The structure and first H NMR spectral assignment of piperazine-C60 adducts

The ¹H NMR spectrum of the piperazine-C₆₀ monoadduct has been assigned for the first time almost 10 years after it was synthesised. The preparation and characterisation of the first (C2-substituted piperazine)-C₆₀ monoadduct are also described, revealing the C2-substituent as occupying an exo position on the addend.     

A solution to de Groot’s absolute cone conjecture

A compactum X is an ‘absolute cone’ if, for each of its points x, the space X is homeomorphic to a cone with x corresponding to the cone point. In 1971, J. de Groot conjectured that each n-dimensional absolute cone is an n-cell. In this paper, we give a complete solution to that conjecture. In particular, we show that the conjecture is true for n≤3 and false for n≥5. For n=4, the absolute cone conjecture is true if and only if the 3-dimensional Poincaré Conjecture is true.     

Beating the System: Course Structure and Student Strategies in a Traditional Introductory Undergraduate Physics Course for Nonmajors

The purpose of this study was to describe relationships among instructor and student goals, course design, and student strategies for learning physics in a traditional introductory undergraduate physics course for nonmajors. The procedures included 16 hours ofnonparticipant observation, during which detailed field notes and photographs were taken and documents were collected. Audiotaped open-ended interviews were given to instructors and students, and all students participated in a limited survey. The data were analyzed using qualitative methods of the Chicago School. Results indicated that both differing goals of students and instructors and the structure of the course inhibited the understanding of physics and were conducive to students engaging in unexpected behaviors designed to help them successfully pass the course. The consequences of the structure of the course and subsequent student behaviors inhibited their understanding and appreciation of physics and deterred them from enrolling in further science courses. The paper includes implications for teaching introductory college physics.     

Synthesis and characterization of hyperbranched polymers with increased chemical versatility for imprint lithographic resists

Hyperbranched polymers were prepared from a variety of mono‐ and difunctional monomers and used in the development of novel UV‐imprint lithography (UV‐IL) resists. The unique physical and chemical properties of these hyperbranched materials significantly increase the range of molecular systems that could be imprinted. Traditional challenges, such as the use of monomers that have low boiling points or the use of insoluble/highly crystalline momomers, are overcome by the preparation of hyperbranched polymers that incorporate these repeat units. In addition, the low viscosity of the hyperbranched macromolecules and the large number of reactive chain ends overcome many difficulties that are traditionally associated with the use of polymeric materials as imprint resists. Hyperbranched polymers containing up to 12 mol % pendant vinyl groups, needed for secondary crosslinking during imprinting, were prepared with a wide range of repeat unit structures and successfully imprinted with features from tens of microns to ∼ 100 nm. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6238–6254, 2008     

Synthesis of substituted benzo[b]thiophenes by acid-catalyzed cyclization of thiophenylacetals and ketones

Benzo[b]thiophenes substituted at the 3 position with methyl or carboxymethyl and at the 5 position with methyl, methoxy, chloro, bromo and nitro were prepared by cyclization of thiophenyl-acetals and ketones using a suspension of polyphosphoric acid in refluxing chlorobenzene. The overall efficiency of this method is superior to literature procedures because of the lower temperature and the limited amount of PPA used.     

Order estimates for irreducible projections in L2 of a nilmanifold

Let π be an irreducible representation occurring in $\text{L}$²(Г?N), where N is a nilpotent Lie group and Γ is a discrete, cocompact subgroup. The projection onto the π-equivariant subspace is given by convolution against a distribution D_π. For certain π, we obtain an estimate on the order of D_π. The condition on π involves an extension of the “canonical objects” associated to elements of the Kirillov orbit of π; there does not appear to be an example in the literature where it is not satisfied.     

Low-energy baryosynthesis

We consider general constraints on baryosynthesis in low-energy SU(3) × SU(2) × U(1) theories. We find in general that phenomenologically acceptable models exist, which are unifiable at higher energies-but which all require exotic fermion content.