Lost in Translation: Examining Translation Errors Associated With Mathematical Representations

Translation errors and conceptual misunderstandings made by students translating among graphical, tabular, and symbolic representations of linear functions were examined. The study situated student errors in the context of the “Translation‐Verification Model” developed specifically for the purpose of explaining student behavior during the process of translating relationships from one mathematical representation to another. Three distinct error types were identified to explain student performance. An examination of the error types revealed that specific translation errors tend to occur at different stages of the translation process. Translation errors are also related to “attribute density,” the amount of information inherently encoded in a given representation. The findings of the study have implications for teaching linear relationships—student weaknesses and strengths are identified.     

Molecular simulation of liquid water confined inside graphite channels: thermodynamics and structural properties

We carried out molecular dynamics simulations to describe the properties of water inside a narrow graphite channel. Two stable phases were found: a low-density one made of water clusters adsorbed on the graphite sheets and a liquid one that fills the entire channel, forming several layers around a bulk-like region. We analyzed the interfacial structure, orientational order, water residence times in several regions, and hydrogen bonding of this last water phase, calculating also a quantity of electrochemical interest, the probability of electron tunneling through interfacial water. The results are in good qualitative agreement with the available experimental data.     

EPR Study of 5-Chlorosalicylate-Cu(II)-3-Pyridylmethanol Ternary Complex Systems in Frozen Water–Methanol Solutions

Two copper(II) ternary complex systems containing 5-chlorosalicylic acid (5-ClsalH) and different copper(II) salts with varying 3-pyridylmethanol (ron = ronicol) concentration, system I [CuSO₄ (aq) +2(5-ClsalH(solv)) + xron(l)] and system II [Cu(ac)₂(aq) + 2(5-ClsalH(solv)) + xron(l)], where x = 0, 2, 4, 6 and 8, were prepared and studied by electron paramagnetic resonance (EPR) spectroscopy in frozen water–methanol solutions to observe the effects of different copper(II) salts and varying neutral ligand concentration on the formation of resulting complexes in solution. The trend in g-values (g _|| > g _⊥ > 2.0023) indicates that the unpaired electron on the copper ion is localized in the d_{x² - y²} d_{{x}^{\rm{2}} - {y}^{\rm{2}}} orbital. The detailed analysis of the second-derivative Cu(II) EPR spectra has shown well-resolved ¹⁴N superhyperfine splitting in the perpendicular part of the axially symmetric spectra. The resolution of nitrogen superhyperfine multiplet patterns increased with increase in the ronicol concentration (ligand-to-metal ratio x). The number of superhyperfine lines was found to be constant (nonet) when x > 4 for system I and x ≥ 4 for system II. This fact indicates that for these x-values four equivalent nitrogen atoms could be coordinated to the central copper atom in the equatorial plane of both systems.     

Gafchromic® EBT films for ion dosimetry

For dose delivery to patients, scanning ion beams are going to be increasingly used in the upcoming ion beam therapy facilities. Especially carbon ion beams are able to produce steep dose gradients. However, the currently used method for patient dose verification, employing ionization chamber arrays, provides a spatial resolution of 1 cm only. As continuous media, EBT films, widely used in photon therapy, are interesting candidates to be used for this purpose. The EBT film is the ancestor of the currently available EBT2 film. In our contribution two dimensional dosimetry and film response quenching in ion beams were investigated. For a real ¹²C patient plan a good qualitative agreement with the planned dose distribution including a high signal-to-noise ratio and a good resolution in the measured photon-equivalent dose was found. The depth-dose response of EBT films for a ¹²C ion beam shows response quenching, which rises towards the Bragg peak. It was quantified by the relative efficiency determined at different depths. Furthermore, the relative efficiency was measured in monoenergetic proton and carbon ion beams. All the measured efficiencies show no significant dependency on the dose up to the highest measured doses of 6 Gy. However, differences between proton and carbon ions as well as between carbon ion beams of different energies were observed. The measurements reveal, that the use of EBT films for absolute dose verification measurements requires to take the relative efficiency into account, dependent on the ion type and energy.     

