Quadratic functions and smoothing surface singularities

A quadratic-time algorithm for smoothing interval functions

In many real-life applications, physical considerations lead to the necessity to consider the smoothest of all signals that is consistent with the measurement results. Usually, the corresponding optimization problem is solved in statistical context. In this paper, we propose a quadratic-time algorithm for smoothing an interval function. This algorithm, given n + 1 intervals x0, . . . ,xn with 0...

Surface plasmons and singularities.

We apply the conformal transformation technique to study systematically a variety of singular plasmonic structures, including two-dimensional sharp edges, rough surfaces, and nanocrescents. These structures are shown to exhibit two distinct features. First, different from a planar metallic surface, the surface plasmon excitations on the examined structures have a lower bound cutoff at a finite ...

Plurisubharmonic functions and their singularities

The theme of these lectures is local and global properties of plurisubharmonic functions. First differential inequalities defining convex, subharmonic and plurisubharmonic functions are discussed. It is proved that the marginal function of a plurisubharmonic function is plurisubharmonic under certain hypotheses. We study the singularities of plurisubharmonic functions using methods from convexi...

Combined Laplacian and Optimization-based Smoothing for Quadratic Mixed Surface Meshes

Quadratic elements place stringent requirements on a surface mesh smoother. One of the biggest challenges is that a good linear element may become invalid when mid-side nodes are introduced. To help alleviate this problem, a new objective function for optimization-based smoothing is proposed for triangular and quadrilateral elements, linear or quadratic. Unlike the current popular approaches, t...

Quadratic Functions, Optimization, and Quadratic Forms