12,447 research outputs found
Skinner-Rusk approach to time-dependent mechanics
The geometric approach to autonomous classical mechanical systems in terms of
a canonical first-order system on the Whitney sum of the tangent and cotangent
bundle, developed by R. Skinner and R. Rusk, is extended to the time-dependent
framework
Anyons as spinning particles
A model-independent formulation of anyons as spinning particles is presented.
The general properties of the classical theory of (2+1)-dimensional
relativistic fractional spin particles and some properties of their quantum
theory are investigated. The relationship between all the known approaches to
anyons as spinning particles is established. Some widespread misleading notions
on the general properties of (2+1)-dimensional anyons are removed.Comment: 29 pages, LaTeX, a few corrections and references added; to appear in
Int. J. Mod. Phys.
Linear Differential Equations for a Fractional Spin Field
The vector system of linear differential equations for a field with arbitrary
fractional spin is proposed using infinite-dimensional half-bounded unitary
representations of the group. In the case of
-dimensional nonunitary representations of that group, ,
they are transformed into equations for spin- fields. A local gauge symmetry
associated to the vector system of equations is identified and the simplest
gauge invariant field action, leading to these equations, is constructed.Comment: 15 pages, LATEX, revised version of the preprint DFTUZ/92/24 (to be
published in J. Math. Phys.
Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication
This paper proposes a novel class of distributed continuous-time coordination
algorithms to solve network optimization problems whose cost function is a sum
of local cost functions associated to the individual agents. We establish the
exponential convergence of the proposed algorithm under (i) strongly connected
and weight-balanced digraph topologies when the local costs are strongly convex
with globally Lipschitz gradients, and (ii) connected graph topologies when the
local costs are strongly convex with locally Lipschitz gradients. When the
local cost functions are convex and the global cost function is strictly
convex, we establish asymptotic convergence under connected graph topologies.
We also characterize the algorithm's correctness under time-varying interaction
topologies and study its privacy preservation properties. Motivated by
practical considerations, we analyze the algorithm implementation with
discrete-time communication. We provide an upper bound on the stepsize that
guarantees exponential convergence over connected graphs for implementations
with periodic communication. Building on this result, we design a
provably-correct centralized event-triggered communication scheme that is free
of Zeno behavior. Finally, we develop a distributed, asynchronous
event-triggered communication scheme that is also free of Zeno with asymptotic
convergence guarantees. Several simulations illustrate our results.Comment: 12 page
Note on islands in path-length sequences of binary trees
An earlier characterization of topologically ordered (lexicographic)
path-length sequences of binary trees is reformulated in terms of an
integrality condition on a scaled Kraft sum of certain subsequences (full
segments, or islands). The scaled Kraft sum is seen to count the set of
ancestors at a certain level of a set of topologically consecutive leaves is a
binary tree.Comment: 4 page
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