A Six-Vertex Theorem for Bounding Normal Planar Curves

We prove that the number of vertices of a smooth normal planarcurve is at least 6, if it bounds a surface other than the disk.     

Radiotracer studies of the antitumor metallocene molybdocene dichloride with biomolecules

Neutron irradiation of Cp₂MoCl₂ for 24 h afforded the radiotracer Cp₂⁹⁹MoCl₂ which was characterised by UV–Vis spectroscopy and thin layer chromatography. Binding experiments with the thiol containing protein human serum albumin (HSA) or calf thymus DNA, were monitored for ⁹⁹Mo using a gamma counter. Under the conditions investigated, molar ratios of binding of 0.2:1 (Cp₂MoCl₂:DNA) and 9.4:1 (Cp₂MoCl₂:HSA) were calculated. The results are consistent with in vitro coordination studies that have shown strong preferential interaction of Cp₂MoCl₂ with thiols versus other donor sites in biomolecules including DNA.     

Mayberry-Murasugi's formula for links in homology 3-spheres

We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

Anomalous capacitance of quantum well double-barrier diodes

The S-parameters of several different quantum well double barrier diodes have been measured. A technique has been developed for measuring whisker contacted diodes with and HP 8510B automatic network analyzer. Special coaxial mounts using K-connectors were designed to enable measurements up to 20 GHz. The voltage-dependent conductance and capacitance were derived from the measured reflection coefficient of each device. The C/V characteristics were observed to exhibit an anomalous increase at voltages corresponding the the negative differential resistance region (NDR). These are the first reported S-parameter measurements in the negative differential resistance region of quantum well double barrier diodes. A theory is presented that explains, in part, the observed results.     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

Teachers in transition: Moving towards CAS-supported classrooms

In the near future many teachers may be required to incorporate CAS into their teaching practices. Based on classroom observations and interviews over two years, this paper reports how two teachers made the transition from using graphics calculators to CAS calculators while teaching differential calculus to upper secondary school students. Both teachers taught with CAS in ways that were consistent with their beliefs about learning and teaching. Over two years, the teachers' teaching approaches and purpose for use of technology were stable and seemed to be underpinned by their beliefs about learning. In contrast, both teachers made changes to the content they taught (and thus what they used technology for) in response to new institutional knowledge. Content choice seemed to be underpinned by the teachers' purpose for teaching. Other influences impacted on what the teachers taught and how they taught it: the teachers' content knowledge, their pedagogical content knowledge, and the lack of legitimacy of CAS as a tool for learning and during examinations in the trial school and wider educational community. The extent of differences noted between the responses of just two teachers indicates that there will be many responses to using CAS in classrooms, as teachers aim to achieve different learning goals and interpret their responsibilities to students in different ways.     

Rheological and diffusion properties of a dextran-con A polymer in the presence of Insulin and Magnesium

Previous work carried out in our laboratories has focused on the formation and investigation of a dextran and concanavalin A (con A) based gel, which has the ability to alter its conformational structure in the presence and absence of free and terminal glucoses such that a gel–sol phase transition occurs. Here we report the diffusion and rheological investigations in to the effects of the addition of insulin and varyingconcentrations of magnesium chloride hexahydrate (Mg₂Cl₂6H₂O) at 20 and 37 °C. Rheological examination of glucose-sensitive (dextran-con A) gels were conducted using a cone and plate viscometer used in continual rotation and oscillatory modes. The results are interpreted in terms of the structure of the gel network and suggest rheological assessment provides an effective method of assessing the properties of gel systems. The subsequent testing of such formulations in in-vitro diffusion experiments revealed a reduction in the rate of diffusivity in the insulin marker, poly R-478 dye. The performance of this self-regulating drug delivery system has been examined and the addition of insulin and magnesium chloride may alter the way in which the gel operates as a drug delivery device and in the delivery of insulin. This may have implications for other ligands.