Computation of several cyclotomic Swan subgroups

Let denote the locally free class group, that is the group of stable isomorphism classes of locally free -modules, where is the ring of algebraic integers in the number field and is a finite group. We show how to compute the Swan subgroup, , of when , a primitive -th root of unity, , where is an odd (rational) prime so that and 2 is inert in We show that, under these hypotheses, this calculation reduces to computing a quotient ring of a polynomial ring; we do the computations obtaining for several primes a nontrivial divisor of These calculations give an alternative proof that the fields for =11, 13, 19, 29, 37, 53, 59, and 61 are not Hilbert-Speiser.

     

Nontrivial Galois module structure of cyclotomic fields

We say a tame Galois field extension with Galois group has trivial Galois module structure if the rings of integers have the property that is a free -module. The work of Greither, Replogle, Rubin, and Srivastav shows that for each algebraic number field other than the rational numbers there will exist infinitely many primes so that for each there is a tame Galois field extension of degree so that has nontrivial Galois module structure. However, the proof does not directly yield specific primes for a given algebraic number field For any cyclotomic field we find an explicit so that there is a tame degree extension with nontrivial Galois module structure.

     

Sexual differentiation of the zebra finch song system: potential roles for sex chromosome genes

Background  

Recent evidence suggests that some sex differences in brain and behavior might result from direct genetic effects, and not solely the result of the organizational effects of steroid hormones. The present study examined the potential role for sex-biased gene expression during development of sexually dimorphic singing behavior and associated song nuclei in juvenile zebra finches.     

Extracting isovolumes from three-dimensional torso geometry usingPROLOG

Three-dimensional (3D) finite element torso models are widely used to simulate defibrillation field quantities, such as potential, gradient and current density. These quantities are computed at spatial nodes that comprise the torso model. These spatial nodes typically number between 10⁵ and 10⁶, which makes the comprehension of torso defibrillation simulation output difficult. Therefore, the objective of this study is to rapidly prototype software to extract a subset of the geometric model of the torso for visualization in which the nodal information associated with the geometry of the model meets a specified threshold value (e.g., minimum gradient). The data extraction software is implemented in PROLOG, which is used to correlate the coordinate, structural and nodal data of the torso model. A PROLOG-based environment has been developed and is used to rapidly design and test new methods for sorting, collecting and optimizing data extractions from defibrillation simulations in a human torso model for subsequent visualization