Integrating history and philosophy in mathematics education at university level through problem-oriented project work

Through the last three decades several hundred problem-oriented student-directed projects concerning meta-aspects of mathematics and science have been performed in the 2-year interdisciplinary introductory science programme at Roskilde University. Three selected reports from this cohort of project reports are used to investigate and present empirical evidence for learning potentials of integrating history and philosophy in mathematics education. The three projects are: (1) a history project about the use of mathematics in biology that exhibits different epistemic cultures in mathematics and biology. (2) An educational project about the difficulties of learning mathematics that connects to the philosophy of mathematics. (3) A history of mathematics project that connects to the sociology of multiple discoveries. It is analyzed and discussed in what sense students gain first hand experiences with and learn about meta-aspects of mathematics and their mathematical foundation through the problem-oriented student-directed project work.     

Further investigation of mass dimension one fermionic duals

In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic structure and the so called τ-deformation. The former regards the mathematical equivalence of the recent proposed Lorentz preserving dual with the duals of algebraic spinors, from Clifford algebras, showing the consistency and generality of the new dual. Moreover, by revealing its automorphism structure, the hole of the τ-deformation and contrasting the action group orbits with other Lorentz breaking scenarios, we argue that the new mass dimension one dual theory is placed over solid and consistent basis.     

Echo spectroscopy of atomic dynamics in a Gaussian trap via phase imprints

We present a simultaneous analysis of the X¹ Σ ⁺ and the a³ Σ ⁺ electronic ground states of the NaK molecule. Excitation of the [B ¹ Π, c³ Σ ⁺]-system made it possible to record fluorescence to rovibrational levels of both ground states simultaneously with a Fourier-transform spectrometer. For the first time high lying levels in the triplet state with v = 17 and v = 18 were seen, the highest possible v = 19 for ²³Na-³⁹K was not observed. The joint evaluation of the retrieved data leads to accurate potential energy curves, that describe the experimental data within their experimental uncertainty of 0.005 cm⁻¹. Cold collision properties like scattering length and Feshbach resonance positions are calculated with these potentials and compared to other predictions.     

Photocaged pendent thiol polymer brush surfaces for postpolymerization modifications via thiol‐click chemistry

In this work, a postpolymerization surface modification approach is reported that provides pendent thiol functionality along the polymer brush backbone using the photolabile protection chemistry of both o‐nitrobenzyl and p‐methoxyphenacyl thioethers. Poly(2‐hydroxyethyl methacrylate) (pHEMA) brushes were synthesized via surface‐initiated atom transfer radical polymerization, after which the pHEMA hydroxyl groups were esterified with 3‐(2‐nitrobenzylthio)propanoic acid or 3‐(2‐(4‐methoxyphenyl)‐2‐oxoethylthio)propanoic acid to provide the photolabile protected pendent thiols. Addressing the protecting groups with light not only affords spatial control of reactive thiol functionality but enables a plethora of thiol‐mediated transformations with isocyanates and maleimides providing a modular route to create functional polymer surfaces. This concept was extended to block copolymer brush architectures enabling the modification of the chemical functionality of both the inner and outer blocks of the block copolymer surface. © 2012 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2013     

ACOUSTIC DETECTION OF TRIPLET STATES FORMED BY RADICAL PAIR RECOMBINATION IN QUINONE-DEPLETED PHOTOSYNTHETIC REACTION CENTERS, BY MAGNETIC FIELD MODULATION (MAGNETOPHOTOACOUSTIC EFFECT)-A FEASIBILITY STUDY

Abstract –An acoustic method is outlined to detect triplet states formed by radical pair recombination in photosyn-thetic reaction centers. It is based on magnetic field effect on the probability of triplet state formation by recombination. Using a periodically modulated magnetic field in the presence of constant exciting light, a periodic modulation of the triplet state concentration is set in the sample, which is detected through the corresponding modulated heat emission, transduced to acoustic vibration of the gas phase around the sample. This effect is similar to the photoacoustic effect, except that here the light is not modulated. The feasibility of detecting such an effect was proven experimentally, by obtaining a signal from quinone-depleted reaction centers of Rhodobacter sphaeroides. The signal had twice the frequency of the magnetic field modulation; it was proportional to the light intensity and significantly stronger at the lower temperatures (in the investigated range 113–278 K). No signal was obtained from quinone-containing reaction centers, which do not produce triplets. A theoretical outline of the effect and the experimental set-up are described. The "magnitude of the effect was calibrated against ordinary photoacoustic measurements, allowing numerical evaluation of certain parameters of the triplet state ( e.g. triplet energy or yield) with the aid of auxiliary information from the literature.     

A chemical study of thermally activated chromic titanate on silica ethylene polymerization catalysts

Thermally activated ethylene polymerization catalysts which contain chromium and titanium on silica differ from those catalysts which contain only chromium on silica. The characteristics of chromium-titanium catalysts vary with the method of incorporating the titanium and the thermal activation procedure. Titanated catalysts of the kind examined in this article have faster initiation and a higher polymerization rate per unit catalyst weight than corresponding catalysts without titanium. High-density polyethylene produced by this type of titanium-chromium catalyst tends to have a higher melt index and a broader molecular weight distribution than polyethylene made with chromium on silica catalysts. Iodometric titration showed that reduction from the initial hexavalent chromium to trivalent occurs when the dry, catalyst starting material is treated with titanium tetraisopropoxide. A study of the reaction between chromium trioxide and titanium tetraisopropoxide in carbon tetrachloride revealed that (1) it is not necessary to have a reaction between surface silanols and titanium tetraisopropoxide for the reduction to occur, and (2) the reaction product has an absorption near 660 nm in the visible range. Comparison of spectra showed that chromium trioxide on silica reduced by isopropyl alcohol has a shifted absorption, i.e., 600 nm. These findings are interpreted to mean that titanium atoms come sufficiently close to chromium atoms to change their electron density in the starting material and remain close neighbors in the activated catalysts. The interpretation is further supported by ESCA data and leads to the proposal that in this case the activated catalysts contain titanium chromate structures.