Related papers: Tiling of rectangles with squares via Diophantine …
The chapter contains a detailed presentation of the surface integral theory for modelling light diffraction by surface-relief diffraction gratings having a one-dimensional periodicity. Several different approaches are presented, leading…
Considering simultaneous approximation to three numbers, we study the geometry of the sequence of best approximations. We provide a sharper lower bound for the ratio between ordinary and uniform exponent of Diophantine approximation,…
Finding correspondences between 3D shapes is a crucial problem in computer vision and graphics, which is for example relevant for tasks like shape interpolation, pose transfer, or texture transfer. An often neglected but essential property…
The present article studies combinatorial tilings of Euclidean or spherical spaces by polytopes, serving two main purposes: first, to survey some of the main developments in combinatorial space tiling; and second, to highlight some new and…
Inspired by a problem proposed by Mahler, we will address the following related question, 'How well can irrationals in a missing digit set be approximated by rationals with polynomial denominators?' and prove some related results. To…
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
We propose an analytical approach to the conformal mapping of (rectangular) polygons based on the theory of Riemann surfaces and theta functions.
We propose a differentiable nonparametric algorithm, the Delaunay triangulation learner (DTL), to solve the functional approximation problem on the basis of a $p$-dimensional feature space. By conducting the Delaunay triangulation algorithm…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
A classic result of Brooks, Smith, Stone and Tutte associates to any finite planar network with distinguished source and sink vertices, a tiling of a rectangle by smaller subrectangles whose aspect ratios are given by the conductances of…
The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.
In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, which can solve general convex problems satisfying a new…
An $N$-tiling of triangle $ABC$ by triangle $T$ (the `tile') is a way of writing $ABC$ as a union of $N$ copies of $T$ overlapping only at their boundaries. Let the tile $T$ have angles $(\alpha,\beta,\gamma)$, and sides $(a,b,c)$. This…
We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…
In these notes, we begin by recalling aspects of the classical theory of metric Diophantine approximation; such as theorems of Khintchine, Jarn\'{\i}k, Duffin-Schaeffer and Gallagher. We then describe recent strengthening of various…
We construct new Delone sets associated with badly approximable numbers which are expected to have rotationally invariant diffraction. We optimize the discrepancy of corresponding tile orientations by investigating the linear equation…
We study metric Diophantine approximation in local fields of positive characteristic. Specifically, we study the problem of improving Dirichlet's theorem in Diophantine approximation and prove very general results in this context.