Looking Back in Mathematical Modeling: Classroom Observations and Instructional Strategies

Theorists often characterize modeling as a cyclic problem-solving process. One builds the model, assesses its validity with regard to the underlying problem situation, and revises accordingly. The process halts when, in the opinion of the modeler, the model generates a valid solution to the underlying problem. Recent research suggests that students, like experts, employ cyclic modeling processes. Extensive observations of university and high school students’ modeling efforts, however, suggest the use of linear rather than cyclic modeling strategies. That is, novice modelers often fail to look back or revise their initial models. This paper offers empirical evidence on behalf of the linear modeling theory and identifies five factors that promote the use of linear modeling strategies: students’ conceptions of models and the modeling process, the perceived objectives of the modeling activity, constraints on time and resources, statistical misconceptions, and an overall lack of interest. The paper concludes with several promising instructional strategies (strategies that address students’ difficulties and promote reflective modeling behavior), as well as suggestions for future research.     

Study of the reactione + e −→K + K − in the energy range1350 \leqq \sqrt s \leqq 2400 MeV

Thee ⁺ e ^?→K ⁺ K ^? cross section has been measured from about 750 events in the energy interval \(1350 \leqq \sqrt s \leqq 2400 MeV\) with the DM2 detector at DCI. TheK ^± form factor |F _F ^±| cannot be explained by the ρ, ω, ? and ρ′(1600). An additional resonant amplitude at 1650 MeV has to be added as suggested by a previous experiment.     

Comparison between biokinetics of inhaled plutonium nitrate and gadolinium oxide in humans and animals

Due to the paucity of human data after inhalation of different chemical forms of radionuclides, the implications for human exposure are often based on animal studies. This paper describes biokinetic studies of plutonium nitrate and gadolinium oxide in human volunteers and rats. The results, together with information from other studies with radionuclides, suggests that animal studies can be used with advantage for assessing the biokinetic behavior in humans, and for providing guidance on the assessment of intake and optimal monitoring regimens.     

Preparation of polymer colloids by chemical reactions in aerosols. I. Poly(p-tertiarybutylstyrene)

A procedure was developed by which polymer colloids can be prepared by polymerizing aerosol droplets of monomers with an initiator in the vapor state. This work describes the formation of poly(p-tertiarybutylstyrene) particles by exposing the corresponding monomer droplets to trifluoromethanesulfonic acid. It was found that the monomer-to-initiator mass ratio is the critical factor in determining the uniformity and morphology of the particles. Under ideal conditions spheres of narrow size distribution are obtained. Otherwise porous particles or soft particles with whiskers may develop. The aerosol was prepared in a falling film generator, but other procedures for producing monomer droplets may be used.     

The structure and crystallization of thin water films on Pt(111)

When water is adsorbed on Pt(111) above 135 K several different ice structures crystallize, depending on the thickness of the ice layer. At low coverage water forms extended islands of ice with a (square root(37) x square root(37))R25(o) unit cell, which compresses as the monolayer saturates to form a (square root(39) x square root(39))R16(o) structure. The square root(39) low-energy electron diffraction (LEED) pattern becomes more intense as the second layer grows, remaining bright for films up of 10-15 layers and then fading and disappearing for films more than ca. 40 layers thick. The ice multilayer consists of an ordered square root(39) wetting layer, on which ice grows as a crystalline film which progressively loses its registry to the wetting layer. Ice films more than ca. 50 layers thick develop a hexagonal LEED pattern, the entire film and wetting layer reorienting to form an incommensurate bulk ice. These changes are reflected in the vibrational spectra which show changes in line shape and intensity associated with the different ice structures. Thin amorphous solid water films crystallize to form the same phases observed during growth, implying that these structures are thermodynamically stable and not kinetic phases formed during growth. The change from a square root(39) registry to incommensurate bulk ice at ca. 50 layers is associated with a change in crystallization kinetics from nucleation at the Pt(111) interface in thin films to nucleation of incommensurate bulk ice in amorphous solid water films more than 50 layers thick.     

The scope of catalytic enantioselective tandem carbonyl ylide formation-intramolecular [3 + 2] cycloadditions

Catalytic enantioselective tandem carbonyl ylide formation-intramolecular 1,3-dipolar cycloaddition reactions of 2-diazo-3,6-diketoesters show promising scope in terms of asymmetric induction as the tethered alkene/alkyne dipolarophile component is varied. Cycloadditions were found to occur in moderate to very good yields, with a difference in ee exhibited by the electronically different 2-diazo-3,6-diketoesters 1, 25 and 33, 34. Values for ee of up to 90% for alkene dipolarophiles and up to 86% for alkyne dipolarophiles were obtained.     

Deprotonation-electrophile trapping of terminal epoxides

Organolithium-induced deprotonation of terminal epoxides in the presence of appropriate diamine ligands allows trapping with a range of electrophiles, yielding functionalised di- and tri-substituted epoxides in good yields and with control of stereochemistry at the epoxide.     

Electrospray liquid chromatography/mass spectrometry fingerprinting of Acanthophis (death adder) venoms: taxonomic and toxinological implications

Death adders (genus Acanthophis) are unique among elapid snakes in both morphology and venom composition. Despite this genus being among the most divergent of all elapids, the venom has been historically regarded as relatively quite simple. In this study, liquid chromatography/mass spectrometry (LC/MS) analysis has revealed a much greater diversity in venom composition, including the presence of molecules of novel molecular weights that may represent a new class of venom component. Furthermore, significant variation exists between species and populations, which allow for the LC/MS fingerprinting of each species. Mass profiling of Acanthophis venoms clearly demonstrates the effectiveness of this technique which underpins fundamental studies ranging from chemotaxonomy to drug design.