The routes of unity

A model for car following on a closed loop is defined. The stability of the solutions of the model is investigated by considering the evolution of the roots of the corresponding characteristic equation in the complex plane. The solution provides a motivation for investigating the behaviour of the roots of a simple class of algebraic equation.     

Implementing inquiry-oriented curriculum: From the mathematicians’ perspective

As part of an effort to scale up an instructional innovation in abstract algebra, several mathematicians have implemented an inquiry-oriented, group theory curriculum. Three of those mathematicians (co-authors here) also participated in iterative rounds of interviews designed to document and investigate their experiences as they worked to implement this curriculum. Analyses of these interviews uncovered three themes that were important to these mathematicians: coverage, goals for student learning, and the role of the teacher. Here, by drawing on interview data, classroom data, and first person commentaries, we will present and discuss each teacher's perspective on these three themes.     

Using tritium and 222Rn to estimate groundwater discharge and thawing permafrost contributing to surface water in permafrost regions on Qinghai-Tibet Plateau

Journal of Radioanalytical and Nuclear Chemistry - On the Qinghai-Tibet Plateau, permafrost degradation and associated release of permafrost meltwater has undoubtedly modified the annual and...     

Mimicking the Ice Recrystallization Activity of Biological Antifreezes. When is a New Polymer “Active”?

Antifreeze proteins and ice‐binding proteins have been discovered in a diverse range of extremophiles and have the ability to modulate the growth and formation of ice crystals. Considering the importance of cryoscience across transport, biomedicine, and climate science, there is significant interest in developing synthetic macromolecular mimics of antifreeze proteins, in particular to reproduce their property of ice recrystallization inhibition (IRI). This activity is a continuum rather than an “on/off” property and there may be multiple molecular mechanisms which give rise to differences in this observable property; the limiting concentrations for ice growth vary by more than a thousand between an antifreeze glycoprotein and poly(vinyl alcohol), for example. The aim of this article is to provide a concise comparison of a range of natural and synthetic materials that are known to have IRI, thus providing a guide to see if a new synthetic mimic is active or not, including emerging materials which are comparatively weak compared to antifreeze proteins, but may have technological importance. The link between activity and the mechanisms involving either ice binding or amphiphilicity is discussed and known materials assigned into classes based on this.     

High Emittance Electron Beam Source Coupled to Slab Loaded Accelerating Structure

High power line source emitter assembly was coupled to a twin symmetric H-plane slab loaded accelerating structure for beam acceleration. Closed form field analysis of the accelerating structure that includes guideline information regarding modal hierarchy, mode nomenclature, propagation plane, cut-off plane and dispersion relations is presented. Furthermore it was confirmed that by using symmetrically loaded dielectric accelerating structures with one rotated through 90° results in exerting a uniform acceleration impact on a travelling beam passing through the structure.     

An unusual reaction of a Reissert compound involving alkylation,rearrangement, SNAr and SET processes

Reaction of isoquinoline Reissert compound 1 with NaH and then isopropyl iodide in DMF at 22?°C led to four isolated products. Ketone 3 is the expected product of the well-known rearrangement of the intermediate Reissert anion. Cyano lactam 4 results from S_NAr intramolecular displacement of the fluoride ion from the activated aroyl moiety of the anion. Isopropyl lactam 5 is proposed to result from a SET (single electron transfer) process via formation of the radical anion of 4, subsequent loss of the cyanide ion, and coupling of the resultant radical with isopropyl radicals formed via copper used to “stabilize” the alkyl iodide. The expected alkylated product 2 is also formed via a SET process involving electron transfer from the Reissert anion to 4, leading to the Reissert radical. Use of “non-stabilized” bromide or iodide led to 3 and 4, but did not produce 2 or 5.     

On the Upper Limits of Oxidation States in Chemistry

The concept of oxidation state ( OS ) is based on the concept of Lewis electron pairs, in which the bonding electrons are assigned to the more electronegative element. This approach is useful for keeping track of the electrons, predicting chemical trends, and guiding syntheses. Experimental and quantum‐chemical results reveal a limit near +8 for the highest OS in stable neutral chemical substances under ambient conditions. OS =+9 was observed for the isolated [IrO₄]⁺ cation in vacuum. The prediction of OS =+10 for isolated [PtO₄]²⁺ cations is confirmed computationally for low temperatures only, but hasn't yet been experimentally verified. For high OS species, oxidation of the ligands, for example, of O^?2 with formation of ^.O^?1 and O?O bonds, and partial reduction of the metal center may be favorable, possibly leading to non‐Lewis type structures.     

The micro-estimation of cobalt with triphenyl-methylarsonium thiocyanate

Triphenylmethylarsonium thiocyanate is recommended for the colorimetric micro-estimation of cobalt. The procedure is suitable within a range of 10 to 100 mg of cobalt per ml with an accuracy of about 2%. It enables the micro-estimation of cobalt to be carried out on most of its common alloys, no prior separation being required in most cases, and in the others, simple partial separations being sufficient.     

Gas-phase oxidation of Cm+ and Cm2+ --thermodynamics of neutral and ionized CmO

Fourier transform ion cyclotron resonance mass spectrometry was employed to study the products and kinetics of gas-phase reactions of Cm (+) and Cm (2+); parallel studies were carried out with La (+/2+), Gd (+/2+) and Lu (+/2+). Reactions with oxygen-donor molecules provided estimates for the bond dissociation energies, D[M (+)-O] (M = Cm, Gd, Lu). The first ionization energy, IE[CmO], was obtained from the reactivity of CmO (+) with dienes, and the second ionization energies, IE[MO (+)] (M = Cm, La, Gd, Lu), from the rates of electron-transfer reactions from neutrals to the MO (2+) ions. The following thermodynamic quantities for curium oxide molecules were obtained: IE[CmO] = 6.4 +/- 0.2 eV; IE[CmO (+)] = 15.8 +/- 0.4 eV; D[Cm-O] = 710 +/- 45 kJ mol (-1); D[Cm (+)-O] = 670 +/- 40 kJ mol (-1); and D[Cm (2+)-O] = 342 +/- 55 kJ mol (-1). Estimates for the M (2+)-O bond energies for M = Cm, La, Gd, and Lu are all intermediate between D[N 2-O] and D[OC-O] - that is, 167 kJ mol (-1) < D[M (2+)-O] < 532 kJ mol (-1) - such that the four MO (2+) ions fulfill the thermodynamic requirement for catalytic oxygen-atom transport from N2O to CO. It was demonstrated that the kinetics are also favorable and that the CmO (2+), LaO (2+), GdO (2+), and LuO (2+) dipositive ions each catalyze the gas-phase oxidation of CO to CO2 by N2O. The CmO 2 (+) ion appeared during the reaction of Cm (+) with O 2 when the intermediate, CmO (+), was not collisionally cooled - although its formation is kinetically and/or thermodynamically unfavorable, CmO 2 (+) is a stable species.