41,602 research outputs found
Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
The local geometry of a Riemannian symmetric space is described completely by
the Riemannian metric and the Riemannian curvature tensor of the space. In the
present article I describe how to compute these tensors for any Riemannian
symmetric space from the Satake diagram, in a way that is suited for the use
with computer algebra systems. As an example application, the totally geodesic
submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
The submission also contains an example implementation of the algorithms and
formulas of the paper as a package for Maple 10, the technical documentation
for this implementation, and a worksheet carrying out the computations for the
space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical
documentatio
Geometrization of the Gauge Connection within a Kaluza-Klein Theory
Within the framework of a Kaluza-Klein theory, we provide the geometrization
of a generic (Abelian and non-Abelian) gauge coupling, which comes out by
choosing a suitable matter fields dependence on the extra-coordinates.
We start by the extension of the Nother theorem to a multidimensional
spacetime being the direct sum of a 4-dimensional Minkowski space and of a
compact homogeneous manifold (whose isometries reflect the gauge symmetry); we
show, how on such a ``vacuum'' configuration, the extra-dimensional components
of the field momentum correspond to the gauge charges. Then we analyze the
structure of a Dirac algebra as referred to a spacetime with the Kaluza-Klein
restrictions and, by splitting the corresponding free-field Lagrangian, we show
how the gauge coupling terms outcome.Comment: 10 pages, no figure, to appear on Int. Journ. Theor. Phy
A dynamic ridesharing dispatch and idle vehicle repositioning strategy with integrated transit transfers
We propose a ridesharing strategy with integrated transit in which a private
on-demand mobility service operator may drop off a passenger directly
door-to-door, commit to dropping them at a transit station or picking up from a
transit station, or to both pickup and drop off at two different stations with
different vehicles. We study the effectiveness of online solution algorithms
for this proposed strategy. Queueing-theoretic vehicle dispatch and idle
vehicle relocation algorithms are customized for the problem. Several
experiments are conducted first with a synthetic instance to design and test
the effectiveness of this integrated solution method, the influence of
different model parameters, and measure the benefit of such cooperation.
Results suggest that rideshare vehicle travel time can drop by 40-60%
consistently while passenger journey times can be reduced by 50-60% when demand
is high. A case study of Long Island commuters to New York City (NYC) suggests
having the proposed operating strategy can substantially cut user journey times
and operating costs by up to 54% and 60% each for a range of 10-30 taxis
initiated per zone. This result shows that there are settings where such
service is highly warranted
A stochastic user-operator assignment game for microtransit service evaluation: A case study of Kussbus in Luxembourg
This paper proposes a stochastic variant of the stable matching model from
Rasulkhani and Chow [1] which allows microtransit operators to evaluate their
operation policy and resource allocations. The proposed model takes into
account the stochastic nature of users' travel utility perception, resulting in
a probabilistic stable operation cost allocation outcome to design ticket price
and ridership forecasting. We applied the model for the operation policy
evaluation of a microtransit service in Luxembourg and its border area. The
methodology for the model parameters estimation and calibration is developed.
The results provide useful insights for the operator and the government to
improve the ridership of the service.Comment: arXiv admin note: substantial text overlap with arXiv:1912.0198
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