Cationic dirhodium carboxylate-catalyzed synthesis of dihydropyrimidones from propargyl ureas

Cationic Rh(II) complexes are able to catalyze the regioselective hydroamination of propargyl ureas in a 6-endo fashion. This transformation permits access to interesting substitution patterns of dihydropyrimidines, which have found use as nucleotide exchange factor inhibitors.     

Ligand-modulated palladium oxidation catalysis: mechanistic insights into aerobic alcohol oxidation with the Pd(OAc)(2)/pyridine catalyst system

Pd(OAc)(2):pyridine (1:4) is an efficient catalyst system for the oxidation of alcohols with molecular oxygen. A mechanistic study of this reaction reveals that pyridine promotes the aerobic oxidation of palladium(0) but inhibits the oxidation of alcohol by palladium(II). Kinetic results reveal that turnover-limiting substrate oxidation consists of (i) formation of a palladium(II)-alkoxide, (ii) pyridine dissociation, and (iii) beta-hydride elimination. These results provide a framework for the design and/or screening of more effective aerobic oxidation catalysts.     

Conformational Dynamics in the Core of Human Y145Stop Prion Protein Amyloid Probed by Relaxation Dispersion NMR

Microsecond to millisecond timescale backbone dynamics of the amyloid core residues in Y145Stop human prion protein (PrP) fibrils were investigated by using ¹⁵N rotating frame (R_1ρ) relaxation dispersion solid-state nuclear magnetic resonance spectroscopy over a wide range of spin-lock fields. Numerical simulations enabled the experimental relaxation dispersion profiles for most of the fibril core residues to be modelled by using a two-state exchange process with a common exchange rate of 1000 s⁻¹, corresponding to protein backbone motion on the timescale of 1 ms, and an excited-state population of 2 %. We also found that the relaxation dispersion profiles for several amino acids positioned near the edges of the most structured regions of the amyloid core were better modelled by assuming somewhat higher excited-state populations (∼5–15 %) and faster exchange rate constants, corresponding to protein backbone motions on the timescale of ∼100–300 μs. The slow backbone dynamics of the core residues were evaluated in the context of the structural model of human Y145Stop PrP amyloid.     

PBL as a pedagogical approach for integrated STEM: Evidence from prospective teachers

Problem-based learning (PBL) and science, technology, engineering, and mathematics (STEM) are two acronyms widely visible in education literature today. However, few studies have explored these in connection with one another, specifically with regard to teacher preparation. This study investigated how 47 prospective elementary teachers developed PBL units and how they integrated STEM and other disciplines into those units. It also addressed the affordances and constraints of integrated STEM as perceived by the prospective elementary teachers. Data sources in this multimethod study included PBL units and interviews. Findings revealed that all of the units integrated at least two of the STEM disciplines, as well as literacy, in a variety of ways. The prospective teachers articulated perceived benefits of integrated STEM, such as: making connections across content areas, preparing students for the real world, teaching students that failure is not a bad thing, and providing future opportunities. They also addressed perceived barriers of integrated STEM, such as: having limited experience with the content, diminishing the effect of individual content areas, and needing better curriculum alignment. Overall, this study provides evidence that PBL can be a pedagogical approach to integrate STEM. Implications for teachers, teacher educators, and curriculum specialists are discussed.     

Some useful integer arrays for the teaching of generalization skills

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example presented, the subjects in question are absolute values, graphs and solutions of equations, and domains of definition. These are unified by the problem of finding an analytic expression for a square and triangle and their interiors. In the course of the development, basic notions such as the additive property of areas and convexity are introduced. The approach presented in the article was tried with secondary school teachers participating in professional development workshops and with students at a technical college; the teachers and students responded enthusiastically to the material.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

A Note on twin primes and the modular ring Z 6

The modular ring ?₆ defines integers via (6r _i + (i ? 3)) where i is the class and r _i the row when tabulated in an array. Since only Classes 2₆ and 4₆ contain odd primes, this modular ring is ideally suited to the analysis of twin primes. The calculations are facilitated by the use of the right-end digit (RED) technique.     

Assessing views of coaching via a video-based tool

Mathematics coaches represent a unique group of didacticians, or individuals who work with practicing teachers. Twenty-eight mathematics coaches participated in this exploratory study, which used video viewing to examine the coach–teacher dynamic. To gather data about participants’ views of effective coaching practices, we developed the Video Assessment of Coaching instrument, which provided coaches with opportunities to express their views of effective practice and implementation. The participants expressed views of effective coaching that often did not align with those of coaching authors. The significance of this research lies in its efforts to document the views that mathematics coaches develop as practitioners, as an early step in the examination of the relationships between the views of coaches and coaches’ effectiveness in improving teacher practice, knowledge, and attitudes.     

Phosphinoferrocenylaminophosphines as novel and practical ligands for asymmetric catalysis

[structure: see text] A new series of ligands with a novel phosphine-aminophosphine ligation design as depicted in structure 1 has been prepared on a ferrocenylethyl backbone. These BoPhoz ligands of structure 2 have afforded exceedingly high activity and enantioselectivity in the rhodium-catalyzed asymmetric hydrogenation of dehydro-alpha-amino acid derivatives, itaconic acids, and alpha-ketoesters. These air-stable ligands are readily prepared from cost-effective and non-pyrophoric intermediates.