Thinness and the heat equation

On the thinness and proper thinness of a graph

Graphs with bounded thinness were defined in 2007 as a generalization of interval graphs. In this paper we introduce the concept of proper thinness, such that graphs with bounded proper thinness generalize proper interval graphs. We study the complexity of problems related to the computation of these parameters, describe the behavior of the thinness and proper thinness under three graph operati...

The Heat Equation

Geometric Heat Equation and

We propose a geometric smoothing method based on local curvature in shapes and images which is governed by the geometric heat equation and is a special case of the reaction-diiusion framework proposed by 28]. For shapes, the approach is analogous to the classical heat equation smoothing, but with a renormalization by arc-length at each innnitesimal step. For images, the smoothing is similar to ...

Heat Equation and Potential Burgers Equation

In this work, we construct the general solution to the Heat Equation (HE) and to many tensor structures associated to the Heat Equation, such as Symmetries, Lagrangians, Poisson Brackets (PB) and Lagrange Brackets (LB), using newly devised techniques that may be applied to any linear equation (e.g., Schrödinger Equation in field theory, or the small-oscillations problem in mechanics). In partic...

Heat Equation and Multipliers via the Wave Equation

Recently, Nagel and Stein studied the b-heat equation, where b is the Kohn Laplacian on the boundary of a weakly-pseudoconvex domain of finite type in C. They showed that the Schwartz kernel of e b satisfies good “off-diagonal” estimates, while that of e b −π satisfies good “on-diagonal” estimates, where π denotes the Szegö projection. We offer a simple proof of these results, which easily gene...