Student interpretations of the terms in first-order ordinary differential equations in modelling contexts

A study of first-year undergraduate students′ interpretational difficulties with first-order ordinary differential equations (ODEs) in modelling contexts was conducted using a diagnostic quiz, exam questions and follow-up interviews. These investigations indicate that when thinking about such ODEs, many students muddle thinking about the function that gives the quantity to be determined and the equation for the quantity's rate of change, and at least some seem unaware of the need for unit consistency in the terms of an ODE. It appears that shifting from amount-type thinking to rates-of-change-type thinking is difficult for many students. Suggestions for pedagogical change based on our results are made.     

Tunable asymmetric fibre ring resonator

A fibre ring resonator with coupling via an asymmetric twin-core single-mode coupler with variable mismatch is analysed. It is found that by varying the mismatch in the coupler the resonance conditions of the ring are also changed. Suitable choices of device parameters allow the resonance to be tuned over a range of wavelenths by altering the coupler mismatch.     

Organocatalytic enantioselective Friedel-Crafts reaction of pyrrole derivatives with imines

A highly enantioselective Friedel-Crafts reaction of pyrrole derivatives with N-acyl imines catalyzed by chiral phosphoric acids was developed. The reactions produced the pyrrole derivatives in high yields and enantioselectivity.     

Multiphoton ionization detected by fourier-transform mass spectrometry

Ions produced by multiphoton ionization (MPI) of naphthalene, fluoranthene and triphenylene have been detected by Fourier-transform mass spectrometry (FT MS). Paret ions are produced very efficiently at 250 and 222 nm with pulse energies as low as 1 mJ. With FT MS a complete, high-resolution mass spectrum is obtained for each laser pulse.