The combinatorial dimension relative to an arbitrary fractional Cartesian product is defined. Relations between dimensions in certain archetypal instances are derived. Random sets with arbitrarily prescribed dimensions are produced; in particular, scales of combinatorial dimension are shown to be continuously and independently calibrated. A combinatorial concept of cylindricity is key. © 2004 W...

We present a Cartesian closed category ELoc of equilocales, which contains the category Loc of locales as a reflective full subcategory. The embedding of Loc into ELoc preserves products and all exponentials of exponentiable locales.

The paper’s main objective is to propose a new controller for robot manipulators on Cartesian Coordinates with formal stability proof. To verify the proposed controller’s behavior we need to compare it against the Cartesian PD controller, this comparison is accomplish by means of the Performance Index method that is an advantage to obtain a Scalar value of the sum of the error. Key–Words: Carte...

A Cartesian grid generation methodology is developed for unsteady control volume computational fluid dynamic (CFD) solvers. Arbitrary combinations and numbers of moving and stationary boundaries are allowed to exist in the two-dimensional Cartesian grid template. Specific definitions for the possible cases, CFD solver requirements and moving geometry handling algorithms of Cartesian grids are d...

The G_DACG (Genetic Discovery of Additive Cartesian Granule feature models) constructive induction algorithm is presented as a means of automatically identifying rulebased Cartesian granule feature models from example data. G_DACG combines the powerful search capabilities of genetic programming with a rather novel and cheap fitness function based upon the semantic separation of learnt concepts ...

We use the link between the existence of tilings in Manhattan metric with {1}-bowls and minimum total dominating sets of Cartesian products of paths and cycles. From the existence of such a tiling, we deduce the asymptotical values of the total domination numbers of these graphs and we deduce the total domination numbers of some Cartesian products of cycles. Finally, we investigate the problem ...

Purpose Many sick adults and children are unable to perform long breath-holds required for conventional, Cartesian phase-contrast (PC) sequences. Using a prospectivelytriggered spiral PCMR sequence accelerated with sensitivity encoding (SENSE), it should be possible to achieve high resolution PCMR data in a short breath-hold. The aim of this study was to compare flow volumes measured using: a) ...

A graph G is 1-homogeneous if certain isomorphisms between similarly embedded induced subgraphs of G extend to automorphisms of G. We show that the only connected composite 1-homogeneous graphs are the cube, and Kn ×K2 and Kn ×Kn with n ≥ 2.

Cartesian differential categories were introduced to provide an abstract axiomatization of categories of differentiable functions. The fundamental example is the category whose objects are Euclidean spaces and whose arrows are smooth maps. Monoidal differential categories provide the framework for categorical models of differential linear logic. The coKleisli category of any monoidal differenti...