Photochemical synthesis of α-oxygenated benzothiophenedioxides

The photochemical synthesis of 1-hydroxy[b]benzo-1,3-dihydrothiophene-2,2-dioxides from orthomethylbenzaldehyde and its analogs is described. Some of the chemistry of these α-oxygenated sulfones, including exchange of the 1-hydroxy group with various alkoxy groups and the thermal reversion of these oxygenated derivatives to trappable 1-alkoxy-substituted o-quinodimethanes has been investigated.     

Controlled process for polymer micromachining using designed pulse trains of a UV solid state laser

A flexible workstation equipped with a solid state laser operating at 266 nm wavelength was used to machine holes in polyethylene terephthalate, polyimide and polycarbonate. An optical pulse picker was employed to reduce the high repetition rates of the laser, while a breakthrough sensor was used to avoid over-drilling of through holes. For each material, different repetition rates and designed pulse trains were tested to improve feature quality and process efficiency. Although the three polymers had very different reactions at this wavelength they all showed an improvement in feature quality with decreasing repetition rate due to a reduction in thermal effects. Up to 10 kHz the average depth per pulse remained unchanged and afterwards a slight increase was observed but this was accompanied by large uncertainties. Bursts of pulses at 40 kHz inserted inside the low repetition rate pulse train reduced the drilling time and the amount of debris redeposited without affecting the feature quality. It was found that a number of cleaning pulses after perforation eliminates the heat affected zone around exits. Holes with entrance diameters below 20 μm and exit diameters as small as 2 μm were obtained with high repeatability.     

‘I’m worried about the correctness’: undergraduate students as producers of screencasts of mathematical explanations for their peers – lecturer and student perceptions

Undergraduate mathematics is traditionally designed and taught by content experts with little contribution from students. Indeed, there are signs that there is resistance from mathematics lecturers to involve students in the creation of material to support their peers – notwithstanding the fact that students have been successfully engaged as co-creators of material in other disciplines. There appears to be little research into what issues may lead to reservations to using student-created content in mathematics learning. This paper takes a case study approach to investigate the reasons for lecturers’ resistance to undergraduate student contributions to learning material, in particular with a view to the production of screencasts of mathematical explanations. It also investigates the views of students producing mathematical screencasts. This study is part of a larger research project investigating undergraduate involvement in mathematics module design. Four second-year students, who were producing mathematics screencasts as part of an internship, and five academics, were interviewed to gain an understanding of their views of the value of student screencasts. The interviews focused on the particular contributions students make to screencasts, outcomes for the students and level of lecturer acceptance of these resources. We argue that students benefit from creating screencasts for their peers by gaining deeper mathematical understanding, improved technological skills and developing other generic skills required of today's graduates. In contrast, we confirm lecturer resistance to using student-generated screencasts in their teaching materials. Lecturer reservations pertain to students’ lack of mathematical maturity and concerns over the mathematical integrity of the content that students produce. We conclude that close collaboration between students and lecturers during the design and production phases of screencasts may help lecturers overcome reservations, whilst preserving the benefits for students. In addition, we provide evidence that the process is a valuable professional development opportunity for the lecturers themselves.     

The Dual Hilbert–Samuel Function of a Maximal Cohen-Macaulay Module

Let R be a Cohen–Macaulay local ring with a canonical module ω _R . Let I be an 𝔪-primary ideal of R and M, a maximal Cohen–Macaulay R-module. We call the function n??(Hom _R (M, ω _R /I ⁿ⁺¹ω _R )) the dual Hilbert–Samuel function of M with respect to I . By a result of Theodorescu, this function is of polynomial type. We study its first two normalized coefficients. In particular, we analyze the case when R is Gorenstein.     

