Mesoionic Carbene Cobalt Complexes as Multipurpose Catalyst Precursors for Hydrosilylation and Dihydropyrimidinone Synthesis

Metalation of CH₂OH-substituted triazolium salts with CoCl₂ under basic conditions affords C,O-bidentate chelating carbene Co(III) complexes ( 3a , 3b ), while analogous phenyl-substituted triazolium salts produce monodentate carbene Co(II) complexes ( 3c , 3d ). The distinct substituent-induced properties of the metal centers were demonstrated by electrochemical measurements and catalytic activities in two specific processes. The complexes showed appreciable activity in the reduction of C=O bonds through hydrosilylation, with methoxybenzene-functionalized triazolylidene Co(III) complex 3a achieving a high selectivity towards aldehydes vs. ketones with turnover frequencies (TOFs) up to 200 h⁻¹. The C,O-chelate systems were also active catalysts in the Biginelli process, a one-step three-component reaction for efficient dihydropyrimidinone synthesis. Optimization of reaction conditions provides high activity with complex 3a , reaching TOFs of 800 h⁻¹, the highest activity known for cobalt NHC complexes to date.     

Total Synthesis of a Partial Structure from Arabinogalactan and Its Application for Allergy Prevention

Arabinogalactan, a microheterogeneous polysaccharide occurring in plants, is known for its allergy-protective activity, which could potentially be used for preventive allergy treatment. New treatment options are highly desirable, especially in a preventive manner, due to the constant rise of atopic diseases worldwide. The structural origin of the allergy-protective activity of arabinogalactan is, however, still unclear and isolation of the polysaccharide is not feasible for pharmaceutical applications due to a variation of the activity of the natural product and contaminations with endotoxins. Therefore, a pentasaccharide partial structure was selected for total synthesis and subsequently coupled to a carrier protein to form a neoglycoconjugate. The allergy-protective activity of arabinogalactan could be reproduced with the partial structure in subsequent in vivo experiments. This is the first example of a successful simplification of arabinogalactan with a single partial structure while retaining its allergy-preventive potential.     

Titanium Salalen Catalyzed Enantioselective Benzylic Hydroxylation

The titanium complex of the cis-1,2-diaminocyclohexane (cis-DACH) derived Berkessel-salalen ligand is a highly efficient and enantioselective catalyst for the asymmetric epoxidation of terminal olefins with hydrogen peroxide (“Berkessel-Katsuki catalyst”). We herein report that this epoxidation catalyst also effects the highly enantioselective hydroxylation of benzylic C−H bonds with hydrogen peroxide. Mechanism-based ligand optimization identified a novel nitro-salalen Ti-catalyst of the highest efficiency ever reported for asymmetric catalytic benzylic hydroxylation, with enantioselectivities of up to 98 % ee, while overoxidation to ketone is marginal. The novel nitro-salalen Ti-catalyst also shows enhanced epoxidation efficiency, as evidenced by e.g. the conversion of 1-decene to its epoxide in 90 % yield with 94 % ee, at a catalyst loading of 0.1 mol-% only.     

How algebra spoiled recreational problems: A case study in the cross-cultural dissemination of mathematics

This paper deals with a sub-class of recreational problems which are solved by a simple memorized rule resulting from an elementary arithmetical or algebraic solution, called proto-algebraic rules. Their recreational aspect is derived from a surprise or trick solution which is not immediately obvious to the subjects involved. Around 1560 many such problems wane from arithmetic and algebra textbooks to reappear in the eighteenth century. Several hypotheses are investigated why popular Renaissance recreational problems lost their appeal. We arrive at the conclusion that the emergence of algebra as a general problem solving method changed the scope of what is considered recreational in mathematics.     

A class of distributed optimization methods with event-triggered communication

We present a class of methods for distributed optimization with event-triggered communication. To this end, we extend Nesterov’s first order scheme to use event-triggered communication in a networked environment. We then apply this approach to generalize the proximal center algorithm (PCA) for separable convex programs by Necoara and Suykens. Our method uses dual decomposition and applies the developed event-triggered version of Nesterov’s scheme to update the dual multipliers. The approach is shown to be well suited for solving the active optimal power flow (DC-OPF) problem in parallel with event-triggered and local communication. Numerical results for the IEEE 57 bus and IEEE 118 bus test cases confirm that approximate solutions can be obtained with significantly less communication while satisfying the same accuracy estimates as solutions computed without event-triggered communication.     

Spectral properties of generalized Cesàro operators on Hardy and weighted Bergman spaces

We investigate spectral properties of integral operators of the form

Investigating undergraduate mathematics learners’ cognitive engagement with recorded lecture videos

The use of recorded lecture videos (RLVs) in mathematics instruction continues to advance. Prior research at the post-secondary level has indicated a tendency for RLV use in mathematics to be negatively correlated with academic performance, although it is unclear whether this is because regular users are generally weaker mathematics students or because RLV use is somehow depressing student learning. Through the lens of cognitive engagement, a quasi-experimental pre- and post-test design study was conducted to investigate the latter possibility.

Cognitive engagement was operationalized using the Revised Two-Factor Study Process Questionnaire (R-SPQ-2F), which measures learning approaches on two major scales: surface and deep. In two mathematics courses at two universities, in Australia and the UK, participants were administered the questionnaire near the course start and finish. Overall findings were similar in both contexts: a reduction in live lecture attendance coupled with a dependence on RLVs was associated with an increase in surface approaches to learning.

This study has important implications for future pedagogical development and adds to the sense of urgency regarding research into best practices using RLVs in mathematics.