In this paper a computationally effective trajectory generation algorithm of mobile robots is proposed. The algorithm plans a reference path based on Voronoi diagram and Bézier curves, that meet obstacle avoidance criteria. Bézier curves defining the path are created such that the circumference convex polygon of their control points miss all obstacles. To give smoothness, they are connected und...

We consider the Gierer-Meinhardt system with small inhibitor diffusivity and very small activator diffusivity in a bounded and smooth two-dimensional domain. For any given positive integer k we construct a spike cluster consisting of k boundary spikes which all approach the same nondegenerate local maximum point of the boundary curvature. We show that this spike cluster is linearly stable. The ...

On any spacelike hypersurface of constant mean curvature of a Generalized Robertson–Walker spacetime, the hyperbolic angle y between the future-pointing unit normal vector field and the universal time axis is considered. It is assumed that y has a local maximum. A physical consequence of this fact is that relative speeds between normal and comoving observers do not approach the speed of light n...

We introduce a family of conditions on a simplicial complex that we call local klargeness (k ≥ 6 is an integer). They are simply stated, combinatorial and easily checkable. One of our themes is that local 6-largeness is a good analogue of the nonpositive curvature: locally 6-large spaces have many properties similar to nonpositively curved ones. However, local 6-largeness neither implies nor is...

This paper shows that the continuous shearlet transform, a novel directional multiscale transform recently introduced by the authors and their collaborators, provides a precise geometrical characterization for the boundary curves of very general planar regions. This study is motivated by imaging applications, where such boundary curves represent edges of images. The shearlet approach is able to...

Given the Finsler structure (M, F) on a manifold M, a Riemannian structure (M, h) and a linear connection on M are defined. They are obtained as the " average " of the Finsler structure and the Chern connection. This linear connection is the Levi-Civita connection of the Riemannian metric h. The relation between parallel transport of the Chern connection and the Levi-Civita connection of h are ...

terracing is an operator that is applied to potential field data to produce regions of constant field amplitude that are separated by sharp boundaries. magnetic data are usually transformed into pseudo-gravity data (baranov, 1957) prior to the application of terracing. the objective of terracing is ‘to recast potential field maps into a geologic map like format’ (cordell and mccafferty 1989). t...

We show, using purely classical considerations and logical extrapolation of results belonging to point particle theories, that the metric background field in which a string propagates must satisfy an Einstein or an Einstein–like equation. Additionally, there emerge restrictions on the worldsheet curvature, which seems to act as a source for spacetime gravity, even in the absence of other matter...

In this paper, a new ear anatomy feature edge extraction method based on Hessian matrix is proposed. Stable edge is obtained from principal curvature image across scale space. Firstly, the side face image that includes an ear is filtered and forms Gaussian pyramid. Secondly, the 2D gray image in the pyramid was regarded as a surface, maximum and minimum principal curvature and their direction w...