A Framework for Monitoring Progress and Planning Teaching Towards the Effective Use of Computer Algebra Systems

This article suggests a framework to organise a cluster of variables that are associated with students' effective use of computer algebra systems (CAS) in mathematics learning. Based on a review of the literature and from the authors' own teaching experience, the framework identifies the main characteristics of students' interactions with CAS technology and how these may be used to monitor students' developing use of CAS; from this, the framework may be used to plan teaching in order to gain greater benefit from the availability of CAS. Four case studies describing students' development over a semester are reported. These demonstrate a variety of combinations of technical competencies and personal attributes. They indicate the importance of both the technical and personal aspects but suggest that negative attitudes rather than technical difficulties can limit the effective use of CAS. Finally practical suggestions are given for teaching strategies which may promote effective use of CAS.This revised version was published online in September 2005 with corrections to the Cover Date.     

Photochemical expulsion of the neutral monodentate ligand L in Ru(terpy*)(diimine)(L)2+: a dramatic effect of the steric properties of the spectator diimine ligand

A series of photoreactive complexes of the type Ru(terpy*)(N-N)(L)(2+), where terpy* is 4'-(3,5-ditertiobutylphenyl)-2,2':6',2' '-terpyridine, N-N is the bidentate chelate phen or dmp (phen = 1,10-phenanthroline, dmp = 2,9-dimethyl-1,10-phenanthroline), and L is the monodentate ligand dms, MeBN, or MeOBN (dms = dimethyl sulfide, MeBN = 2,6-dimethyl benzonitrile, MeOBN = 2,6-dimethoxybenzonitrile), has been synthesized and fully characterized by proton NMR spectroscopy, electrospray mass spectrometry, and UV-vis spectroscopy. The X-ray structures of four complexes were also obtained. In neat pyridine, the quantum yields for the photosubsitution of L by pyridine were measured and showed dramatic variations depending on the steric interactions between the spectator bidentate ligand and the leaving monodentate ligand L. The use of dmp instead of phen multiplied the photosubstitution efficiency by a factor of 20-50, depending on L. This effect could be qualitatively correlated to the distortions observed in the X-ray structures of the corresponding complexes. The highly distorted structure of Ru(terpy)(dmp)(dms)(PF(6))(2) showed a very high photosubsitution quantum yield phi = 0.36 in neat pyridine. The high photoreactivity of some of the compounds makes them particularly promising as components of future light-driven molecular machines.     

Diels-Alder chemistry on alkene functionalized films

A substrate-independent method has been devised for ring formation at solid surfaces. This entails the aminolysis reaction of allylamine with maleic anhydride pulsed plasma polymer films to yield terminal alkene groups at the surface. Subsequent exposure to 1,3-cyclohexadiene leads to a Diels-Alder type (4 + 2) cycloaddition reaction to give a mixture of endo- and exo-bicyclo[2.2.2]oct-2-ene rings.     

Straightforward synthesis of sphinganines via a serine-derived Weinreb amide

Sphinganines can be synthesized in just three steps from easily prepared serine-derived Weinreb amide 4. Pre-deprotonation of the acidic (N-H and O-H) protons of 4 allows for its efficient conversion to amino ketones 5. Such ketones can be selectively reduced to either erythro- or threo-sphinganines. Partially protected sphinganines 11 are also readily accessible in five steps from 4. Thus, Weinreb amide 4 represents one of the most versatile templates described to date for sphinganine synthesis.     

Effect of OH internal torsion on the OH-stretching spectrum of cis,cis-HOONO

We show that a simple two-dimensional vibrational model can explain most of the features observed in the first and second OH-stretching overtone region of the room temperature cis,cis-HOONO spectrum. The model uses ab initio calculated parameters and includes the OH-stretching mode coupled to the internal torsion of the OH group.     

Ruminant pregastric lipases: experimental evidence of their potential as industrial catalysts in food technology

The historical importance of pregastric enzymes in cheese-making is reviewed and the potential for extending their use is discussed in terms of requiring an understanding of their physicochemical parameters. Commericial extracts from the tongues and epiglotti of suckling lambs and calves and adult goats have been processed to yield partially purified samples of the primary pregastric lipase (PGL). The N-terminal sequence and molecular weight of lamb PGL have been determined.

The activity of lamb and goat PGLs against tributyrin has been determined over a range of pH and temperature values. Optimum conditions were pH 6.4, 43°C, and pH 6.0, 52°C, for lamb and goat PGL respectively. The possible influence of the development of a ruminant multi-chambered stomach on the difference in optimal temperature is discussed. A lengthening of the carboxylic acid chain of homoacid triglycerides causes a decrease in hydrolytic activity of lamb PGL but in all cases only a single free fatty acid was released. Against a series of 4-nitrophenylalkanoate esters, maximum activity was observed against the decanoate ester but, in contrast to hydrolysis of the acetate ester which exhibited full Michaelis-Menten kinetics with increasing substrate concentration, activity against the decanoate ester was restricted to the monomeric substrate. Taurocholate inhibits the activity of lamb PGL at concentrations >8 mM. Values of pK₂ equal to 6.69 and 7.92 respectively have been determined for lamb PGL.

