On Nonlinear Coapproximation in Banach Spaces

The problem of nonlinear coapproximation in Banach spaces is considered, and characterization results and strong coapproximation results are presented.     

A characterization of heat balls by a mean value property for temperatures

We discuss an inverse mean value property of solutions of the heat equation. We show that, under certain conditions, a volume mean value identity characterizes heat balls.

     

The Effectiveness of Process‐Oriented Guided Inquiry Learning to Reduce Alternative Conceptions in Secondary Chemistry

A nonequivalent, control group design was used to investigate student achievement in secondary chemistry. This study investigated the effect of process‐oriented guided inquiry learning (POGIL) in high school chemistry to reduce alternate conceptions related to the particulate nature of matter versus traditional lecture pedagogy. Data were collected from chemistry students in four large high schools and were analyzed using analysis of covariance. The results show that POGIL pedagogy, as opposed to traditional lecture pedagogy, resulted in fewer alternate conceptions related to the particulate nature of matter. Male and female students in the POGIL group posted better posttest scores than their traditional group peers. African‐American and Hispanic students in the POGIL group exhibited achievement gains consistent with Caucasian and Asian students. Further studies are needed to determine the value of POGIL to address achievement gap concerns in chemistry.     

Advances in Transition Metal Seleno- and Tellurocarbonyl Chemistry

In contrast to the ubiquity of transition-metal carbonyl, and (to a lesser extent) thiocarbonyl complexes, transition-metal complexes of carbon monoselenide L_nMCSe and monotelluride L_nMCTe remain scarce. The last few years, however, have seen notable steps towards expanding this chemistry, specifically with regards to new systematic studies on homologous sets of chalcocarbonyl complexes L_nMCE (E=O, S, Se, Te), the first reports of new bi- and polynuclear CSe and CTe bridging complexes and a confluence with metal carbido chemistry. Herein the properties, syntheses and reactions of these rare but fundamentally intriguing compounds are discussed.     

Catalytic Enantioselective Synthesis of Heterocyclic Vicinal Fluoroamines by Using Asymmetric Protonation: Method Development and Mechanistic Study

A catalytic enantioselective synthesis of heterocyclic vicinal fluoroamines is reported. A chiral Brønsted acid promotes aza-Michael addition to fluoroalkenyl heterocycles to give a prochiral enamine intermediate that undergoes asymmetric protonation upon rearomatization. The reaction accommodates a range of azaheterocycles and nucleophiles, generating the C−F stereocentre in high enantioselectivity, and is also amenable to stereogenic C−CF₃ bonds. Extensive DFT calculations provided evidence for stereocontrolled proton transfer from catalyst to substrate as the rate-determining step, and showed the importance of steric interactions from the catalyst's alkyl groups in enforcing the high enantioselectivity. Crystal structure data show the dominance of noncovalent interactions in the core structure conformation, enabling modulation of the conformational landscape. Ramachandran-type analysis of conformer distribution and Protein Data Bank mining indicated that benzylic fluorination by this approach has the potential to improve the potency of several marketed drugs.     

Synthesis of Indolines and Derivatives by Aza‐Heck Cyclization

For the first time, an aza‐Heck cyclization that allows the preparation of indoline scaffolds is described. Using N‐hydroxy anilines as electrophiles, which can be easily accessed from the corresponding nitroarenes, this method provides indolines bearing pendant functionality and complex ring topologies. Synthesis of challenging indolines, such as those bearing fully substituted carbon atoms at C2, is also possible using this method.     

Field effect in small filaments of chalcogenide glasses

A field effect has been measured in a semiconducting chalcogenide glass, of composition Te₂AsSi. The sample was in the form of a fine filament, encapsulated within a rod of insulating glass, with the bias field applied radially. The effect is small, and the change in conductivity increases more slowly with field at high fields than at low fields. The results are explained in terms of a model with a uniform density of bulk states near the Fermi energy and a sharp surface level just below the Fermi energy. There is a depletion layer at the surface at zero bias, hence the surface barrier with no external field varied with each sample.     

Amarts on Riesz Spaces

The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson （Discrete time stochastic processes on Riesz spaces, Indag. Math.,15（2004）, 435-451）. Here we extend the definition of an asymptotic martingale （amart） to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced.