Complex variables in junior high school: the role and potential impact of an outreach mathematician

Outreach mathematicians are college faculty who are trainedin mathematics but who undertake an active role in improvingprimary and secondary education. This role is examined througha study where an outreach mathematician introduced the conceptof complex variables to junior high school students in the UnitedStates with the goal of stimulating their interest in mathematicsand improving their algebra skills. Comparison of pre- and post-testresults showed that ninth-grade students displayed a significantchange in algebraic skills while the eighth-grade students madelittle progress. The outreach mathematician lacked some awarenessof the eighth-grade students’ foundational backgroundand motivation. This illustrates the importance of working moreclosely with the participating teacher, who understands betterthe curriculum and the students’ background knowledge,levels of maturity and levels of motivation.     

A practical depth distribution function for angle-resolved Auger/photoelectron spectroscopy

It is shown that, to a good approximation, over the range of energies (single scattering albedo, ω 0.5) and angles (take-off angle >30°) used in angle-resolved AES and XPS spectroscopy, the depth distribution function (DDF) is approximately exponential with decay length Λ = λ_i(1 + λ_i/λ_tr)^−1/2, for inelastic mean free path (IMFP) λ_i, and transport mean free path λ_tr.

As Λ is also the length measured for the attenuation length experimentally (with either the overlayer technique or from backscatter spectra, equivalent to λ_i, using an interpretation which neglects elastic effects), the CDP may be obtained by straightforward Laplace inversion using experimentally determined attenuation lengths. That is, the correct composition depth profile may be obtained from systematically ignoring elastic scattering.     

Duality in algebra and topology

We apply ideas from commutative algebra, and Morita theory to algebraic topology using ring spectra. This allows us to prove new duality results in algebra and topology, and to view (1) Poincaré duality for manifolds, (2) Gorenstein duality for commutative rings, (3) Benson–Carlson duality for cohomology rings of finite groups, (4) Poincaré duality for groups and (5) Gross–Hopkins duality in chromatic stable homotopy theory as examples of a single phenomenon.     

Voronoi diagrams of random lines and flats

It is proved that, for any fixedd ≽ 3 and 0 ≤k ≤ d - 1, the expected combinatorial complexity of the Euclidean Voronoi diagram ofn random &-flats drawn independently from the uniform distribution onk-flats intersecting the unit ball in ℝ^d is Ξ(n ^d/(d-k)) asn → ∞. A by-product of the proof is a density transformation for integrating over sets ofd + 1k-flats in ℝ^d     

Agricultural engineering — State-of-the-art report

The 1st European Conference of ISTVS held at Rottach-Egern in 1980 is used as the starting point for a review of the state-of-the-art in the design of agricultural vehicles. The functions of these vehicles are divided into three main categories: soil processing, load carrying and self-propulsion. The limitations on design in each of these areas are defined and the relevant papers to the 7th International Conference are discussed in this context. It is concluded that there is still a requirement for the development of lighter, higher speed vehicles with low ground pressure, adequate ground clearance and good suspension. In parallel with the development of this hardware, computer simulation and modelling techniques should be developed to facilitate evaluation of new designs on the drawing board.     

The adsorption of CO on clean and potassium promoted FeO surfaces

The adsorption of CO on a FeO (wustite) surface was investigated using UPS, AES and temperature programmed desorption. These results are compared to those obtained from the same sample following addition of potassium from the decomposition of KOH. CO adsorption was identified following exposure at 300 K to the potassium free surface. The adsorbed species readily desorbs below 500 K. CO adsorption was poisoned by pre-exposure to oxygen at 300 K. This suggests CO is adsorbed at surface oxygen vacancies. CO induced UPS emission features are different from those typically found for CO chemisorbed on transition metal surfaces. The presence of potassium alters the adsorption behavior of CO. The thermal desorption maximum shifts to 625 K. UPS results indicate molecular CO adsorption at 300 K and upon heating to 470 K CO dissociates. The presence of potassium thus promotes CO dissociation on FeO.