Pade approximations and diophantine geometry

Diophantine Approximations, Diophantine Equations, Transcendence and Applications

This article centres around the contributions of the author and therefore, it is confined to topics where the author has worked. Between these topics there are connections and we explain them by a result of Liouville in 1844 that for an algebraic number α of degree n ≥ 2, there exists c > 0 depending only on α such that | α− p q |> c qn for all rational numbers p q with q > 0. This inequality i...

Diophantine Approximations and Toric Deformations

1.1. Let S be a finite set of places of a finite field extension L of a number field K, containing all infinite places. Let E be a vector space over K of dimension N + 1. For v ∈ S, let lv0, · · · , lvN be linearly independent vectors in E ⊗K L. Choose a projective subvariety X defined over K, embedded into the projective space P(E∨) of lines of the dual vector space E∨. Consider the system of ...

Report on Diophantine approximations

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Arithmetic and Diophantine Geometry

Order Reduction using Modified Pole Clustering and Pade Approximations

The authors present a mixed method for reducing the order of the large-scale dynamic systems. In this method, the denominator polynomial of the reduced order model is obtained by using the modified pole clustering technique while the coefficients of the numerator are obtained by Pade approximations. This method is conceptually simple and always generates stable reduced models if the original hi...