In this article we shall give a survey of Hasse’s problem for integral power bases of algebraic number fields during the last half of century. Specifically, we developed this problem for the abelian number fields and we shall show several substantial examples for our main theorem [7] [9], which will indicate the actual method to generalize for the forthcoming theme on Hasse’s problem [15].

This paper is a survey of results obtained by the present author towards proving Rubin’s integral version of Stark’s conjecture for abelian L– functions of arbitrary order of vanishing at the origin. Rubin’s conjecture is stated and its links to the classical integral Stark conjecture for L–functions of order of vanishing 1 are discussed. A weaker version of Rubin’s conjecture formulated by the...

We consider the fermion-boson mapping in three dimensional space-time, in the Abelian case, from the current algebra point of view. We show that in a path-integral framework one can derive a general bosonization recipe leading, in the bosonic language, to the correct equal-time current commutators of the original free fermionic theory.

We develop a new operator quantization scheme for gauge theories where no gauge fixing for gauge fields is needed. The scheme allows one to avoid the Gribov problem and construct a manifestly Lorentz invariant path integral that can be used in the non-perturbative domain. We discuss briefly an application of the method to Abelian projections of QCD.

The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.

Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identity and whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals.

The GPS meteorology (GPS/MET) experiment, led by the Universities Corporation for Atmospheric Research (UCAR), consists of a GPS receiver aboard a low earth orbit (LEO) satellite which was launched on 3 April 1995. During a radio occultation the LEO satellite rises or sets relative to one of the 24 GPS satellites at the Earth's horizon. Thereby the atmospheric layers are successively sounded by...

The set of integral ows on a nite graph ? is naturally an integral lattice 1 (?) in the Euclidean space Ker((1) of harmonic real-valued functions on the edge set of ?. Various properties of ? (bipartite character, girth, complexity, separability) are shown to correspond to properties of 1 (?) (parity, minimal norm, determinant, decomposability). The dual lattice of 1 (?) is identiied to the int...