Under suitable conditions of connectivity or non-bipartiteness, each of the three standard graph products (the Cartesian product, the direct product and the strong product) satisfies the unique prime factorization property, and there are polynomial algorithms to determine the prime factors. This is most easily proved for the Cartesian product. For the other products, current proofs involve a no...

The aim of this paper is to develop a rich set of visual primitives that can be used by a camera-endowed robot as it is exploring a scene and thus generating an attentional sequence––spatio-temporally related sets of visual features. Our starting point is inspired by the work of Gallant et al. on the area V4 response of the macaque monkeys to Cartesian and non-Cartesian stimuli. The novelty of ...

Introduction THE study of topologies on X x Y is motivated by some outstanding deficiencies of the cartesian, that is the usual, topology on the product of spaces. (Throughout this paper all spaces will be assumed to be Hausdorff.) Firstly, the cartesian product of identification maps is not, in general, an identification map. As a consequence certain natural products such as the join and smash...

We present an isoparametric unfitted finite element approach of the CutFEM or Nitsche-XFEM family for simulation two-phase Stokes problems with slip between phases. For generalized Taylor--Hood pair $\mathbf{P}_{k+1}-P_k$, $k\ge1$, we show inf-sup stability property a constant that is independent viscosity ratio, coefficient, position interface respect to background mesh and, course, size. In a...

The category TOP of topological spaces is not cartesian closed, but can be embedded into the cartesian closed category ASSM of assemblies over algebraic lattices, which is a generalisation of Scott's category EQU of equilogical spaces. In this paper, we identify cartesian closed subcategories of assemblies which correspond to well-known separation properties of topology: T 0 ,

A Cartesian network is a modified two-dimensional mesh network consisting of horizontal and vertical networks. At present, two 'traditional' protocols exist for the network: a unicast protocol, and a loop-free broadcast protocol. With the increasing number of multicast applications, there is a clear need for Cartesian Networks to support multicast communications. This paper presents three Carte...

A new kind of parallel mechanism machine called the CGT (Cartesian-Guided Tripod) for three-axis machining, CGP (Cartesian-Guided Pentapod) for five-axis machining, and CGH (Cartesian-Guided Hexapod) for six-axis positioning is presented on this paper. The CGT/CGP/CGH has two kinds of functional independent legs: the driving functional leg and the integrated Cartesian guiding/metrology function...