Attempts to interesterify coconut oil and cocoa butter, and tributyrin and tricaprylin, catalysed by calf PGL were unsuccessful, although positive results obtained using Candida cylindracea encourage further investigation of alternative methods for immobilizing the PGL. Finally, anhydrous milk fat has been hydrolysed by calf, lamb and goat PGLs and the differences in relative amounts of released free fatty acids have been used to explain the differences in taste which arise when Parmesan cheese is produced using different sources of PGL.     

Metal-directed synthesis and photophysical studies of trinuclear v-shaped and pentanuclear x-shaped ruthenium and osmium metallorods and metallostars based upon 4'-(3,5-dihydroxyphenyl)-2,2':6',2''-terpyridine divergent units

A new series of V-shaped trinuclear metallorods and X-shaped pentanuclear metallostars has been prepared by the reaction of metal complexes bearing pendant phenolic functionalities with complexes containing electrophilic ligands. Specifically, {M(tpy)2} motifs (M=Ru or Os; tpy=2,2':6',2'-terpyridine) bearing one or two pendant 3,5-dihydroxyphenyl substituents at the 4-position of the central ring of the tpy have been reacted with the complexes [Ru(tpy)(Xtpy)]2+ (X=Cl or Br) to form new ether-linked species. The energy transfer from ruthenium to osmium in these complexes has been investigated in detail and the efficiency of transfer shown to be highly temperature dependent; the energy transfer is highly efficient at low temperature, whereas at room temperature nonradiative and nontransfer deactivation of the excited {Ru(tpy)2}* domains is most significant.     

Conducting polymers containing in-chain metal centers: electropolymerization of oligothienyl-substituted {M(tpy)2} complexes and in situ conductivity studies, M = Os(II), Ru(II)

The electropolymerization of a series of Ru and Os bis-terpyridine complexes that form rodlike polymers with bithienyl, quaterthienyl, or hexathienyl bridges has been studied. Absorption spectroscopy, scanning electron microscopy, and cyclic voltammetry have been used to characterize the monomers and resulting polymer films. The absolute dc conductivity of the quaterthienyl-bridged {Ru(tpy)2} and {Os(tpy)2} polymers is unusually large and independent of the identity of the metal center at 1.6 x 10(-3) S cm(-1). The maximum conductivity occurs at the formal potential of each redox process, which typically is observed for systems where redox conduction is the dominant charge transport mechanism. Significantly, the dc conductivity of the metal-based redox couple observed in these polymers is 2 orders of magnitude higher thanthat of a comparable nonconjugated system.     

Conversion of ketones into vinyl-oxiranes

A range of 1-(2-propenyl) alcohols was transformed in good yields into vinyl-oxiranes via the allylic bromide.     

Electronic energy transfer and collection in luminescent molecular rods containing ruthenium(II) and osmium(II) 2,2':6',2"-terpyridine complexes linked by thiophene-2,5-diyl spacers

The electronic absorption spectra, luminescence spectra and lifetimes (in MeCN at room temperature and in frozen n-C3H7CN at 77 K), and electrochemical potentials (in MeCN) of the novel dinuclear [(tpy)Ru(3)Os(tpy)]4+ and trinuclear [(tpy)Ru(3)Os(3)Ru(tpy)]6- complexes (3 = 2,5-bis(2,2':6',2'-terpyridin-4-yl)thiophene) have been obtained and are compared with those of model mononuclear complexes and homometallic [(tpy)Ru(3)Ru(tpy)]4+, [(tpy)Os(3)Os(tpy)]4+ and [(tpy)Ru(3)Ru(3)Ru(tpy)]6+ Complexes. The bridging ligand 3 is nearly planar in the complexes, as seen from a preliminary X-ray determination of [(tpy)Ru(3)Ru(tpy)][PF6]4, and confers a high degree of rigidity upon the polynuclear species. The trinuclear species are rod-shaped with a distance of about 3 nm between the terminal metal centres. For the polynuclear complexes, the spectroscopic and electrochemical data are in accord with a significant intermetal interaction. All of the complexes are luminescent (phi in the range 10(-4)-10(-2) and tau in the range 6-340 ns, at room temperature), and ruthenium- or osmium-based luminescence properties can be identified. Due to the excited state properties of the various components and to the geometric and electronic properties of the bridge, Ru --> Os directional transfer of excitation energy takes place in the complexes [(tpy)Ru(3)Os(tpy)]4+ (end-to-end) and [(tpy)Ru(3)Os(3)Ru(tpy)]6+ (periphery-to-centre). With respect to the homometallic case, for [(tpy)Ru(3)Os(3)Ru(tpy)]6+ excitation trapping at the central position is accompanied by a fivefold enhancement of luminescence intensity.