Classification of Extremal Double Circulant Self-Dual Codes of Lengths 64 to 72

Recently extremal double circulant self-dual codes have been classified for lengths n ≤ 62. In this paper, a complete classification of extremal double circulant self-dual codes of lengths 64 to 72 is presented. Almost all of the extremal double circulant singly-even codes given have weight enumerators for which extremal codes were not previously known to exist.     

A short synthesis of (±)-tecomanine via a Pauson-Khand-based route

The N-carboethoxy precursor to (±)-tecomanine has been prepared in 11 steps from 2-methyl-1-buten-3-yne. The key step, Pauson-Khand cyclization of a methylated 5-aza-6-nonen-1-yne succeeds, but only in low yield, a consequence of the dialkyl substitution about the azaenyne framework. Nevertheless, the overall sequence to that point is one of the more efficient to be described.     

Growth of masking as a measure of response growth in hearing-impaired listeners

Growth-of-masking functions were obtained from 19 normal and 5 hearing-impaired listeners using a simultaneous-masking paradigm. When masker and probe frequency are identical, the slope of masking approximates 1.0 for both normal-hearing and impaired listeners. For masker frequencies less than or greater than probe frequency, the slopes for impaired listeners are shallower than those of normals. These findings are consistent with previously reported physiological data (single-fiber rate versus level and AP masking functions) for animals with induced cochlear lesions. Results are discussed in terms of a potential masking technique to estimate the growth of response in normal and impaired ears.     

Derived Lengths of Solvable Groups Having Five Irreducible Character Degrees II

Let G be a solvable group with five character degrees. Suppose that there is some prime p so that G/O ^p (G) is not Abelian. Also, assume that cd(G) contains a degree that is not divisible by p. Under these hypotheses, we show that the derived length of G is at most 4.     

Preservice Elementary Teachers' Use of Mathematics in a Project‐Based Science Approach

The use of a project‐based science (PBS) approach to teaching encourages students to integrate mathematics and science in meaningful ways as they create projects. As a beginning study of how students use mathematics in such an approach, an analysis of 23 projects developed by preservice elementary teachers enrolled in an elementary science course was conducted. Findings showed that students made a number of different types of mathematical errors and underutilized data representation and summary forms. Implications included the importance of developing methods for supporting the use of mathematical tools in utilizing a project‐based approach and considering ways that such tools mediate scientific thinking.