469,953 research outputs found
Componentwise and Cartesian decompositions of linear relations
Let be a, not necessarily closed, linear relation in a Hilbert space
\sH with a multivalued part \mul A. An operator in \sH with \ran
B\perp\mul A^{**} is said to be an operator part of when A=B \hplus
(\{0\}\times \mul A), where the sum is componentwise (i.e. span of the
graphs). This decomposition provides a counterpart and an extension for the
notion of closability of (unbounded) operators to the setting of linear
relations. Existence and uniqueness criteria for the existence of an operator
part are established via the so-called canonical decomposition of . In
addition, conditions are developed for the decomposition to be orthogonal
(components defined in orthogonal subspaces of the underlying space). Such
orthogonal decompositions are shown to be valid for several classes of
relations. The relation is said to have a Cartesian decomposition if
A=U+\I V, where and are symmetric relations and the sum is
operatorwise. The connection between a Cartesian decomposition of and the
real and imaginary parts of is investigated
Determination of the dynamical structure of galaxies using optical spectra
Galaxy spectra are a rich source of kinematical information since the shapes
of the absorption lines reflect the movement of stars along the line-of-sight.
We present a technique to directly build a dynamical model for a galaxy by
fitting model spectra, calculated from a dynamical model, to the observed
galaxy spectra. Using synthetic spectra from a known galaxy model we
demonstrate that this technique indeed recovers the essential dynamical
characteristics of the galaxy model. Moreover, the method allows a
statistically meaningful error analysis on the resulting dynamical quantities.Comment: 14 pages, 14 figures, Latexfile, MNRAS, in pres
Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas
The self-gravitating thermal gas (non-relativistic particles of mass m at
temperature T) is exactly equivalent to a field theory with a single scalar
field phi(x) and exponential self-interaction. We build up perturbation theory
around a space dependent stationary point phi_0(r) in a finite size domain
delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica-
tions (interstellar medium,galaxy distributions).We compute the correlations of
the gravitational potential (phi) and of the density and find that they scale;
the latter scales as 1/r^2. A rich structure emerges in the two-point correl-
tors from the phi fluctuations around phi_0(r). The n-point correlators are
explicitly computed to the one-loop level.The relevant effective coupling turns
out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE)
for the n-point correlator are derived and the RG flow for the effective
coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence
on tau emerges here.lambda(tau) vanishes each time tau approaches discrete
values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior
[lambda(tau) decreasing with increasing tau] is here connected with low density
self-similar fractal structures fitting one into another.For scales smaller
than the points tau_n, ultraviolet unstable behaviour appears which we connect
to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we
get a hierarchy of scales and Jeans lengths following the geometric progression
R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is
expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.Comment: LaTex, 31 pages, 11 .ps figure
Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes
The string propagation equations in axisymmetric spacetimes are exactly
solved by quadratures for a planetoid Ansatz. This is a straight
non-oscillating string, radially disposed, which rotates uniformly around the
symmetry axis of the spacetime. In Schwarzschild black holes, the string stays
outside the horizon pointing towards the origin. In de Sitter spacetime the
planetoid rotates around its center. We quantize semiclassically these
solutions and analyze the spin/(mass) (Regge) relation for the planetoids,
which turns out to be non-linear.Comment: Latex file, 14 pages, two figures in .ps files available from the
author
Effects of a mixed vector-scalar kink-like potential for spinless particles in two-dimensional spacetime
The intrinsically relativistic problem of spinless particles subject to a
general mixing of vector and scalar kink-like potentials () is investigated. The problem is mapped into the exactly solvable
Surm-Liouville problem with the Rosen-Morse potential and exact bounded
solutions for particles and antiparticles are found. The behaviour of the
spectrum is discussed in some detail. An apparent paradox concerning the
uncertainty principle is solved by recurring to the concept of effective
Compton wavelength.Comment: 13 pages, 4 figure
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