79,902 research outputs found
An Overview of Variational Integrators
The purpose of this paper is to survey some recent advances in variational
integrators for both finite dimensional mechanical systems as well as continuum
mechanics. These advances include the general development of discrete
mechanics, applications to dissipative systems, collisions, spacetime integration algorithms,
AVI’s (Asynchronous Variational Integrators), as well as reduction for
discrete mechanical systems. To keep the article within the set limits, we will only
treat each topic briefly and will not attempt to develop any particular topic in
any depth. We hope, nonetheless, that this paper serves as a useful guide to the
literature as well as to future directions and open problems in the subject
Automorphisms of algebras and Bochner`s property for discrete vector orthogonal polynomials
We construct new families of discrete vector orthogonal polynomials that have
the property to be eigenfunctions of some difference operator. They are
extensions of Charlier, Meixner and Kravchuk polynomial systems. The ideas
behind our approach lie in the studies of bispectral operators. We exploit
automorphisms of associative algebras which transform elementary (vector)
orthogonal polynomial systems which are eigenfunctions of a difference operator
into other systems of this type. While the extension of Charlier polynomilas is
well known it is obtained by different methods. The extension of Meixner
polynomial system is new.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1512.0389
Parameterized complexity of machine scheduling: 15 open problems
Machine scheduling problems are a long-time key domain of algorithms and
complexity research. A novel approach to machine scheduling problems are
fixed-parameter algorithms. To stimulate this thriving research direction, we
propose 15 open questions in this area whose resolution we expect to lead to
the discovery of new approaches and techniques both in scheduling and
parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc
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