Heat capacity functions of polystyrene in glassy and in liquid amorphous state and glass transition

The heat capacity or the specific heat is for any crystalline, partially amorphous or completely amorphous substance or material a significant thermodynamic property. The glass transition may be regarded as the melting point of amorphous substances and materials, a transition property of an outstanding technical importance. A crucial point is the fact that the presence of a glass transition is an unequivocal proof of an amorphous content of a material. Furthermore, the change of the specific heat at the glass transition temperature enables the quantitative determination of the amorphicity on a relative or absolute level of any substance or material. The absolute determination of the amorphicity affords a calibration with a reference corresponding to the material under investigation. The crystallinity for this reference substance must be known from the preparation and or by any independent analytical method. The literature data for the specific heat and the glass transition of polystyrene were collected and evaluated. Data were found for the specific heat in literature from 10 to 470 K. The data were unified for each of the reported temperature in a mean value and the corresponding standard deviation was determined. An excellent conformity was found in the glassy state of polystyrene with standard deviations lower than 0.7%. The standard deviations above the glass transition were considerably higher.     

Kinetics of the thermal polishing of the rough glass surface

A simple mathematical model of thermal polishing of rough glass surface as observed by light beam thermal analysis (LBTA) is presented. The rough surface is represented by a triangular profile used for calculation of the light beam intensity attenuation and an equivalent rectangular profile is used for the modeling of the time course of the thermal polishing. Computational results obtained for the NBS 711 viscosity standard glass showed that the characteristic temperature, obtained from the series of LBTA experiments after extrapolation to zero starting surface roughness, does not represent the glass transition temperature, but it corresponds to the viscosity value of about 10⁹ dPa.s. The validity of the proposed model was confirmed by the comparison of simultaneous LBTA and viscosity measurements of CaO-Y₂O₃-Al₂O₃-SiO₂ glasses. This revised version was published online in August 2006 with corrections to the Cover Date.     

Photochemical reactions. 72. Photofragmentation of 14-beta-hydroxy-20-oxo-delta(16)-steroids

On UV. irradiation in i-octane or t-butyl alcohol the α,β-unsaturated δ-hydroxy ketone 2 undergoes fragmentation to the novel 14,15-seco-steroid 3 .     

Selective Adsorption of Functionalized Nanoparticles to Patterned Polymer Brush Surfaces and Its Probing with an Optical Trap

The site‐specific attachment of nanoparticles is of interest for biomaterials or biosensor applications. Polymer brushes can be used to regulate this adsorption, so the conditions for selective adsorption of phosphonate‐functionalized nanoparticles onto micropatterned polymer brushes with different functional groups are optimized. By choosing the strong polyelectrolytes poly(3‐sulfopropyl methacrylate), poly(sulfobetaine methacrylate), and poly[2‐(methacryloyloxy)ethyl trimethylammonium chloride], it is possible to direct the adsorption of nanoparticles to specific regions of the patterned substrates. A pH‐dependent adsorption can be achieved by using the polycarboxylate brush poly(methacrylic acid) (PMAA) as substrate coating. On PMAA brushes, the nanoparticles switch from attachment to the brush regions to attachment to the grooves of a patterned substrate on changing the pH from 3 to 7. In this manner, patterned substrates are realized that assemble nanoparticles in pattern grooves, in polymer brush areas, or substrates that resist the deposition of the nanoparticles. The nanoparticle deposition can be directed in a pH‐dependent manner on a weak polyelectrolyte, or is solely charge‐dependent on strong polyelectrolytes. These results are correlated with surface potential measurements and show that an optical trap is a versatile method to directly probe interactions between nanoparticles and polymer brushes. A model for these interactions is proposed based on the optical trap measurements.     

Temperature dependent nano indentation of thin polymer films with the scanning force microscope

The scanning force microscope (SFM) was used to investigate the temperature dependent micro mechanical properties of polymethylmethacrylate (PMMA) films with a thickness of 35 nm in the range of the radius of gyration. Force-distance curves were performed in the glass transition range to create permanent nanometric indentations with maximal forces up to 4 μN. Quantitative measurements of the indentation depth during and after application of the force, hysteresis energy and slope of the loading part are carried out as function of sample temperature and applied force. The glass transition of the polymer film can be clearly identified by the change of the mechanical properties of the polymer. Surprisingly, only a small change of elasticity at the glass transition is observed.