23,376 research outputs found
On spectral types of semialgebraic sets
In this work we prove that a semialgebraic set is
determined (up to a semialgebraic homeomorphism) by its ring
of (continuous) semialgebraic functions while its ring of
(continuous) bounded semialgebraic functions only determines besides a
distinguished finite subset . In addition it holds that the
rings and are isomorphic if and only if
is compact. On the other hand, their respective maximal spectra
and endowed with the Zariski topology are always homeomorphic and
topologically classify a `large piece' of . The proof of this fact requires
a careful analysis of the points of the remainder associated with formal paths.Comment: 22 page
A liquid crystal analogue of the cosmic string
We consider the propagation of light in a anisotropic medium with a
topological line defect in the realm of geometrical optics. It is shown that
the effective geometry perceived by light propagating in such medium is that of
a spacial section of the cosmic string spacetime.Comment: 3 pages, 2 figures. Modern Physics Letters A, accepted for
publicatio
Pathway Weathering in Granitoid Rocks from Central Region of Angola: Geochemical and Mineralogical Data
The Central Region of Angola is characterized by the abundance of granitoid rocks, whose weathering âin situâ originated the so-called residual soils. The textural, geochemical and mineralogical properties of these soils depend not only on the chemical composition of parent rock, but mainly on the local climatic and geomorphological characteristics.
In the study area, sampling sites were selected, which extend from the region of Kwanza- Norte (Kassenda, Dondo) through Kwanza-Sul (Cangulo, Quibala and Waco Kungo) until the plateau of Huambo, where samples of fresh rock, weathered rock and its residual soil were collected along each weathering profile.
Chemical analytical data were determined using X-ray fluorescence (XRF) analysis of the major and minor elements, whereas mineralogical data were determined using X-ray diffraction (XRD), on the samples of rock and on the respective residual soil.
The results obtained and their comparative analysis between the sampling sites, as well as along each weathering profile is presented.
This paper allows contributing to the knowledge of the geochemical weathering in tropical areas, as is the case of Angola
Semiclassical Propagation of Wavepackets with Real and Complex Trajectories
We consider a semiclassical approximation for the time evolution of an
originally gaussian wave packet in terms of complex trajectories. We also
derive additional approximations replacing the complex trajectories by real
ones. These yield three different semiclassical formulae involving different
real trajectories. One of these formulae is Heller's thawed gaussian
approximation. The other approximations are non-gaussian and may involve
several trajectories determined by mixed initial-final conditions. These
different formulae are tested for the cases of scattering by a hard wall,
scattering by an attractive gaussian potential, and bound motion in a quartic
oscillator. The formula with complex trajectories gives good results in all
cases. The non-gaussian approximations with real trajectories work well in some
cases, whereas the thawed gaussian works only in very simple situations.Comment: revised text, 24 pages, 6 figure
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