Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework based on a single g ...
Existing works for depth estimation and image deblurring in the presence of depth-dependent blur work with the assumption of a multi-layered scene wherein each layer is modeled in the form of a fronto-parallel plane. In this work, we attempt to relax these ...
We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...
Diffractive optical elements (DOEs) which consist of microstructure surface relief permit the generation of the spatial distribution of light beams by using a single element. Due to their compact size, design flexibility, and mass productivity, they are us ...
A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...
Let F be a fixed graph. The rainbow Turan number of F is defined as the maximum number of edges in a graph on n vertices that has a proper edge-coloring with no rainbow copy of F (i.e., a copy of F all of whose edges have different colours). The systematic ...
We report the experimental observation of the 1/2 < 111 > edge dislocation dipole formation and annihilation in ultra-high purity Fe using transmission electron microscopy (TEM) in-situ straining. The observation is confirmed by TEM image simulations. The ...
A graph drawn in the plane is called k-quasi-planar if it does not contain k pair-wise crossing edges. It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best k ...
A topological graph G is a graph drawn in the plane with vertices represented by points and edges represented by continuous arcs connecting the vertices. If every edge is drawn as a straight-line segment, then G is called a geometric graph. A k-grid in a t ...
