The groupoid interpretation of dependent type theory given by Hofmann and Streicher associates to each closed type a category whose objects represent the elements of that type and whose maps represent proofs of equality of elements. The categorial structure ensures that equality is reflexive (identity maps) and transitive (closure under composition); the groupoid structure, which demands that e...

We describe the point and contact equivalence groupoids of an important class two-dimensional quasilinear hyperbolic equations. In particular, we prove that this is normalized in usual sense with respect to transformations, its groupoid generated by first-order prolongation groupoid, vertex group wave equation a family admissible transformations between trivially Darboux-integrable

The junction tree representation provides an attractive structural property for organizing a decomposable graph. In this study, we present a novel stochastic algorithm which we call the Christmas tree algorithm for building of junction trees sequentially by adding one node at a time to the underlying decomposable graph. The algorithm has two important theoretical properties. Firstly, every junc...

The notion of recognition of a language by a finite semigroup can be generalized to recognition by finite groupoids, i.e. sets equipped with a binary operation ‘ · ’ which is not necessarily associative. It is well known that L can be recognized by a groupoid iff L is context-free. But it is also known that some subclasses of groupoids can only recognize regular languages. For example, loops re...

We define the decomposition property for partial actions of discrete groups on C⁎-algebras. Decomposable systems appear naturally in practice, and many commonly occurring can be decomposed into with property. For instance, any action a finite group is an iterated extension decomposable systems. Partial are always globalizable amenable, regardless acting group, their globalization explicitly des...

We will show that deformation quantization in skein theory of oriented 3-manifolds is induced from a topological deformation quantization of the fundamental 2-groupoid of the space of immersions of circles in M . The structure of skein module and its relations with string topology homomorphisms appear through representations of the groupoid structure into the set the objects. The deformation of...