Some Examples of Valued Fields

Some Examples of Valued Fields

The purpose of this paper is to use generalized power series to provide two classes of examples of valued elds. In the rst set of examples the valued elds are henselian, in general not maximal, with given residue eld and value group. In the second set of examples, the valued elds are all maximal and their families of residue elds and value groups form chains. In both cases, these elds possess a...

Some Steinhaus type theorems over valued fields

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FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

In this note we first redefine the notion of a fuzzy hypervectorspace (see [1]) and then introduce some further concepts of fuzzy hypervectorspaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervectorspaces over valued fields. Finally, we briefly discuss on the convex (balanced)hull of a given fuzzy set of a hypervector space.

Some examples of matrix-valued orthogonal functions having a differential and an integral operator as eigenfunctions

The aim of this paper is to show some examples of matrix-valued orthogonal functions on the real line which are simultaneously eigenfunctions of a second-order differential operator of Schrödinger type and an integral operator of Fourier type. As a consequence we derive integral representations of these functions as well as other useful structural formulas. Some of these functions are plotted t...

Amalgamating valued fields