How Focusing Phenomena in the Instructional Environment Support Individual Students' Generalizations

This article sets forth a way of connecting the classroom instructional environment with individual students' generalizations. To do so, we advance the notion of focusing phenomena, that is, regularities in the ways in which teachers, students, artifacts, and curricular materials act together to direct attention toward certain mathematical properties over others. The construct of focusing phenomena emerged from an empirical study conducted during a 5-week unit on slope and linear functions in a high school classroom using a reform curriculum. Qualitative evidence from interviews with 7 students revealed that students interpreted the m value in y = b + mx as a difference rather than a ratio as a result of counterproductive generalization afforded by focusing phenomena. Classroom analysis revealed 4 focusing phenomena, which regularly directed students' attention to various sets of differences rather than to the coordination of quantities.     

Building mass spectrometers and a philosophy of research

Development of the techniques of ion kinetic energy spectrometry and mass-analyzed ion kinetic energy spectrometry is described. The extension of these concepts to the method of tandem mass spectrometry for direct mixture analysis is traced, and a rationale for the construction of hybrid mass spectrometers is presented. Collisions of polyatomic ions with surfaces are discussed as an outgrowth of gaseous collisions. An attempt is made to describe a philosophy of research that guided the construction of a dozen mass spectrometers and the exploration of organic ion chemistry in as many contexts.     

ABNORMAL EMBRYONIC DEVELOPMENT OF THE AMERICAN SEA URCHIN FOLLOWING ILLUMINATION OF GAMETES WITH VISIBLE LIGHT FROM A PHOTOTHERAPY UNIT

Abstract— The unfertilized oocytes and spermatozoa of the American sea urchin ( Arbacia punctulata ) were exposed to phototherapy lights in order to determine the effect of this treatment regimen on post-irradiation fertilization and embryonic development. Light treatment revealed dose-dependent abnormalities in fertilization and subsequent embryonic development.     

Linked porphyrin systems

Porphyrin monomers, 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin ( 1 ), 5,10-(dipyridyl)-15,20-(diphenyl)-porphyrin ( 2 ), and 5,15-(dipyridyl)-10,20-{diphenyl)porphyrin ( 3 ), were linked by hydrocarbon chains to form a series of dimers, trimers and polymers. The 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin monomers were linked by 2, 4, 6, 8 and 10 carbon chains through the alkylation of the pyridine nitrogens using the appropriate diiodoalkane to form positively charged linked dimers 4–8 . A trimer 12 was synthesized from two 5-(monopyridyl)-10,15,20-(triphenyl)porphyrin and one 5,10-(dipyridyl)-15,20-(diphenyl)porphyrin linked by a six carbon chain. Hydrocarbon linked (5,10-(dipyridyl)-15,20-(diphenyl)porphyrin)_n ( 13 ) and (5,15-(dipyridyl)-10,20-(diphenyl)porphyrin)_n ( 14 ) were also prepared.     

Intermolecular interactions in pi-stacked conjugated molecules. Synthesis,structure, and spectral characterization of alkyl bithiazole oligomers

Syntheses are reported of new 4,4'-dialkyl-2,2'-bithiazole oligomers that have alkenoxy side chains that are capable of easy conversion to oligomers with functionalized side chains, e.g., terminally substituted hydroxy chains. The crystal structures of two representative oligomers (4,4',4' ',4' "-tetra-(2-propenoxymethyl)-2,2',5',5' ',2' ',2' "-quaterthiazole (3P2) and 4,4',4' ',4' "-tetra-(3-hydroxypropyloxymethyl)-2,2',5',5' ',2' ',2' "-quaterthiazole (3H2)) were determined; 3P2 crystallizes in a pi-stacked motif with two molecules per unit cell, whereas 3H2 forms pi-stacks that are linked with hydrogen bonds to form infinite two-dimensional sheets with one molecule per unit cell. A comparison of the UV-vis spectra of the compounds in solution and in the solid state provides unequivocal evidence for the presence of a Davydov splitting, W(D) approximately 0.2 eV, in solid 3P2. The spectra are interpreted in the framework of molecular exciton theory to extract a value of the intermolecular transfer integral, J approximately 0.2 eV, for a total exciton bandwidth of ca. 0.8 eV. Monte Carlo calculations were used to determine the density of states of the exciton band and the absorption and emission line shapes of the 0 <-- 0 transition. It is suggested that the "three-humped" absorption profile typical of partially crystalline, regioregular polymers is the "optical signature" of pi-stacking.     

Simple method for the quantitative examination of extra column band broadening in microchromatographic systems

In recent years capillary chromatography has gained popularity for trace analyses. Most often UV or electrochemical detection is employed because the small peak volumes make post-column derivatization challenging. We have developed a simple method based on flow injection for determining contributions to peak broadening from post-column reactors. The only requirement for application of our methodology is that diffusion be in the Taylor regime so that radial concentration gradients are relaxed enabling mixing purely by diffusion.     

