Related papers: Finding an Ellipse Tangent to finitely many given …
We derive finite difference equations of infinite order for theta hypergeometric series and investigate the space of their solutions. In general, such infinite series diverge, we describe some constraints on the parameters when they do…
We apply the twisting technique that was first introduced in \cite{CK} and later generalized in \cite{QCQ} to obtain an infinite family of adequate, homogeneous or alternative links from a given adequate, homogeneous or alternative link,…
Let $(X,\omega_0):=(\mathbb{C}/\Lambda,0)$ denote the elliptic curve associated to the lattice $\Lambda$, $X_2:=\{\omega_0,\cdots, \omega_3\}$ its set of half-periods and $\wp:X \to \mathbb{P}^1$ the usual Weierstrass $\wp$ function, with a…
We consider a class of large superposed states, obtained from dimer coverings on spin-1/2 isotropic lattices, whose potential usefulness ranges from organic molecules to quantum computation. We show that they are genuinely multiparty…
This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…
A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…
When approximating elliptic problems by using specialized approximation techniques, we obtain large structured matrices whose analysis provides information on the stability of the method. Here we provide spectral and norm estimates for…
This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.
This paper has been withdrawn owing a re-arrangement of two previously submitted papers. The new version of the theoretical work on the triaxial shape of dark matter haloes can be found at the ArXiv astro-ph list (CO) as article 1104.2905
We present experimental evidence to support the widely held belief that one half of all elliptic curves have infinitely many rational points. The method used to gather this evidence is a refinement of an algorithm due to the author which is…
A (multi)set of segments in the plane may form a TSP tour, a matching, a tree, or any multigraph. If two segments cross, then we can reduce the total length with the following flip operation. We remove a pair of crossing segments, and…
Boundary differentiability is shown for solutions of nondivergence elliptic equations with unbounded drift
Integrals related to the surface area of arbitrary ellipsoids are derived, evaluated, and compared with each other and existing integrals found in the literature. We clarify the literature on the ellipsoid area problem, which dates back to…
We give a characterization for the extreme points of the convex set of correlation matrices with a countable index set. A Hermitian matrix is called a correlation matrix if it is positive semidefinite with unit diagonal entries. Using the…
This thesis poses a selection of recent research of the author in a common context. It starts with a selected review on research concerning the role entanglement might play at quantum phase transitions and introduces measures for…
We give explicit formulas for the number of distinct elliptic curves over a finite field, up to isomorphism, in the families of Legendre, Jacobi, Hessian and generalized Hessian curves.
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…
This version has been withdrawn. The new and final version is on ArXiv 1103.4878
This is a significant revision of the early version of this paper which was posted last December. The speculative section has been removed in light of some recent results of Morita and Kawazumi. Numerous typos have been fixed. The companion…
For a Hamilton-Jacobi equation defined on a network, we introduce its vanishing viscosity approximation. The elliptic equation is given on the edges and coupled with Kirchhoff-type conditions at the transition vertices. We prove that there…