A class of exact solutions of the dispersionless Toda hierarchy constrained by a string equation is obtained. These solutions represent deformations of analytic curves with a finite number of nonzero harmonic moments. The corresponding τ -functions are determined and the emergence of cusps is studied.

A quasisymmetric graph is a curve whose projection onto a line is a quasisymmetric map. We show that this class of curves is related to solutions of the reduced Beltrami equation and to a generalization of the Zygmund class Λ∗. This relation makes it possible to use the tools of harmonic analysis to construct nontrivial examples of quasisymmetric graphs and of quasiconformal maps.

We investigate geometric curvature energies on closed curves involving integral versions of the Menger curvature. In particular, we prove geometric variants of Morrey-Sobolev and Morrey-space imbedding theorems, which may be viewed as counterparts to respective results on one-dimensional sets in the context of harmonic analysis. Mathematics Subject Classification (2010): 28A75 (primary); 53A04,...

Harmonic weak Maass forms of half-integral weight are the subject of many recent works. They are closely related to Ramanujan’s mock theta functions, their theta lifts give rise to Arakelov Green functions, and their coefficients are often related to central values and derivatives of Hecke L-functions. We present an algorithm to compute harmonic weak Maass forms numerically, based on the automo...

$\mathcal{H}-$holomorphic curves are solutions of a specific modification the pseudoholomorphic curve equation in symplectizations involving harmonic $1-$form as perturbation term. In this paper we compactify moduli space with priori bounds on $1-$forms.

The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it mig...

In the early days of quantum mechanics, Schrödinger noticed that oscillations of a wave packet in a one-dimensional harmonic potential well are periodic and, in contrast to those in anharmonic potential wells, do not experience distortion over time. This original idea did not find applications up to now since an exact one-dimensional harmonic resonator does not exist in nature and has not been ...

We study the streamlines of ?-harmonic functions in planar convex rings. include polygons. The points where can meet are characterized: they lie on certain curves. gradient has constant norm along outside set meeting points, infinity-ridge.

Utility and meaning in the behavior of an agent are highly contingent on the agent's ability to semantically embed its actions in the context of its environment. Such an ability is cloned into an agent using a class of intelligent motion controllers that are called motion planners. Designing a motion planner is not an easy task. A planner is the hub that integrates the internal environment of a...