We give an infinite dimensional generalized Weierstrass representation for spacelike constant mean curvature (CMC) surfaces in Minkowski 3-space R2,1. The formulation is analogous to that given by Dorfmeister, Pedit and Wu for CMC surfaces in Euclidean space, replacing the group SU2 with SU1,1. The non-compactness of the latter group, however, means that the Iwasawa decomposition of the loop gr...

Kodaira and Néron classified and described the geometry of the special fibers of the Néron model of an elliptic curve defined over a discrete valuation ring with a perfect residue field. Tate described an algorithm to determine the special fiber type by manipulating the Weierstrass equation. In the case of non-perfect residue fields, we discover new fiber types which are not on the Kodaira-Néro...

In this paper, we develop a technique to compute the Weierstrass Gap Sequence at a given point, no matter if simple or singular, on a plane curve, with respect to any linear system V ⊆ H(C,OC (n)). This technique can be useful to construct examples of curves with Weierstrass points of given weight, or to look for conditions for a sequence to be a Weierstrass Gap Sequence. We use this technique ...

We discuss and examine Weierstrass’ main contributions to approximation theory. §1. Weierstrass This is a story about Karl Wilhelm Theodor Weierstrass (Weierstraß), what he contributed to approximation theory (and why), and some of the consequences thereof. We start this story by relating a little about the man and his life. Karl Wilhelm Theodor Weierstrass was born on October 31, 1815 at Osten...

This paper proposes new explicit formulas for the doubling and addition steps in Miller’s algorithm to compute the Tate pairing on elliptic curves in Weierstrass and in Edwards form. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in addition and d...

We characterize the complex differential equations of form $${{dy} \over {dx}} = {a_n}(x){y^n} + {a_{n - 1}}(x){y^{n 1}} \cdots {a_1}(x)y {a_0}(x),$$ where aj(x) are meromorphic functions in variable x for j 0,…,n that admit either a Weierstrass first integral or inverse integrating factor.

A new and simple approach for calculating the eigenstructure of a regular matrix pencil is presented. This proposed approach transforms the generalized eigenvalues problem into a usual eigenvalues problem, and it also can be used to calculate the Weierstrass form of a regular matrix pencil. Mathematics Subject Classification: 93B55

We study different computable versions of Baire’s Category Theorem in computable analysis. Similarly, as in constructive analysis, different logical forms of this theorem lead to different computational interpretations. We demonstrate that, analogously to the classical theorem, one of the computable versions of the theorem can be used to construct interesting counterexamples, such as a computab...

— We study threefolds X ⊂ Pr having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not h...