3,654 research outputs found
Additive combinatorics methods in associative algebras
We adapt methods coming from additive combinatorics in groups to the study of
linear span in associative unital algebras. In particular, we establish for
these algebras analogues of Diderrich-Kneser's and Hamidoune's theorems on
sumsets and Tao's theorem on sets of small doubling. In passing we classify the
finite-dimensional algebras over infinite fields with finitely many
subalgebras. These algebras play a crucial role in our linear version of
Diderrich-Kneser's theorem. We also explain how the original theorems for
groups we linearize can be easily deduced from our results applied to group
algebras. Finally, we give lower bounds for the Minkowski product of two
subsets in finite monoids by using their associated monoid algebras.Comment: In this second version, we clarify and extend the domain of validity
of Diderrich-Kneser's theorem for associative algebras. We simplify the
proofs and we also add a section on Kneser's and Hamidoune's theorem in
monoi
Einfluss von Komorbiditäten auf das Überleben von Patienten mit therapieassoziierter Akuter Myeloischer Leukämie
Phase synchronization in tilted deterministic ratchets
We study phase synchronization for a ratchet system. We consider the
deterministic dynamics of a particle in a tilted ratchet potential with an
external periodic forcing, in the overdamped case. The ratchet potential has to
be tilted in order to obtain a rotator or self-sustained nonlinear oscillator
in the absence of external periodic forcing. This oscillator has an intrinsic
frequency that can be entrained with the frequency of the external driving. We
introduced a linear phase through a set of discrete time events and the
associated average frequency, and show that this frequency can be synchronized
with the frequency of the external driving. In this way, we can properly
characterize the phenomenon of synchronization through Arnold tongues, which
represent regions of synchronization in parameter space, and discuss their
implications for transport in ratchets.Comment: 14 pages, 6 figures, Physica A, in pres
Circumbinary Ring, Circumstellar disks and accretion in the binary system UY Aurigae
Recent exo-planetary surveys reveal that planets can orbit and survive around
binary stars. This suggests that some fraction of young binary systems which
possess massive circumbinary disks (CB) may be in the midst of planet
formation. However, there are very few CB disks detected. We revisit one of the
known CB disks, the UY Aurigae system, and probe 13CO 2-1, C18O 2-1, SO
5(6)-4(5) and 12CO 3-2 line emission and the thermal dust continuum. Our new
results confirm the existence of the CB disk. In addition, the circumstellar
(CS) disks are clearly resolved in dust continuum at 1.4 mm. The spectral
indices between the wavelengths of 0.85 mm and 6 cm are found to be
surprisingly low, being 1.6 for both CS disks. The deprojected separation of
the binary is 1.26" based on our 1.4 mm continuum data. This is 0.07" (10 AU)
larger than in earlier studies. Combining the fact of the variation of UY Aur B
in band, we propose that the CS disk of an undetected companion UY Aur Bb
obscures UY Aur Ba. A very complex kinematical pattern inside the CB disk is
observed due to a mixing of Keplerian rotation of the CB disk, the infall and
outflow gas. The streaming gas accreting from the CB ring toward the CS disks
and possible outflows are also identified and resolved. The SO emission is
found to be at the bases of the streaming shocks. Our results suggest that the
UY Aur system is undergoing an active accretion phase from the CB disk to the
CS disks. The UY Aur B might also be a binary system, making the UY Aur a
triple system.Comment: 14 pages, 11 figures; accepted for publication in Ap
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