Recently, several works by a number of authors have provided characterizations integral undirected Cayley graphs over generalized dihedral groups and dicyclic groups. We generalize unify these results in two different ways. Firstly, we work arbitrary non-abelian finite admitting an abelian subgroup index 2. Secondly, our main result actually characterizes mixed such groups, the spirit very rece...

Even though the (untwisted) Whitehead doubling operation kills all known abelian invariants of knots (and makes them topologically slice), we show that it does not kill the rational function that equals to the 2-loop part of the Kontsevich integral.

We present a very accurate formula counting norms of normal integral bases in tame abelian extensions of the rational eld. The methods used include applications of Schmidt's Subspace Theorem, Baker's Theorem and the Hardy-Littlewood Method, all from diophantine approximation.

The surface area of a general n-dimensional ellipsoid is represented as an Abelian integral, which can readily be evaluated numerically. If there are only 2 values for the semi-axes then the area is expressed as an elliptic integral, which reduces in most cases to elementary functions. The capacity of a general n-dimensional ellipsoid is represented as a hyperelliptic integral, which can readil...

let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

Let G be a finite group. For each integral representation ρ of G we consider ρ−decomposable principally polarized abelian varieties; that is, principally polarized abelian varieties (X,H) with ρ(G)−action, of dimension equal to the degree of ρ, which admit a decomposition of the lattice for X into two G−invariant sublattices isotropic with respect to IH , with one of the sublattices ZG−isomorph...

It is shown that the application of the non-Abelian Stokes theorem to the computation of the operators constructed with Wilson loop will lead to ambiguity, if the gauge field under consideration is a non-trivial one. This point is illustrated by the specific examples of the computation of a non-local operator. The non-Abelian Stokes theorem is widely applied to compute Wilson loop (closed nonAb...

The effective string action of the color-electric flux tube in the U(1)×U(1) dual Ginzburg-Landau (DGL) theory is studied by performing a path-integral analysis by taking into account the finite thickness of the flux tube. The DGL theory, corresponding to the low-energy effective theory of Abelian-projected SU(3) gluodynamics, can be expressed as a [U(1)]3 dual Abelian Higgs (DAH) model with a ...