Determining Minimal Polynomial of Proper Element by Using Higher Degree Traces

Modern communication engineerings, such as elliptic curve cryptographies, often requires algebra on finite extension field defined by modulus arithmetic with an irreducible polynomial. This paper provides a new method to detemine the minimal (irreducible) polynomial of a given proper element in finite extension field. In the conventional determination method, as we have to solve the simultaneous equations, the computation is very involved. In this paper, the well known "trace" is extended to higher degree traces. Using the new traces, we yield the coefficient formula of the desired minimal polynomial. The new method becomes very simple without solving the simultaneous equations, and about twice faster than the conventional method in computation speed

Eighteenth Year of the Gulf of Maine Environmental Monitoring Program

This report summarizes the metals and organic contaminant data associated with the collection and analyses of blue mussel (Mytilus edulis) tissue from selected sites along the Gulf of Maine coast during the 2008 sampling season. Contaminant monitoring is conducted by the Gulfwatch Program for the Gulf of Maine Council on the Marine Environment (GOMC). A subset of these data is compared with analytical results from earlier Gulfwatch monitoring (2001-2007). Statistical analyses are limited to descriptive measures of replicates from selected sampling sites and include: arithmetic means, and appropriate measures of variance. The primary purpose of this report is to present the current annual results, present graphical representation of spatial and temporal trends and identify potential outliers in order to provide investigators and other interested persons with contemporary information concerning water quality in the Gulf of Maine, as reflected by uptake into resident shellfish (mussels and clams)

A new non-arithmetic lattice in PU(3,1)

We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1)

The arithmetic of QM-abelian surfaces through their Galois representations

This note provides an insight to the diophantine properties of abelian surfaces with quaternionic multiplication over number fields. We study the fields of definition of the endomorphisms on these abelian varieties and the images of the Galois representations on their Tate modules. We illustrate our results with several explicit examples.Comment: To appear in J. Algebr