Mathematical modelling of the oxidation of nickel titanium alloys

A one-dimensional bulk reaction model for the oxidation of nickeltitanium is formulated, with preferential oxidation of titaniumbeing included. The modelling is directed at the better understandingof the dominant mechanisms involved in the oxidation processand their significance for the biocompatibility of the alloy.Two different regimes for the relative diffusivities of oxygenand the metals are investigated. By assuming fast bulk reactions,different asymptotic structures emerge in different parameterregimes and the resulting models take the form of moving boundaryproblems. Different profiles of nickel concentration are obtained:in particular a nickel-rich layer (observed in practice) ispresent below the oxide/metal interface for the case when oxygenand the metals diffuse at comparable rates.     

Experimental design and the optimization of a polymer supported palladium complex for use in the Heck reaction

Optimization of the Heck reaction of 4-bromoacetophenone with styrene by a polymer supported, sulfur-containing palladacycle, varying 6 factors at a total of 28 different levels, corresponding to 5760 different possibilities was undertaken. Conversion improved from 34%, with large observable leaching to 88% with no leaching. This was accomplished using a Design of Experiments approach facilitated by the Statistical Design Package, MODDE 7.0^TM.     

A Faster Deterministic Maximum Flow Algorithm

Cheriyan and Hagerup developed a randomized algorithm to compute the maximum flow in a graph with n nodes and m edges in O(mn + n² log²n) expected time. The randomization is used to efficiently play a certain combinatorial game that arises during the computation. We give a version of their algorithm where a general version of their game arises. Then we give a strategy for the game that yields a deterministic algorithm for computing the maximum flow in a directed graph with n nodes and m edges that runs in time O(mn(log_{m/n log n}n)). Our algorithm gives an O(mn) deterministic algorithm for all m/n = Ω(n^ε) for any positive constant ε, and is currently the fastest deterministic algorithm for computing maximum flow as long as m/n = ω(log n).     

Mössbauer and X-ray diffraction characterization of Fe60Al40 coatings prepared by thermal spraying

Microstructured (atomized) and nanostructured (milled) Fe₆₀Al₄₀ powders together with their corresponding coatings synthesized by High Velocity Oxy-fuel (HVOF) or Atmospheric Plasma Spray (APS) thermal spraying techniques have been characterized by Mössbauer Spectroscopy (MS) and X-ray Diffraction (XRD). The evolution of the microstructure and the atomic ordering degree in the powders and coatings are discussed at the light of the various processing conditions. The operational correlation between the parameters of the duplex morphology of coatings and the processing parameters is discussed.     

Corrigendum: The complexity of counting graph homomorphisms

We close a gap in the proof of Theorem 4.1 in our paper “The complexity of counting graph homomorphisms” [Random Structures Algorithms 17 (2000), 260–289]. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.