How to grow it? Strategies of mathematical development presented by the example of enumerating certain set partitions

Mathematische Semesterberichte - We describe in the form of a dialogue a development of various reflections on the combinatorics of set partitions; among the topics we pursue are...     

Rhodium-Mediated Stoichiometric Synthesis of Mono-, Bi-, and Bis-1,2-Azaborinines: 1-Rhoda-3,2-azaboroles as Reactive Precursors

A series of highly substituted 1,2-azaborinines, including a phenylene-bridged bis-1,2-azaborinine, was synthesized from the reaction of 1,2-azaborete rhodium complexes with variously substituted alkynes. 1-Rhoda-3,2-azaborole complexes, which are accessible by phosphine addition to the corresponding 1,2-azaborete complexes, were also found to be suitable precursors for the synthesis of 1,2-azaborinines and readily reacted with alkynyl-substituted 1,2-azaborinines to generate new regioisomers of bi-1,2-azaborinines, which feature directly connected aromatic rings. Their molecular structures, which can be viewed as boron-nitrogen isosteres of biphenyls, show nearly perpendicular 1,2-azaborinine rings. The new method using rhodacycles instead of 1,2-azaborete complexes as precursors is shown to be more effective, allowing the synthesis of a wider range of 1,2-azaborinines.     

A new method for the determination of the 34S/32S ratio of water-soluble sulphur in soil

A new method for the determination of the ³⁴S/³²S ratio of water-extractable sulphate in soil is described. Soils are extracted directly with deionized water, which is evaporated down. The remaining residue is then rehydrated and transferred to tin cups containing an adsorbent and mixed with an oxygen donor (V₂O₅). Samples are then analysed using a continuous flow isotope ratio mass spectrometer. The new method requires around 10?g soil per determination, compared to much larger amounts (up to kilograms) of soil required for the previous methods. Sample preparation and subsequent analysis is quick and efficient. The method is demonstrated using a number of soils collected from around the world to provide a range of determined δ³⁴S values. The δ³⁴S values of water-extractable sulphur were broadly similar to those of the soil total sulphur.     

Control concepts for a parallel manipulator with flexible links

Light-weight robots are advantageous considering the low energy consumption and the low material cost. However, in light-weight structures significant oscillations can occur which make the control very challenging. Objective of this research is end-effector trajectory tracking of a parallel manipulator with flexible links. Hereby, only the manipulator's drives are used, and no additional actuation on the flexible bodies is considered. For accurate trajectory tracking, feedforward control of the manipulator is used based on inverse dynamics and servo-constraints, combined with feedback control of the drive positions. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Study of the polymerization of acrylic resins by photocalorimetry: interactions between UV initiators and absorbers

Photocurable finishes should be extensively used for industrial wood joinery in the near future even if some technical problems have still to be solved and if the durability of the finishing system has to be enhanced. In a previous work, we studied the curing reaction of acrylic resins containing some particular photoinitiators by photocalorimetry and showed that curing can be achieved under daylight with these compounds (i.e. solving the problem of restoration on site). The aim of this work is to enhance the durability of these systems by incorporating UV absorbers into the formulations. The consequences of such an addition onto the curing kinetics are again investigated by photocalorimetry.     

Inhibition of corrosion of commercial mild steel in presence of tetrazole derivatives in acid medium

The inhibitive influence of tetrazole derivatives namely, 1-(9¹-acridinyl)-5-(4′-aminophenyl) tetrazole, 1-(9′-acridinyl)-5-(4′-hydroxy phenyl) tetrazole and 1-(9′-acridinyl)-5-(4′-chlorophenyl) tetrazole on the corrosion of commercial mild steel in 1 N hydrochloric acid medium was studied by weight loss method. The monolayer adsorption has been confirmed by fitting the data to the Langmuir adsorption isotherm. Weight loss studies have been carried out at 303K, 318K and 333K. Thermodynamic parameters like heat of adsorption, activation energy and free energy change have been calculated. The maximum inhibition of efficiency of tetrazole derivatives, 1-(9′-acridinyl)-5-(4′-amoinophenyl) tetrazole, 1-(9′acridinyl)-5-(4′-hydroxyphenyl) tetrazole and 1-(9′-acridinyl)-5-(4′-Chlorphenyl) tetrazole was found to be 60.59%, 89.00% and 92.74, respectively. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, India, Nov. 28–30, 2003.     

Inhibition of corrosion of aluminium in presence of fluorescein in basic medium

The influence of Fluorescein in conjunction with calcium oxide on the corrosion of Aluminium in 1.0 N NaOH was studied by galvanostatic studies and weight loss studies. It has been found that the inhibition of corrosion of aluminium increased with the increasing concentration of the inhibitor. The maximum inhibition efficiency of fluorescein alone was found to be 30.80%. However, the addition of calcium oxide increased the maximum inhibition efficiency to 53.71%. The corrosion process was found to be under the anodic control, in the presence or in the absence of inhibitor. The inhibition was found to be mixed type. Paper presented at the 2nd International Conference on Ionic Devices, Anna University, Chennai, Inida, Nov. 28–30, 2003.     

Spectroscopic and Biological Testing of Photobleaching of Porphyrins in Solutions*

The photobleaching of protoporphyrin IX (PP IX) and hematoporphyrin derivative (HpD) solutions was followed using three different methods: spectrophotometry, fluorometry and photodynamically induced cytotoxicity. The latter entails photoirradiation of HT29 human colon adenocarcinoma cells in the presence of preirradiated solutions of HpD and PP IX (λ 415 nm). The highest cytotoxicity was observed in the presence of unirradiated dye and decreased with the time of preirradiation. This decay in photocytotoxicity was further used to determine the porphyrin photobleaching kinetics in solution. For both sensitizers, quantum yields of photobleaching obtained by matching fluoresence were higher than that obtained from absorbance measurements (10 and 11 times for HpD and PP IX, respectively). This difference reflects preferential photobleaching of photolabile monomeric forms compared to aggregates. The highest quantum yield was obtained in the biological test (decay in cytotoxicity) which was 14 times higher for HpD and 30 times higher for PP IX than the quantum yield obtained from absorbance measurements. The absence of correlation between biological and fluorescence measurements has to be taken into account in the in vivo situation. Dark storage of preirradiated sensitizers (37°C, 24 h) completely restored photocytotoxity for PP IX but only partially for HpD, whereas fluorescence patterns were partially restored for both sensitizers.