOAC INTERNATIONAL guidelines for validation of microbiological methods for food and environmental surfaces, is considered. It is demonstrated that under certain conditions, the observed confidence of this confidence interval can be rather low, so that statistical minimum requirements are not fulfilled. A new profile likelihood confidence interval based on a latent random laboratory effect approach is proposed. Observed confidence levels for this confidence interval demonstrate its applicability already for a small number of laboratories.     

A Puckered Singlet Cyclopentane‐1,3‐diyl: Detection of the Third Isomer in Homolysis

In the photochemical denitrogenation of 1,4‐diaryl‐2,3‐diazabicyclo[2.2.1]heptane ( AZ6 ) bearing sterically hindered substituents, a curious new absorption band at about 450 nm was observed under low‐temperature matrix conditions, together with the previously well‐characterized planar singlet diradical pl‐¹ DR6 with λ_max=≈580 nm. The 450 nm species was electron paramagnetic resonance (EPR)‐silent. Instead of generating the planar diradical pl‐¹ DR6 and the precursor azoalkane AZ6 upon warming, the ring‐closed bicyclo[2.1.0]pentane derivative SB6 , that is, the AZ6 denitrogenation product was identified. Based on product analysis, low‐temperature spectroscopic observations, high‐level quantum‐mechanical computations, viscosity effect, and laser‐flash photolysis, the puckered singlet diradicaloid puc‐¹ DR6 was assigned to the new 450 nm absorption. The latter was detected experimentally at the same time as the planar singlet diradical pl‐¹ DR6 . Sterically demanding substituents as well as viscosity impediments were essential for the detection of the experimentally hitherto unknown puckered singlet cyclopentane‐1,3‐diyl diradicaloid puc‐¹ DR6 , that is, the third isomer in homolysis. The present findings should stimulate future work on the mechanistically fascinating stereoselectivity documented in the formation of bicyclo[2.1.0]pentanes during the 2,3‐diazabicyclo[2.2.1]heptane denitrogenation.     

On certain arithmetic functions involving the greatest common divisor

The paper deals with asymptotics for a class of arithmetic functions which describe the value distribution of the greatest-common-divisor function. Typically, they are generated by a Dirichlet series whose analytic behavior is determined by the factor ζ²(s)ζ(2s − 1). Furthermore, multivariate generalizations are considered.     

On the quantification of OH*, CH*, and C2* chemiluminescence in flames

Absolute concentrations of all important chemiluminescent species, OH–A, CH–A, CH–B, and C₂-d have been measured for the first time in methane-oxygen flames at low pressure. The optical detection system for chemiluminescence measurements has been calibrated with Rayleigh and Raman scattering of a cw laser, with the latter approach yielding superior results. The measured ratio between the concentration of CH–B and CH–A suggests that the electronically excited CH* is formed close to thermal equilibrium. Introduction of different rate constants for reactions leading to CH–A and CH–B were not necessary to explain the experimental results. Results are compared with a recent numerical model. Deviations in profile shape and peak positions are relatively small for stoichiometric flames, but become more pronounced in richer mixtures. Larger discrepancies are observed for the absolute concentrations, depending on the chemiluminescent species and the stoichiometry. In an attempt to find an alternative method for the quantification of chemiluminescent species, MIR-CRDS has been performed around 3.9 μm. While H₂O and OH–X could be measured, the sensitivity was not high enough to detect the low sub-ppb concentration of OH–A—in part due to the limited reflectivity of mirrors in the MIR, in part due to a significant background of hot H₂O lines.     

A concise and stereoselective chemoenzymatic synthesis of Sitophilate,the male-produced aggregation pheromone of Sitophilus granarius (L.)

(2S,3R)-Sitophilate, the male-produced aggregation pheromone of the granary weevil Sitophilus granarius (L.) was prepared stereoselectively using a novel chemoenzymatic approach in 50% overall yield. The synthetic design was based on an enantioselective fungal reduction of ethyl 2-methyl-3-oxopentanoate with a strain of Aureobasidium pullulans (CCM H1), followed by a Mitsunobu inversion at C3. The last step in the synthetic sequence was a lipase-mediated transesterification using the commercially available Candida antarctica B lipase (CaL B, Novozym 435) using microwave irradiation under solvent-free conditions.