5,977 research outputs found
Isotropic covariance functions on graphs and their edges
We develop parametric classes of covariance functions on linear networks and
their extension to graphs with Euclidean edges, i.e., graphs with edges viewed
as line segments or more general sets with a coordinate system allowing us to
consider points on the graph which are vertices or points on an edge. Our
covariance functions are defined on the vertices and edge points of these
graphs and are isotropic in the sense that they depend only on the geodesic
distance or on a new metric called the resistance metric (which extends the
classical resistance metric developed in electrical network theory on the
vertices of a graph to the continuum of edge points). We discuss the advantages
of using the resistance metric in comparison with the geodesic metric as well
as the restrictions these metrics impose on the investigated covariance
functions. In particular, many of the commonly used isotropic covariance
functions in the spatial statistics literature (the power exponential,
Mat{\'e}rn, generalized Cauchy, and Dagum classes) are shown to be valid with
respect to the resistance metric for any graph with Euclidean edges, whilst
they are only valid with respect to the geodesic metric in more special cases.Comment: 6 figures, 1 tabl
Energy and angular momentum of general 4-dimensional stationary axi-symmetric spacetime in teleparallel geometry
We derive an exact general axi-symmetric solution of the coupled
gravitational and electromagnetic fields in the tetrad theory of gravitation.
The solution is characterized by four parameters (mass), (charge),
(rotation) and (NUT). We then, calculate the total exterior energy using
the energy-momentum complex given by M{\o}ller in the framework of
Weitzenbck geometry. We show that the energy contained in a sphere is
shared by its interior as well as exterior. We also calculate the components of
the spatial momentum to evaluate the angular momentum distribution. We show
that the only non-vanishing components of the angular momentum is in the Z
direction.Comment: Latex. Will appear in IJMP
A set-valued framework for birth-and-growth process
We propose a set-valued framework for the well-posedness of birth-and-growth
process. Our birth-and-growth model is rigorously defined as a suitable
combination, involving Minkowski sum and Aumann integral, of two very general
set-valued processes representing nucleation and growth respectively. The
simplicity of the used geometrical approach leads us to avoid problems arising
by an analytical definition of the front growth such as boundary regularities.
In this framework, growth is generally anisotropic and, according to a
mesoscale point of view, it is not local, i.e. for a fixed time instant, growth
is the same at each space point
Fingerprint Analysis with Marked Point Processes
We present a framework for fingerprint matching based on marked point process
models. An efficient Monte Carlo algorithm is developed to calculate the
marginal likelihood ratio for the hypothesis that two observed prints originate
from the same finger against the hypothesis that they originate from different
fingers. Our model achieves good performance on an NIST-FBI fingerprint
database of 258 matched fingerprint pairs
Kerr-Newman Solution and Energy in Teleparallel Equivalent of Einstein Theory
An exact charged axially symmetric solution of the coupled gravitational and
electromagnetic fields in the teleparallel equivalent of Einstein theory is
derived. It is characterized by three parameters ``the gravitational mass
, the charge parameter and the rotation parameter " and its
associated metric gives Kerr-Newman spacetime. The parallel vector field and
the electromagnetic vector potential are axially symmetric. We then, calculate
the total energy using the gravitational energy-momentum. The energy is found
to be shared by its interior as well as exterior. Switching off the charge
parameter we find that no energy is shared by the exterior of the Kerr-Newman
black hole.Comment: 11 pages, Latex. Will appear in Mod. Phys. Lett.
Simple Model for Wet Granular Materials with Liquid Clusters
We propose a simple phenomenological model for wet granular media to take
into account many particle interaction through liquid in the funicular state as
well as two-body cohesive force by a liquid bridge in the pendular state. In
the wet granular media with small liquid content, liquid forms a bridge at each
contact point, which induces two-body cohesive force due to the surface
tension. As the liquid content increases, some liquid bridges merge, and more
than two grains interact through a single liquid cluster. In our model, the
cohesive force acts between the grains connected by a liquid-gas interface. As
the liquid content increases, the number of grains that interact through the
liquid increases, but the liquid-gas interface may decrease when liquid
clusters are formed. Due to this competition, our model shows that the shear
stress has a maximum as a function of the liquid-content.Comment: 6 pages, 8 figures. Discussion is updated. Accepted for publication
in EP
Energy Contents of Gravitational Waves in Teleparallel Gravity
The conserved quantities, that are, gravitational energy-momentum and its
relevant quantities are investigated for cylindrical and spherical
gravitational waves in the framework of teleparallel equivalent of General
Relativity using the Hamiltonian approach. For both cylindrical and spherical
gravitational waves, we obtain definite energy and constant momentum. The
constant momentum shows consistency with the results available in General
Relativity and teleparallel gravity. The angular momentum for cylindrical and
spherical gravitational waves also turn out to be constant. Further, we
evaluate their gravitational energy-momentum fluxes and gravitational pressure.Comment: 14 pages, accepted for publication in Mod. Phys. Lett.
Cox processes driven by transformed Gaussian processes on linear networks -- A review and new contributions
There is a lack of point process models on linear networks. For an arbitrary
linear network, we consider new models for a Cox process with an isotropic pair
correlation function obtained in various ways by transforming an isotropic
Gaussian process which is used for driving the random intensity function of the
Cox process. In particular we introduce three model classes given by log
Gaussian, interrupted, and permanental Cox processes on linear networks, and
consider for the first time statistical procedures and applications for
parametric families of such models. Moreover, we construct new simulation
algorithms for Gaussian processes on linear networks and discuss whether the
geodesic metric or the resistance metric should be used for the kind of Cox
processes studied in this paper
Elementary analysis of the special relativistic combination of velocities, Wigner rotation, and Thomas precession
The purpose of this paper is to provide an elementary introduction to the
qualitative and quantitative results of velocity combination in special
relativity, including the Wigner rotation and Thomas precession. We utilize
only the most familiar tools of special relativity, in arguments presented at
three differing levels: (1) utterly elementary, which will suit a first course
in relativity; (2) intermediate, to suit a second course; and (3) advanced, to
suit higher level students. We then give a summary of useful results, and
suggest further reading in this often obscure field.Comment: V1: 25 pages, 6 figures; V2: 22 pages, 5 figures. The revised version
is shortened and the arguments streamlined. Minor changes in notation and
figures. This version matches the published versio
The evolution of field early-type galaxies to z~0.7
We have measured the Fundamental Plane (FP) parameters for a sample of 30
field early-type galaxies (E/S0) in the redshift range 0.1<z<0.66. We find
that: i) the FP is defined and tight out to the highest redshift bin; ii) the
intercept \gamma evolves as d\gamma/dz=0.58+0.09-0.13 (for \Omega=0.3,
\Omega_{\Lambda}=0.7), or, in terms of average effective mass to light ratio,
as d\log(M/L_B)/dz=-0.72+0.11-0.16, i.e. faster than is observed for cluster
E/S0 -0.49+-0.05. In addition, we detect [OII] emission >5\AA in 22% of an
enlarged sample of 42 massive E/S0 in the range 0.1<z<0.73, in contrast with
the quiescent population observed in clusters at similar z. We interpret these
findings as evidence that a significant fraction of massive field E/S0
experiences secondary episodes of star-formation at z<1.Comment: ApJ Letters, in pres
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