Synthesis of cis- and trans-3-aminocyclohexanols by reduction of β-enaminoketones

We describe a protocol developed for the preparation of β-enaminoketones derived from 1,3-cyclohexanediones, and their subsequent reduction by sodium in THF-isopropyl alcohol to afford cis- and trans-3-aminocyclohexanols.     

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.     

Derivations on a C1-algebra and its double dual

Let A be a C¹-algebra and X a Banach A-module. The module action of A on X gives rise to module actions of $\text{A}{}^7$ on $\text{X}{}^1$ and $\text{X}{}^7$, and derivations of A into X (resp. $\text{X}{}^1$) extend to derivations of $\text{A}{}^7$ into $\text{X}{}^7$ (resp. $\text{X}{}^1$). If A is nuclear, and X is a dual Banach A-module with $\text{X}{}^1$ weakly sequentially complete, then every derivation of A into X is inner. Under the same hypothesis on A, the extension to the finite part of $\text{A}{}^7$ of any derivation of A into any dual Banach A-module is inner, as are all derivations of A into $\text{A}{}^1$. Every derivation of a semifinite von Neumann algebra into its predual is inner.     

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.