Investigating secondary students beliefs about mathematical problem-solving

Many studies over the past 30 years have highlighted the important role of students’ beliefs for successful problem-solving in mathematics. Given the recent emphasis afforded to problem-solving on the reformed Irish secondary school mathematics curriculum, the main aim of this study was to identify Irish students’ (n = 975) beliefs about the field. A quantitative measure of these beliefs was attained through the use of the Indiana Mathematical Belief Scale, an existing 30-item (five-scale) self-report questionnaire. A statistical analysis of the data revealed that students who were further through their secondary education had a stronger belief that not all problems could be solved by applying routine procedures. In contrast, the same students held less positive beliefs than their younger counterparts that they could solve time-consuming problems and that conceptual understanding was important. The analysis also indicated that gender had a significant impact on three of the five belief scales.     

Fusion around the barrier for 7Li+12C

Fusion cross-sections for the ⁷Li + ¹²C reaction have been measured at energies above the Coulomb barrier by the direct detection of evaporation residues. The heavy evaporation residues with energies below 3 MeV could not be separated out from the α-particles in the spectrum and hence their contribution was estimated using statistical model calculations. The present work indicates that suppression of fusion cross-sections due to the breakup of ⁷Li may not be significant for ⁷Li + ¹²C reaction at energies around the barrier.     

Projective remoteness planes

A new axiomatization involving incidence and remoteness of planes with nondivision coordinate rings is introduced and a coordinatization theorem is obtained. A geometric process of splitting points and lines to obtain another plane with the same coordinates is described. It is also shown that a group of Steinberg type is parametrized by a nonassociative ring. The notion of elementary basis sets for an associative ring is introduced and constructions of projective and affine planes are given. A plane with reflections determining a system of rotations is shown to have commutative, associative coordinates.     

The scattering matrices for a non-spherical scalar-relativistic potential

The scattering matrices for a non-spherical scalar-relativistic potential are written down. A new formula is derived that makes it possible to evaluate quite easily a necessary angular integration.     

Speciation and biosynthetic variation in four dictyoceratid sponges and their cyanobacterial symbiont, Oscillatoria spongeliae

Four species of marine sponges (Phylum Porifera, Order Dictyoceratida), which contain the filamentous cyanobacterial symbiont Oscillatoria spongeliae, were collected from four locations in Palau. The halogenated natural products associated with the symbiont were characterized from each sample, revealing that each species contained either chlorinated peptides, brominated diphenyl ethers, or no halogenated compounds. Analysis of the host sponges and the symbionts indicated that each species of sponge contained a distinct strain of morphologically similar cyanobacteria. Although cospeciation may be present in this group, we have identified that at least one host switching event has occurred in this symbiosis. Only the strain of O. spongeliae in the sponge containing the chlorinated compounds possessed genes involved in the biosynthesis of chlorinated leucine precursors, indicating that the chemical variation observed in these animals has a genetic foundation.     

pH dependent self-assembly of dimetallic lanthanide complexes

pH dependent self-association has been observed in a series of DO3A-derived lanthanide complexes bearing a carboxylate group that can act as a bridging ligand at high pH, switching on the luminescence from the lanthanide.