Zero Set Structure of Real Analytic Beltrami Fields

Real Closed Fields with Nonstandard Analytic Structure

We consider the ordered field which is the completion of the Puiseux series field over R equipped with a ring of analytic functions on [−1, 1]n which contains the standard subanalytic functions as well as functions given by tadically convergent power series, thus combining the analytic structures from [DD] and [LR3]. We prove quantifier elimination and o–minimality in the corresponding language...

Real Closed Fields with Nonstandard and Standard Analytic Structure

We consider the ordered field which is the completion of the Puiseux series field over R equipped with a ring of analytic functions on [−1, 1]n which contains the standard subanalytic functions as well as functions given by tadically convergent power series, thus combining the analytic structures from [DD] and [LR3]. We prove quantifier elimination and o–minimality in the corresponding language...

Fields with Analytic Structure

We present a unifying theory of fields with certain classes of analytic functions, called fields with analytic structure. Both real closed fields and Henselian valued fields are considered. For real closed fields with analytic structure, o-minimality is shown. For Henselian valued fields, both the model theory and the analytic theory are developed. We give a list of examples that comprises, to ...

Computing Beltrami Fields

Abstract. For solving the non-linear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is sol...

Zero - energy Fields on Real ProjectiveSpaceToby