29,681 research outputs found
New results on production matrices for geometric graphs
We present novel production matrices for non-crossing partitions, connected geometric graphs, and k-angulations, which provide another way of counting the number of such objects. For instance, a formula for the number of connected geometric graphs with given root degree, drawn on a set of n points in convex position in the plane, is presented. Further, we find the characteristic polynomials and we provide a characterization of the eigenvectors of the production matrices.Postprint (author's final draft
Production matrices for geometric graphs
We present production matrices for non-crossing geometric graphs on point sets in convex position, which allow us to derive formulas for the numbers of such graphs. Several known identities for Catalan numbers, Ballot numbers, and Fibonacci numbers arise in a natural way, and also new formulas are obtained, such as a formula for the number of non-crossing geometric graphs with root vertex of given degree. The characteristic polynomials of some of these production matrices are also presented. The proofs make use of generating trees and Riordan arrays.Postprint (updated version
Evaluation of the mean cycle time in stochastic discrete event dynamic systems
We consider stochastic discrete event dynamic systems that have time
evolution represented with two-dimensional state vectors through a vector
equation that is linear in terms of an idempotent semiring. The state
transitions are governed by second-order random matrices that are assumed to be
independent and identically distributed. The problem of interest is to evaluate
the mean growth rate of state vector, which is also referred to as the mean
cycle time of the system, under various assumptions on the matrix entries. We
give an overview of early results including a solution for systems determined
by matrices with independent entries having a common exponential distribution.
It is shown how to extend the result to the cases when the entries have
different exponential distributions and when some of the entries are replaced
by zero. Finally, the mean cycle time is calculated for systems with matrices
that have one random entry, whereas the other entries in the matrices can be
arbitrary nonnegative and zero constants. The random entry is always assumed to
have exponential distribution except for one case of a matrix with zero row
when the particular form of the matrix makes it possible to obtain a solution
that does not rely on exponential distribution assumptions.Comment: The 6th International Conference on Queueing Theory and Network
Applications (QTNA'11), Aug. 23-26, 2011, Seoul, Korea; ACM, New York, ISBN
978-1-4503-0758-
On the max-algebraic core of a nonnegative matrix
The max-algebraic core of a nonnegative matrix is the intersection of column
spans of all max-algebraic matrix powers. Here we investigate the action of a
matrix on its core. Being closely related to ultimate periodicity of matrix
powers, this study leads us to new modifications and geometric
characterizations of robust, orbit periodic and weakly stable matrices.Comment: 27 page
Virtual manufacturing: prediction of work piece geometric quality by considering machine and set-up
Lien vers la version éditeur: http://www.tandfonline.com/doi/full/10.1080/0951192X.2011.569952#.U4yZIHeqP3UIn the context of concurrent engineering, the design of the parts, the production planning and the manufacturing facility must be considered simultaneously. The design and development cycle can thus be reduced as manufacturing constraints are taken into account as early as possible. Thus, the design phase takes into account the manufacturing constraints as the customer requirements; more these constraints must not restrict the creativity of design. Also to facilitate the choice of the most suitable system for a specific process, Virtual Manufacturing is supplemented with developments of numerical computations (Altintas et al. 2005, Bianchi et al. 1996) in order to compare at low cost several solutions developed with several hypothesis without manufacturing of prototypes. In this context, the authors want to predict the work piece geometric more accurately by considering machine defects and work piece set-up, through the use of process simulation. A particular case study based on a 3 axis milling machine will be used here to illustrate the authors’ point of view. This study focuses on the following geometric defects: machine geometric errors, work piece positioning errors due to fixture system and part accuracy
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