Virtual encounters: the murky and furtive world of mathematical inventiveness

Based on Châtelet’s insights into the nature of mathematical inventiveness, drawn from historical analyses, we propose a new way of framing creativity in the mathematics classroom. The approach we develop emphasizes the social and material nature of creative acts. Our analysis of creative acts in two case studies involving primary school classrooms also reveals the characteristic ways in which digital technologies can occasion such acts.     

Gold-catalyzed regiospecific intermolecular hydrothiolation of allenes

AuBr₃-catalyzed regiospecific intermolecular hydrothiolation of aromatic allenes and aromatic thiols afforded the corresponding dithioacetals in good yields at 0 °C in 5 min.     

On H‐immersions

For a fixed multigraph H, possibly containing loops, with V(H) = {h₁,…, h_k}, we say a graph G is H‐linked if for every choice of k vertices v₁,…,v_k in G, there exists a subdivision of H in G such that v_i represents h_i (for all i). An H‐immersion in G is similar except that the paths in G, playing the role of the edges of H, are only required to be edge disjoint. In this article, we extend the notion of an H‐linked graph by determining minimum degree conditions for a graph G to contain an H‐immersion with a bounded number of vertex repetitions on any choice of k vertices. In particular, we extend results found in [2,3,5]. © 2007 Wiley Periodicals, Inc. J Graph Theory 57: 245–254, 2008     

Sliding Mode Optimization in Dynamic LTI Systems

This paper deals with the problem of constrained optimization in dynamic linear time-invariant (LTI) systems characterized by a control vector dimension less than that of the system state vector. The problem consists in designing a control signal capable of generating a system state evolution confined to the feasible region delimited by a number of inequality constraints less than or equal to the number of control vector components, as well as of steering the state trajectory to an equilibrium point where a prespecified cost function depending on the system state is being minimized. The finite-time convergence to a vicinity of order of the optimal equilibrium point is proved.     

Determination of thorium isotopes in bastnaesite ores

A procedure for the determination of alpha-emitting thorium isotopes in bastnaesite ores has been developed. The refractory sample was completely decomposed by potassium fluoride fusion in a platinum crucible followed by transposition to a pyrosulfate fusion. The pyrosulfate cake was dissolved in HCl and the resulting precipitate dissolved in DTPA solution; thorium was coprecipitated as hydroxide using cerium present in bastnaesite as natural carrier. Thorium was then extracted into a TOPO solution, separated by using Dowex 1-X8 for anionic exchange, electrodeposited and finally analyzed by alpha-spectrometry. Thorium was also determined spectrophotometrically using Arsenazo as a colorimetric reagent. The thorium yield of the above discussed chemical procedure is more than 85%.     

Determination of gamma-hydroxybutyric acid (GHB) in plasma and urine by headspace solid-phase microextraction and gas chromatography/positive ion chemical ionization mass spectrometry

A new method for the qualitative and quantitative analysis of gamma-hydroxybutyric acid (GHB) in plasma and urine samples is described. It involves the conversion of GHB to gamma-butyrolactone (GBL), its subsequent headspace solid-phase microextraction (SPME), and detection by gas chromatography/positive ion chemical ionization mass spectrometry (GC/PICI-MS), using D(6)-GBL as internal standard. The assay is linear over a plasma GHB range of 1-100 microg/mL (n = 5, r = 0.999) and a urine GHB range of 5-150 microg/mL (n = 5, r = 0. 998). Relative intra- and inter-assay standard deviations, determined for plasma and urine samples at 5 and 50 microg/mL, are all below 5%. The method is simple, specific and reasonably fast. It may be applied for clinical and forensic toxicology as well as for purposes of therapeutic drug monitoring.     

Dual-mechanism kinetics of polyphenylene sulfide (PPS) melt-crystallization

This investigation demonstrates that polyphenylene sulfide (PPS) crystallizes in a unique dual-mechanistic fashion in which 8% of the material by volume crystallizes instantaneously, while the remaining material crystallizes in a time dependent fashion. These rapid melt-crystallization kinetics are quantitatively modeled using a dual-mechanistic model approach which is based on the methodology first observed by Velisaris and Seferis in polyetheretherketone (PEEK) crystallization. The crystallization model is then used to accurately predict both isothermal and for the first time non-isothermal crystallization behavior over a wide spectrum of cooling rates utilizing the same model parameters. Specifically, this work identifies and models the initial fast crystallization kinetics of PPS. Additionally, the versatility of the Velisaris and Seferis dual-mechanistic model has been established with PPS, by simply showing that it is a special case of the generalized dual-crystallization kinetics methodology.