Gestures, Speech, and the Sprouting of Signs: A Semiotic-Cultural Approach to Students' Types of Generalization

To improve our understanding of novice students' production of symbolic algebraic expressions, this article contrasts students' presymbolic and symbolic procedures in generalizing activities. Although a significant amount of previous research on the learning of algebra has dealt with students' errors in the mastering of the algebraic syntax, the semiotic cultural theoretical approach presented here focuses on the role that body, discourse, and signs play when students' refer to mathematical objects. Three types of generalizations are identified: factual, contextual, and symbolic. The results suggest that the passage from presymbolic to symbolic generalizations requires a specific kind of rupture with the ostensive gestures and contextually based key linguistic terms underpinning presymbolic generalizations. This rupture means a disembodiment of the students' previous spatial temporal embodied mathematical experience.     

First Investigation of 115In in the High Spin Regime

The ¹¹⁵In nucleus was studied by means of γ-ray spectroscopic measurements. This nucleus was populated with the ¹⁰⁰Mo(¹⁸O, p2n)¹¹⁵In reaction and a charged-particle detector array was used to identify the proton evaporation channel. A level scheme with 17 new transitions is presented and compared with theoretical predictions based on the particle + core model.     

Far infrared laser frequencies of CH3OD and N2H4

The frequencies of 26 laser lines with wavelengths between 57 and 534 m have been measured in the optically pumped laser gases CH₃OD and N₂H₄. A pair of stabilized cw 12_{CO 2} lasers was used as a frequency standard for the heterodyne frequency measurements. Seven of the 26 lines are new.     

Stability and rheology of emulsions containing sodium caseinate: combined effects of ionic calcium and alcohol

We have investigated the combined effect of ionic calcium and ethanol on the visual creaming behavior and rheology of sodium caseinate-stabilized emulsions (4 wt% protein, 30 vol% oil, pH 6.8, mean droplet diameter 0.4 microm). A range of ionic calcium concentrations, expressed as a calcium/caseinate molar ratio R, was adjusted prior to homogenization and varying concentrations of ethanol were added shortly after homogenization. A stability map was produced on the basis of visual creaming behavior over a minimum period of 8 h for different calcium/caseinate/ethanol emulsion compositions. A single narrow stable (noncreaming) region was identified, indicating limited cooperation between calcium ions and ethanol. The shear-thinning behavior of the caseinate-stabilized emulsions is typical of systems undergoing depletion flocculation. Addition of calcium ions and/or ethanol was found to lead to a pronounced reduction in viscosity and the onset of Newtonian flow. The state of aggregation was correlated with emulsion microstructure from confocal laser scanning microscopy. Time-dependent rheology (18 h) with a density-matched oil phase (1-bromohexadecane) revealed that the visually stable emulsions were time-independent low-viscosity fluids. Surface coverage data showed that increasing amounts of caseinate were associated with the oil-water interface with increasing R and ethanol content. A decrease in free calcium ions in the aqueous phase with moderate increases in R and ethanol content was observed, which is consistent with greater calcium-caseinate binding (aggregation). Ostwald ripening occurred at the high-ethanol emulsion compositions that were stable to depletion flocculation. While the coarsening rate was low, this can account for the cream plug formation observed during gravity creaming experiments. The caseinate emulsion with no ionic calcium or ethanol exhibits depletion flocculation from excess nonadsorbed caseinate submicelles. Addition of calcium ions reduces the submicelle number density via specific calcium-binding in the aqueous phase (fewer, larger calcium-caseinate aggregates) and at the droplet surface (increased surface coverage). Nonspecific ethanol-induced (calcium-dependent) caseinate submicelle aggregation in the bulk phase and on the droplet surface (increased surface coverage) culminates in a reduction in the number density of caseinate submicelles. A narrow window of inhibition of depletion flocculation occurs in systems containing both calcium ions and ethanol, both species combining to aggregate the protein and so reduce the density of free submicelles.     

