Accurate dynamic simulation with robust handling of intermittent contact is necessary for a wide range of robotics problems, including the design of parts feeding devices, manipulation and kinodynamic planning, and designing grasp strategies. In this paper we present an implicit time-stepping scheme for dynamic simulation of multibody systems with intermittent contact by incorporating the conta...

There is a prevalent myth in Computer Vision that the gradient weighted algebraic distance, the so-called “Sampson Error,” is a first order approximation of the distance from a point to a curve or surface. In truth, however, it is the exact geometric distance to the first order approximation of the curve. The linguistic difference is subtle, but mathematically, the two statements are at odds. I...

Let α be a real algebraic number greater than 1. We establish an effective lower bound for the distance between integral power of and its nearest integer.

A graph is edge-distance-regular when it is distance-regular around each of its edges and it has the same intersection numbers for any edge taken as a root. In this paper we give some (combinatorial and algebraic) proofs of the fact that every edge-distance-regular graph Γ is distance-regular and homogeneous. More precisely, Γ is edge-distance-regular if and only if it is bipartite distance-reg...

Given a perfect coloring of graph, we prove that the $L_1$ distance between two rows adjacency matrix graph is not less than corresponding parameter coloring. With help an algebraic approach, deduce corollaries this result for $2$-colorings, colorings in distance-$l$ graphs and distance-regular graphs. We also provide examples when obtained property reject several putative matrices infinite

The concept of weak algebraic hyperstructures or Hv-structures constitutes a generalization of the well-known algebraic hyperstructures (semihypergroup, hypergroup and so on). The overall aim of this paper is to present an introduction to some of the results, methods and ideas about chemical examples of weak algebraic hyperstructures. In this paper after an introduction of basic definitions and...

Algebraic systems are constructed from which series of maximum distance separable (mds) codes are derived. The methods use unit and idempotent schemes.

Dissipative Hamiltonian (DH) systems are an important concept in energy based modeling of dynamical systems. One of the major advantages of the DH formulation is that system properties are encoded in an algebraic way. For instance, the algebraic structure of DH systems guarantees that the system is automatically stable. In this paper the question is discussed when a linear constant coefficient ...

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. In this paper we introduce the concept of algebraic distance on hypergraphs and demonstrate its use as an algorithmic component in the coars...

In this chapter, we present an algebraic framework in which a set of simple, intuitive operations applicable to music can be flexibly combined to realize a target application and generate music. We formalize the concept of time-span tree introduced by Lerdahl and Jackendoff (1983) in their Generative Theory of Tonal Music (GTTM) and define the distance between time-span trees, on the hypothesis...