We propose in this letter a motion planning method for legged robot locomotion based on Geometric Heat Flow framework. The task is challenging due to the hybrid nature of dynamics and contact constraints. encode constraints into Riemannian inner product, product defined so that short curves correspond admissible motions system. rely affine geometric heat flow deform an arbitrary path connecting...

Since 1915, statisticians have been applying Fisher’s Z-transformation to Pearson product-moment correlation coefficients. We offer new geometric interpretations of this transformation.

We consider the invariant measure of a homogeneous continuoustime Markov process in the quarter-plane. The basic solutions of the global balance equation are the geometric distributions. We first show that the invariant measure can not be a finite linear combination of basic geometric distributions, unless it consists of a single basic geometric distribution. Second, we show that a countable li...

During inspection of 21 frozen breaded raw shrimp processors, 861 finished product units (retail packages) and 778 line samples were collected and analyzed bacteriologically. The bacteriological results for the finished product samples collected in plants with poor and good sanitary controls are presented and compared. The samples consisted of 4 to 38 units (retail packages) of the finished pro...

In this paper we develop several algebraic structures on the simplicial cochains of a triangulated manifold and prove they converge to their differential-geometric analogues as the triangulation becomes small. The first such result is for a cochain cup product converging to the wedge product on differential forms. Moreover, we show any extension of this product to a C∞algebra also converges to ...

It is shown that under suitable conditions an eigenvalue of a product of companion matrices has geometric multiplicity equal to one. The result is used to show that for a class of Random Walks in Periodic Environments recurrence is equivalent to a product of companion matrices having 1 as an eigenvalue of algebraic multiplicity greater than one.

A finite Blaschke product is a product of finitely many automorphisms of the unit disk. This brief survey covers some of the main topics in the area, including characterizations of Blaschke products, approximation theorems, derivatives and residues of Blaschke products, geometric localization of zeros, and selected other topics.

To realize concurrent engineering, different product development stages must be linked to each other on the basis of an integrated and consistent product information model. Features are used as information units for associating specific sets of geometric entities. In this paper, semantics of design and machining features are discussed. Furthermore, feature association and unification for inform...

It is shown that under suitable conditions an eigenvalue of a product of companion matrices has geometric multiplicity equal to one. The result is used to show that for a class of Random Walks in Periodic Environments recurrence is equivalent to a product of companion matrices having 1 as an eigenvalue of algebraic multiplicity greater than one.

We use van Kampen diagram techniques to give a new geometric proof of Baumslag and Roseblade’s result that a non–free finitely presented subgroup of a direct product of two free groups is virtually a product of subgroups of the factors.