Force mode atomic force microscopy as a tool for protein folding studies

The advent of a new class of force microscopes designed specifically to “pull” biomolecules has allowed non-specialists to use force microscopy as a tool to study single-molecule protein unfolding. This powerful new technique has the potential to explore regions of the protein energy landscape that are not accessible in conventional bulk studies. It has the added advantage of allowing direct comparison with single-molecule simulation experiments. However, as with any new technique, there is currently no well described consensus for carrying out these experiments. Adoption of standard schemes of data selection and analysis will facilitate comparison of data from different laboratories and on different proteins. In this review, some guidelines and principles, which have been adopted by our laboratories, are suggested. The issues associated with collecting sufficient high quality data and the analysis of those data are discussed. In single-molecule studies, there is an added complication since an element of judgement has to be applied in selecting data to analyse; we propose criteria to make this process more objective. The principal sources of error are identified and standardised methods of selecting and analysing the data are proposed. The errors associated with the kinetic parameters obtained from such experiments are evaluated. The information that can be obtained from dynamic force experiments is compared, both quantitatively and qualitatively to that derived from conventional protein folding studies.     

Viscoelastic properties of single polysaccharide molecules determined by analysis of thermally driven oscillations of an atomic force microscope cantilever

We report on single molecule measurements of the viscoelastic properties of the polysaccharide dextran using a new approach which involves acquiring the power spectral density of the thermal noise of an atomic force microscope cantilever while holding the single molecule of interest under force-clamp conditions. The attractiveness of this approach when compared with techniques which use forced oscillations under constant loading rate conditions is that it is a near-equilibrium measure of mechanical response which provides a more relevant probe of thermally driven biomolecular dynamics. Using a simple harmonic oscillator model of the cantilever-molecule system and by subtracting the response of the free cantilever taking into account hydrodynamic effects, the effective damping zetamol and elastic constant kmol of a single molecule are obtained. The molecular elasticity measured by this new technique shows a dependence on applied force that reflects the chair-boat conformational transition of the pyranose rings of the dextran molecule which is in good agreement with values obtained directly from the gradient of a conventional constant loading rate force-extension curve. The molecular damping is also seen to follow a nontrivial dependence on loading which we suggest indicates that it is internal friction and not work done on the solvent that is the dominant dissipative process.     

Viscoelastic measurements of single molecules on a millisecond time scale by magnetically driven oscillation of an atomic force microscope cantilever

The dynamical nature of biomolecular systems means that knowledge of their viscoelastic behavior is important in fully understanding function. The linear viscoelastic response can be derived from an analysis of Brownian motion. However, this is a slow measurement and technically demanding for many molecular systems of interest. To address this issue, we have developed a simple method for measuring the full linear viscoelastic response of single molecules based on magnetically driven oscillations of an atomic force microscope cantilever. The cantilever oscillation frequency is periodically swept through the system resonance in less than 200 ms allowing the power spectrum to be obtained rapidly and analyzed with a suitable model. The technique has been evaluated using dextran, a polysaccharide commonly used as a test system for single molecule mechanical manipulation experiments. The monomer stiffness and friction constants were compared with those derived from other methods. Excellent agreement is obtained indicating that the new method accurately and, most importantly, rapidly provides the viscoelastic response of a single molecule between the tip and substrate. The method will be a useful tool for studying systems that change their structure and dynamic response on a time scale of 100-200 ms, such as protein folding and unfolding under applied force.     

Superdeformation in the N = Z nucleus 36Ar: experimental, deformed mean field, and spherical shell model descriptions

A superdeformed rotational band has been identified in 36Ar, linked to known low-spin states, and observed to its high-spin termination at Ipi = 16(+). Cranked Nilsson-Strutinsky and spherical shell model calculations assign the band to a configuration in which four pf-shell orbitals are occupied, leading to a low-spin deformation beta(2) approximately 0.45. Two major shells are active for both protons and neutrons, yet the valence space remains small enough to be confronted with the shell model. This band thus provides an ideal case to study the microscopic structure of collective rotational motion.