We apply our own software package and its extensions ([16, 14, 15, 18]) for visualisations and animations in mathematics to the graphical representation of neighbourhoods in certain relative and weak topologies that arise in the theories of dual spaces of sequence spaces and of matrix transformations between FK spaces. The paper contains a short introduction to some of the main concepts of our ...

2 Naive Surplus Theory 2.1 Consumers who buy 0 or 1 unit I introduce the concept of surplus in one of the simplest models of demand. [This is the model underlying (Bakos and Brynjolfsson, 1999).] Consider a very large population of K consumers facing a market for a single good. Each consumer will buy either one or zero units of this good (per period), depending on the price. Each consumer has a...

Recap: Last time we introduced the principal elements of skeletal models and discussed forward kinematics. Recall that a skeletal model consists of a collection of joints, which have been joined into a rooted tree structure. Each joint of the skeleton is associated with a coordinate frame which specifies its position and orientation in space. Each joint can be rotated (subject to sum constraint...

Motion retiming is an important tool used to edit character animations. It consists of changing the time at which an action occurs during an animation. One example might be editing an animation of a person playing football to change the precise time at which the ball is kicked. It is, nevertheless, a non-trivial task to retime the motion of a set of joints, since spatio-temporal correlation exi...

For the FK representation of the Ising model, we prove that the slab percolation threshold coincides with the critical temperature in any dimension d > 3.

In this paper we combine a survey of the most important topological properties of kinematic maps that appear in robotics, with the exposition of some basic results regarding the topological complexity of a map. In particular, we discuss mechanical devices that consist of rigid parts connected by joints and show how the geometry of the joints determines the forward kinematic map that relates the...

1. N o t a t i o n a n d pre l iminary ideas . A sequence space is a vector subspace of the space co of all real (or complex) sequences. A sequence space E with a locally convex topology r is called a Kspace if the inclusion map E —* co is continuous, when co is endowed with the product topology (co = II^Li (R)*). A i£-space E with a Frechet (i.e., complete, metrizable and locally convex) topol...

Given a set of affine varieties in <3, i.e. planes, lines, and points, the problem tackled in this paper is that of finding all possible configurations for these varieties that satisfy a set of pairwise euclidean distances between them. Many problems in Robotics –such as the forward kinematics of parallel manipulators or the contact formation problem between polyhedral models– can be formulated...

This paper concerns the presentation and analysis of a type of three translational degrees of freedom (DoFs) parallel cube-manipulator. The parallel manipulators are the topology architectures of the DELTA robot and Tsai’s manipulator, respectively, which have three translational DoFs. In the design, the three actuators are arranged according to the Cartesian coordinate system, which means that...