We study the differentiable structure and the homotopy type of some spaces related to the Grassmannian of closed linear subspaces of an infinite dimensional Hilbert space, such as the space of Fredholm pairs, the Grassmannian of compact perturbations of a given space, and the essential Grassmannians. We define a determinant bundle over the space of Fredholm pairs. We lift the composition of Fre...

This paper presents a new computational method for identifying side faces of thin-walled solids that can be excluded from the first step of conformal transformation from a tet mesh to an all-hex mesh. By excluding such side faces, all-hex meshes created by the conformal transformation method better align with the boundary of the side faces and tend to exhibit better scaled Jacobian quality. The...

In this paper we present a new family of minimal spectrally arbitrary patterns which allow for arbitrary spectrum by using the Nilpotent-Jacobian method introduced in [3]. The novel approach here is that we use the Intermediate Value Theorem to avoid finding an explicit nilpotent realization of the new minimal spectrally arbitrary patterns.

Are every two separated nets in the plane bilipschitz equivalent? In the late 1990s, Burago and Kleiner and, independently, McMullen resolved this beautiful question negatively. Both solutions are based on a construction of a density function that is not realizable as the Jacobian determinant of a bilipschitz map. McMullen’s construction is simpler than the Burago–Kleiner one, and we provide a ...

We present an efficient endomorphism for the Jacobian of a curve C of genus 2 for divisors having a Non disjoint support. This extends the work of Costello in [12] who calculated explicit formulæ for divisor doubling and addition of divisors with disjoint support in JF(C) using only base field operations. Explicit formulæ is presented for this third case and a different approach for divisor dou...

In the early 1990s, Flynn gave an explicit description of the Jacobian of a genus 2 hyperelliptic curve to perform efficient arithmetic on these objects. In this paper, we give a generalization of Flynn’s work when the ground field has characteristic 2. More precisely, we give an explicit description of both the Jacobian and the Kummer surface. We also give (and explain how we found) explicit f...

We provide explicit formulae for realising the group law in Jacobians of superelliptic curves of genus 3 and C3,4 curves. It is shown that two distinct elements in the Jacobian of a C3,4 curve can be added with 150 multiplications and 2 inversions in the field of definition of the curve, while an element can be doubled with 174 multiplications and 2 inversions. In superelliptic curves, 10 multi...

Within uncertain technological progress, a firm has to decide when to update its technology and select a new one among a non-decreasing range over time. Under constant return to scale, the best existing technology is implemented. Replacement is triggered not only when the firm operated technology is sufficiently obsolete but also the wedge between the latest and the state of the arts grades is ...

In this paper, dependent and independent variable transformations are introduced to solve a generalized sinh–Gordon equation by using the binary F-expansion method and the knowledge of elliptic equation and Jacobian elliptic functions. Many different new exact solutions such as double periodic wave and complex wave solutions are obtained. Some previous results are extended. 2013 Elsevier Inc. A...