We consider several possibilities on how to select a Filippov sliding vector field on a codimension 2 singularity surface Σ , intersection of two codimension 1 surfaces. We discuss and compare several, old and new, approaches, under the assumption that Σ is nodally attractive. Of specific interest is the selection of a smoothly varying Filippov sliding vector field. As a result of our analysis ...

Aspects of the geometric discretization of electromagnetic fields on simplicial lattices are considered. First, the convenience of the use of exterior differential forms to represent the field quantities through their natural role as duals (cochains) of the geometric constituents of the lattice (chains = nodes, edges, faces, volumes) is briefly reviewed. Then, the use of the barycentric subdivi...

In recent years, a wide range of generalized barycentric coordinates has been suggested. However, all of them lack control over derivatives. We show how the notion of barycentric coordinates can be extended to specify derivatives at control points. This is also known as Hermite interpolation. We introduce a method to modify existing barycentric coordinates to higher order barycentric coordinate...

We quantify conditions that ensure that a signed measure on a Riemannian manifold has a well defined centre of mass. We then use this result to quantify the extent of a neighbourhood on which the Riemannian barycentric coordinates of a set of n+1 points on an n-manifold provide a true coordinate chart, i.e., the barycentric coordinates provide a di↵eomorphism between a neighbourhood of a Euclid...

We propose a novel system which can transform a recipe into any selected regional style (e.g., Japanese, Mediterranean, or Italian). This system has three characteristics. First the system can identify the degree of dietary style mixture of any selected recipe. Second, the system can visualize such dietary style mixtures using barycentric Newton diagrams. Third, the system can suggest ingredien...

In this paper we discuss cordial labeling in context of barycentric subdivision of shell graph, complete bipartite graph Kn,n and wheel graph. AMS subject classification: 05C78.

We discuss three conceivable scenarios of extension and/or modification of the IAU relativistic resolutions on time scales and spatial coordinates beyond the Standard IAU Framework. These scenarios include: (1) the formalism of the monopole and dipole moment transformations of the metric tensor replacing the scale transformations of time and space coordinates; (2) implementing the parameterized...

We prove that the (d − 2)-nd barycentric subdivision of every convex d-ball is shellable. This yields a new characterization of the PL property in terms of shellability: A sphere or a ball is PL if and only if it becomes shellable after sufficiently many barycentric subdivisions. This improves results by Whitehead, Zeeman and Glaser. Moreover, we show the Zeeman conjecture is equivalent to the ...