Experiencing the space we share: rethinking subjectivity and objectivity

Mathematics in schools exists substantially as pedagogical material crafted for supposed modes of apprehension. But of course such apprehension depends on how we understand mathematical objects and how we understand human subjects. The apprehension of mathematical objects is examined through sessions with student teachers researching their own spatial awareness from a pedagogical point of view. The paper is guided by the recent work of Alain Badiou whose philosophical model develops a Lacanian conception of human subjectivity and defines a new conception of objectivity. In this model the conception of subjectivity comprises a refusal to allow humans to settle on certain self-images that have fuelled psychology and set the ways in which humans are seen as apprehending the mathematically defined world. The assertion of an object, meanwhile, is associated with finding a place for it in a given supposed world, and it may reconfigure that world. The composite model understands learning as shared participation in renewal where there is a mutual dependency between the growth of human subjects and of mathematical objects. Renewal is referenced to a diversity of ever shifting discursive parameters that enable learning through negotiating the spaces within which we operate and the objects those spaces allow. Learning to teach then comprises developing sensitivity towards the discursive spaces that allow others to build objects. The paper provides examples from teacher education activities centred in addressing these concerns.     

TMG catalyzed cyclopropanation of cyclopentenone. Illustration by a simple synthesis of bicyclo[3.1.0]hexane-2-one derivatives

The catalytic preparation of bicyclo[3.1.0]hexane-2-one-6-carboxylic acid ethyl ester 1 is described by cyclopropanation of cyclopentenone using 1,1,3,3-tetramethylguanidine (TMG) as a catalyst in high yield and high diastereoselectivity. This process has been applied to an efficient synthesis of the important intermediate, β-hydroxyl cyclopentanone 2.     

Structural induced control of energy transfer within Zn(II)-porphyrin dendrimers

We report on a study of singlet-singlet annihilation kinetics in a series of Zn(II)-porphyrin-appended dendrimers, where the energy transfer efficiency is significantly improved by extending the molecular chain that connects the light-harvesting chromophores to the dendrimeric backbone with one additional carbon. For the largest dendrimer having 64 Zn(II)-porphyrins, only approximately 10% of the excitation intensity is needed in order to observe the same extent of annihilation in the dendrimers with the additional carbon in the connecting chain as compared to those without. Complete annihilation, until only one chromophore remains excited, now occurs within subunits of seven chromophores, when half of the chromophores are excited. The improvement of the annihilation efficiency in the largest dendrimer with 64 porphyrins can be explained by the presence of a the two-step delayed annihilation process, involving energy hopping from excited to nonexcited chromophores prior to annihilation. In the smallest dendrimer with only four chromophores, delayed annihilation is not present, since the direct annihilation process is more efficient than the two-step delayed annihilation process. As the dendrimer size increases and the chances of originally exciting two neighboring chromophores decreases, the delayed annihilation process becomes more visible. The additional carbon, added to the connecting chain, results in more favorable chromophore distances and orientations for energy hopping. Hence, the improved energy transfer properties makes the Zn(II)-porphyrin-appended dendrimers with the additional carbon promising candidates as light-harvesting antennas for artificial photosynthesis.     

Structural development of mercaptophenol self-assembled monolayers and the overlying mineral phase during templated CaCO3 crystallization from a transient amorphous film

Formation of biomineral structures is increasingly attributed to directed growth of a mineral phase from an amorphous precursor on an organic matrix. While many in vitro studies have used calcite formation on organothiol self-assembled monolayers (SAMs) as a model system to investigate this process, they have generally focused on the stability of amorphous calcium carbonate (ACC) or maximizing control over the order of the final mineral phase. Little is known about the early stages of mineral formation, particularly the structural evolution of the SAM and mineral. Here we use near-edge X-ray absorption spectroscopy (NEXAFS), photoemission spectroscopy (PES), X-ray diffraction (XRD), and scanning electron microscopy (SEM) to address this gap in knowledge by examining the changes in order and bonding of mercaptophenol (MP) SAMs on Au(111) during the initial stages of mineral formation as well as the mechanism of ACC to calcite transformation during template-directed crystallization. We demonstrate that formation of ACC on the MP SAMs brings about a profound change in the morphology of the monolayers: although the as-prepared MP SAMs are composed of monomers with well-defined orientations, precipitation of the amorphous mineral phase results in substantial structural disorder within the monolayers. Significantly, a preferential face of nucleation is observed for crystallization of calcite from ACC on the SAM surfaces despite this static disorder.