We extend the notion of singular vectors to context Diophantine approximation real numbers with elements a totally number field K. For $$m\ge 1$$ , we establish version Dani’s correspondence in fields and prove that under class ‘friendly measures’ $$K_S^m$$ set has measure zero. Here S is Archimedean valuations K $$K_S$$ product completions $$\sigma (K)$$ \in S$$ . On other hand, show existence...

An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...

his paper tests for evidence in support of the purchasing power parity (PPP) in the bilateral real exchange rate series of the South African rand against the US dollar. The importance of considering structural breaks in the PPP test is illustrated. Using standard unit root tests without considering structural breaks, the study is unable to reject the null hypothesis of a unit root in the exchan...