3,995 research outputs found
Submersions, Hamiltonian systems and optimal solutions to the rolling manifolds problem
Given a submersion with an Ehresmann connection ,
we describe how to solve Hamiltonian systems on by lifting our problem to
. Furthermore, we show that all solutions of these lifted Hamiltonian
systems can be described using the original Hamiltonian vector field on
along with a generalization of the magnetic force. This generalized force is
described using the curvature of along with a new form of
parallel transport of covectors vanishing on . Using the
Pontryagin maximum principle, we apply this theory to optimal control problems
and to get results on normal and abnormal extremals. We give a
demonstration of our theory by considering the optimal control problem of one
Riemannian manifold rolling on another without twisting or slipping along
curves of minimal length.Comment: 31 page
Asymptotics of Invariant Metrics in the normal direction and a new characterisation of the unit disk
We give improvements of estimates of invariant metrics in the normal
direction on strictly pseudoconvex domains. Specifically we will give the
second term in the expansion of the metrics. This depends on an improved
localisation result and estimates in the one variable case. Finally we will
give a new characterisation of the unit disk in in terms of the
asymptotic behaviour of quotients of invariant metrics
A Fatou-Bieberbach domain in C^2 which is not Runge
We give an example of a Fatou-Bieberbach domain which is not Runge in C^2
Funeral insurance
Funeral insurance has existed at least since antiquity, and it remains popular in many parts of Africa today. Yet the study of funeral insurance as a distinct form of insurance has hitherto been neglected. This paper presents a model in which funeral insurance combines regular life insurance with a restriction on how the payout is spent. The model predicts that there is an intermediate range of income and wealth where funeral insurance is demanded. The prediction is tested on a nationally representative sample of black South African households, a setting where both life and funeral insurance are widely available. The model also gives conditions under which funeral insurance is not demanded at any level of income and wealth. This may explain why funeral insurance is less popular in developed countries, even among the relatively poor.
Acoustic multipole sources from the Boltzmann equation
By adding a particle source term in the Boltzmann equation of kinetic theory,
it is possible to represent particles appearing and disappearing throughout the
fluid with a specified distribution of particle velocities. By deriving the
wave equation from this modified Boltzmann equation via the conservation
equations of fluid mechanics, multipole source terms in the wave equation are
found. These multipole source terms are given by the particle source term in
the Boltzmann equation. To the Euler level in the momentum equation, a monopole
and a dipole source term appear in the wave equation. To the Navier-Stokes
level, a quadrupole term with negligible magnitude also appears.Comment: 5 pages, to be published in Proceedings of the 36th Scandinavian
Symposium on Physical Acoustic
- âŠ