Let $m>1$ and $\mathfrak {d} \neq 0$ be integers such that $v_{p}(\mathfrak {d}) \neq m$ for any prime p. We construct a matrix $A(\mathfrak {d})$ of size $(m-1) \times (m-1)$ depending on only of $\mathfrak {d}$ with the following property: For any tame $ \mathbb {Z}/m \mathbb {Z}$ -number field K of discriminant $\mathfrak {d}$ , the matrix $A(\mathfrak {d})$ represents the Gram matrix of the integral trace-zero form of K. In particular, we have that the integral trace-zero form of tame cyclic number fields is determined by the degree and discriminant of the field. Furthermore, if in addition to the above hypotheses, we consider real number fields, then the shape is also determined by the degree and the discriminant.

The immunogold technique is a valuable method for labeling cellular macromolecules. However, multiple labeling using colloidal gold (cAu) nanoparticles of different sizes presents certain drawbacks; namely, as particle size increases, there is a decreased labeling efficiency and diminished spatial resolution with respect to the locations of labeled epitopes. Both concerns also limit the utility of heavy metal particles for comparative analysis of labeling densities. To minimize the variables due to differential labeling efficiencies, the best solution would be to conduct multiple labeling with particles of similar size. Consequently, some parameter other than size is necessary to distinguish each label type. In this study, we report the synthesis of colloidal palladium (cPd) nanoparticles of similar size but having two distinct shapes, umbonate and faceted, which are readily distinguishable from spherical colloidal gold particles. Their utility and fidelity as labels using a human platelet whole-mount model is also demonstrated.

The use of a shoal analysis and patch estimation system (SHAPES) to analyse hydro-acoustic data is discussed. SHAPES was used to detect and characterise sardine schools from four echo integration surveys off the coast of South Africa. Methods of school detection and characterisation, assumptions made and corrections applied to school variables are presented. Measurements of school morphology and internal school features are discussed and compared to other relevant works. Significant relationships were established, both between measures of school morphology and internal density structure. Several variables showed significant differences between surveys. Composite factors derived from principle component analyses showed that morphological variables are the most important school descriptors. No differences in the loading of composite factors between surveys are evident. This suggests an inherent spatial and temporal stability in sardine school characteristics. This fact may prove beneficial for comparisons of school structure between co-occurring fish species and possibly aid fish school identification in the future.