Comparative pyrolysis upcycling of polystyrene waste: thermodynamics, kinetics, and product evolution profile

Pyrolysis is one important way to treat polystyrene waste and upcycle it into useful materials. A comparative pyrolysis study of virgin polystyrene (VPS) and two types of commonly used polystyrene products, expanded polystyrene (EPS) and polystyrene container (CPS) was carried out. Various values were found in the thermodynamic study and kinetic study of VPS, EPS, and CPS pyrolysis, suggesting distinct thermal degradation characteristics of these materials. The energy barrier order of the pyrolysis processes was EPS, CPS, VPS, showing activation energy of 230, 219, and 145 kJ mol^?1, respectively. The order of amount of heat absorbed was EPS, CPS, VPS, with enthalpy of 224, 213, and 139 kJ mol^?1, respectively. The reaction favorability order was EPS, CPS, and VPS with Gibbs free energy of 118, 132, and 210 kJ mol^?1, respectively. Thermogravimetric analysis indicated the use of high heating rate would increase the reaction rate and shorten the reaction time. Product evolution profiles showed that VPS and CPS pyrolysis produced mainly aromatics, while EPS pyrolysis produced aromatics at the initial phase of the reaction and aliphatic hydrocarbon at the latter phase. The diverse pyrolysis behaviors of VPS, EPS, and CPS demonstrated that an examination on different polystyrene materials was desired to optimize the pyrolysis conditions and product distribution, and thus benefit the process of valuable materials recovery.     

Synthesis of mesocyclic and macrocyclic polythioethers using the cesium dithiolate technique

The mesocyclic trithioethers, 1,4,7-trithiacyclodecane, 1,4,7-trithiacycloundecane, 1,4,8-trithiacycloundecane, and 1,5,9-trithiacyclododecane; the mesocyclic trithioether ketones, 1,4,7-trithiacyclodecan-9-one; 1,4,8-trithiacycloundecan-6-one, and 1,5,9-trithiacyclododecan-3-one; and the mesocyclic trithioether alcohols, 1,4,7-trithiacyclodecan-9-ol, 1,4,8-trithiacycloundecan-6-ol, and 1,5,9-trithiacyclododecan-3-ol, have been synthesized using the cesium dithiolate technique. In some cases, the corresponding macrocyclic hexathioether was isolated from the reaction mixture in addition to the mesocyclic trithioether; 1,4,7,11,14,17-hexathiacycloeicosane, 1,4,7,11,14,17-hexathiacycloeicosan-9,19-dione, 1,4,7,12,15,18-hexathiacyclodocosane, and 1,5,9,13,17,21-hexathiacyclotetracosane. Single-crystal X-ray structures have been determined for 1,5,9-trithiacyclododecan-3-ol and 1,4,7,12,15,18-hexathiacyclodocosane. For 1,5,9-trithiacyclododecane-3-ol, the compound crystallizes in the monoclinic space group, C2/c, with a = 10.5926( 9 ) Å, b = 15.582(2) Å, c = 13.6015(8) Å, β = 98.186(6)⁰, Z = 8, and R = 0.038. The macrocycle, 1,4,7,12,15,18-hexathiacyclodocosane, crystallizes in the orthorhombic space group, Pbca, with a = 21.406(5) Å, b = 9.810(2) Å, c = 10.225(2) Å, Z = 4, and R = 0.020.     

Nanoimprinted substrates for high-yield production of topological insulator nanoribbons

We present a growth process mediated by nanoimprinted nanostructures specifically for producing bismuth selenide (Bi₂Se₃) topological insulator nanoribbons with a high yield. In this process, topological insulator nanostructures are grown on nanoimprinted gratings by using a nanoparticle-catalyzed vapor–liquid–solid mechanism. In comparison with the growth processes performed on flat and randomly rough substrates, such a nanograting-mediated growth method produces topological insulator nanoribbons with a higher yield (～15?000 nanoribbons/mm²), a narrower average ribbon width (w _avg<60 nm), and a higher uniformity in ribbon width (σ<30 nm); effectively suppresses the formation of other unwanted morphologies; and also results in the axial growth of nanoribbons along specific in-plane directions relative to pre-structured gratings. Such technical merits of nanograting-mediated growth are attributed to the preferential nucleation of Bi₂Se₃ crystal seeds and the concomitant pinning of catalytic nanoparticles at ordered grating edges. Finally, Aharonov–Bohm interference oscillations in the magnetoresistance were observed and demonstrated the coherent transport of electrons through topological surface states of Bi₂Se₃ nanoribbons. This growth process in combination with large-area nanoimprint lithography could serve as an important foundation for nanomanufacturing topological insulator nanoribbons with controllable feature size, large-area uniformity, and ordering, suitable for applications in future low-dissipation nanoelectronics.