An iron-catalysed chemo- and regioselective tetrahydrofuran synthesis

An intermolecular ring expansion reaction of an aryl epoxide with several dienes, acrylates, enynes or styrenes under iron catalysis, generated tetrahydrofuran derivatives in a highly chemo- and regioselective fashion. The process could be used in an unprecedented way for the one step synthesis of racemic calyxolane A and calyxolane B with acceptable diastereoselectivity.     

Hippocampal activity during the transverse patterning task declines with cognitive competence but not with age

Background  

The hippocampus is a brain region that is particularly affected by age-related morphological changes. It is generally assumed that a loss in hippocampal volume results in functional deficits that contribute to age-related cognitive decline. In a combined cross-sectional behavioural and magnetoencephalography (MEG) study we investigated whether hippocampal-associated neural current flow during a transverse patterning task - which requires learning relational associations between stimuli - correlates with age and whether it is modulated by cognitive competence.     

Orientational preferences of aromatic guests in dimeric capsules of tetraurea calix[4]arenes--MD and NMR studies

Molecular dynamics (MD) simulations have been performed for complexes of a dimeric capsule of a tetraurea calixarene with a series of twelve aromatic guests. A distinct orientational preference and a restriction of the internal mobility was found which depend on the size and electronic properties of the guests. The results are in agreement with the CIS values obtained from (1)H NMR spectroscopic measurements and with complexation selectivities obtained by competition experiments.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Fatou Components of Attracting Skew-Products

We investigate the existence of wandering Fatou components for polynomial skew-products in two complex variables. In 2004, the non-existence of wandering domains near a super-attracting invariant fiber was shown in Lilov (Fatou theory in two dimensions, PhD thesis, University of Michigan, 2004). In 2014, it was shown in Astorg et al. (Ann Math, arXiv:1411.1188 [math.DS], 2014) that wandering domains can exist near a parabolic invariant fiber. In Peters and Vivas (Math Z, arXiv:1408.0498, 2014), the geometrically attracting case was studied, and we continue this study here. We prove the non-existence of wandering domains for subhyperbolic attracting skew-products; this class contains the maps studied in Peters and Vivas (Math Z, arXiv:1408.0498, 2014). Using expansion properties on the Julia set in the invariant fiber, we prove bounds on the rate of escape of critical orbits in almost all fibers. Our main tool in describing these critical orbits is a possibly singular linearization map of unstable manifolds.     

Optimising a general repair kit problem with a service constraint

Field services are a particular type of after-sales service performed at the customer’s location where technicians repair malfunctioning machines. The inventory decisions about which spare part types to take to the repair site and in what quantities is called the repair kit problem. This problem is characterized by an order-based performance measure since a customer is only satisfied when all required spare parts are available to fix the machine. As a result, the service level in the decision making process is defined as a job fill rate. In this paper we derive a closed-form expression for the expected service level and total costs for the repair kit problem in a general setting, where multiple units of each part type can be used in a multi-period problem. Such an all-or-nothing strategy is a new characteristic to investigate, but commonly used in practice. Namely, items are only taken from the inventory when all items to perform the repair are available in the right quantity. We develop a new algorithm to determine the contents of the repair kit both for a service and cost model while incorporating this new expression for the job fill rate. We show that the algorithm finds solutions which differ on average 0.2% from optimal costs. We perform a case study to test the performance of the algorithm in practice. Our approach results in service level improvements of more than 30% against similar holding costs.     

Effect of the shear layer on the etching behavior of 6060 aluminum extrusion alloys

The occurrence of preferential grain etching (PGE) during alkaline etching of aluminum extrusion alloys from the 6XXX series is often linked to the presence of certain impurity elements such as zinc, causing an undesired etching appearance. In the presented work, an additional culprit in this context is identified, which has not been investigated yet. A clear relation between PGE and the presence of a subsurface shear layer is identified for extruded Al 6060 alloys containing 0.02 and 0.06 wt% Zn. This shear layer can be distinguished from the bulk of the metal by its difference in crystallographic texture as visualized by electron backscatter diffraction (EBSD). For the Zn enriched alloy, the <111>//ND grains are etched away faster than grains with other orientations, resulting in the grainy appearance typical for PGE. Independent of the Zn content in the alloy, once the shear layer is removed and <111>//ND grains are practically absent on the new surface, the depths variations caused by preferential etching disappear. Instead, the surface of the alloy is attacked uniformly by the caustic etch bath.     

Exploring mathematical connections of pre-university students through tasks involving rates of change

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.