This paper deals with the motion interpolation of an object that satisfies the kinematic constraints imposed by planar 6R closed chains. The paper brings together the well-known kinematics of planar 6R closed chains and the freeform rational motions to synthesize the constrained piecewise rational motions in the Cartesian space. The methodology adopted in this paper is based on transforming the...

Polynomial functors (over Set or other locally cartesian closed categories) are useful in the theory of data types, where they are often called containers. They are also useful in algebra, combinatorics, topology, and higher category theory, and in this broader perspective the polynomial aspect is often prominent and justifies the terminology. For example, Tambara’s theorem states that the cate...

We extend the Theory of Computation on real numbers, continuous real functions, and bounded closed Euclidean subsets, to compact metric spaces (X, d): thereby generically including computational and optimization problems over higher types, such as the compact ‘hyper’ spaces of (i) nonempty closed subsets of X w.r.t. Hausdorff metric, and of (ii) equicontinuous functions on X . The thus obtained...

We present a model construction for the Calculus of Constructions (CC) where all dependencies are carried out in a set-theoretical setting. The Soundness Theorem is proved and as a consequence of it Strong Normalization for CC is obtained. Some other applications of our model constructions are: showing that CC 4Classical logic is consistent (by constructing a model for it} and showing that the ...

In [Wells, 1990] the second author introduced the notion of form, a graph-based method of specification of mathematical structures that generalizes Ehresmann’s sketches. In [Bagchi and Wells, 1996], the authors produced a structure for forms which provides a uniform proof theory based on finite-limit constructions for many types of forms, including all types of sketches and also forms that can ...

The inspiration for this paper is a result proved by Michael Smyth which states that Gordon Plotkin's category SFP is the largest cartesian closed category of domains. Although this category is easily enough motivated from concepts in domain theory and category theory, it is clearly harder to describe and less \elementary" than the most popular categories of domains for denotational semantics. ...

Infinite contexts and their corresponding lattices are of theoretical and practical interest since they may offer connections with and insights from other mathematical structures which are normally not restricted to the finite cases. In this paper we establish a systematic connection between formal concept analysis and domain theory as a categorical equivalence, enriching the link between the t...