2,447 research outputs found
Maximal subgroups and PST-groups
A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable groups, and maximal subgroups, Arch. Math. (Basel), 2011, 96(1), 19-25] presented some new characterisations of soluble T-groups. The main goal of this paper is to establish PT- and PST-versiosn of Kaplan's results, which enables a better understanding of the relationships between these classes
Effect of partial ionization on wave propagation in solar magnetic flux tubes
Observations show that waves are ubiquitous in the solar atmosphere and may
play an important role for plasma heating. The study of waves in the solar
corona is usually based on linear ideal magnetohydrodynamics (MHD) for a fully
ionized plasma. However, the plasma in the photosphere and the chromosphere is
only partially ionized. Here we investigate theoretically the impact of partial
ionization on MHD wave propagation in cylindrical flux tubes in the two-fluid
model. We derive the general dispersion relation that takes into account the
effects of neutral-ion collisions and the neutral gas pressure. We take the
neutral-ion collision frequency as an arbitrary parameter. Particular results
for transverse kink modes and slow magnetoacoustic modes are shown. We find
that the wave frequencies only depend on the properties of the ionized fluid
when the neutral-ion collision frequency is much lower that the wave frequency.
For high collision frequencies realistic of the solar atmosphere ions and
neutrals behave as a single fluid with an effective density corresponding to
the sum of densities of both fluids and an effective sound velocity computed as
the average of the sound velocities of ions and neutrals. The MHD wave
frequencies are modified accordingly. The neutral gas pressure can be neglected
when studying transverse kink waves but it has to be taken into account for a
consistent description of slow magnetoacoustic waves. The MHD waves are damped
due to neutral-ion collisions. The damping is most efficient when the wave
frequency and the collision frequency are of the same order of magnitude. For
high collision frequencies slow magnetoacoustic waves are more efficiently
damped than transverse kink waves. In addition, we find the presence of
cut-offs for certain combinations of parameters that cause the waves to become
non-propagating.Comment: Accepted for publication in A&
Measuring the purity of a qubit state: entanglement estimation with fully separable measurements
Given a finite number of copies of a qubit state we compute the maximum
fidelity that can be attained using joint-measurement protocols for estimating
its purity. We prove that in the asymptotic limit,
separable-measurement protocols can be as efficient as the optimal
joint-measurement one if classical communication is used. This in turn shows
that the optimal estimation of the entanglement of a two-qubit state can also
be achieved asymptotically with fully separable measurements. The relationship
between our global Bayesian approach and the quantum Cramer-Rao bound is also
discussed.Comment: 5 pages, 1 figure, RevTeX, improved versio
Optimal full estimation of qubit mixed states
We obtain the optimal scheme for estimating unknown qubit mixed states when
an arbitrary number N of identically prepared copies is available. We discuss
the case of states in the whole Bloch sphere as well as the restricted
situation where these states are known to lie on the equatorial plane. For the
former case we obtain that the optimal measurement does not depend on the prior
probability distribution provided it is isotropic. Although the
equatorial-plane case does not have this property for arbitrary N, we give a
prior-independent scheme which becomes optimal in the asymptotic limit of large
N. We compute the maximum mean fidelity in this asymptotic regime for the two
cases. We show that within the pointwise estimation approach these limits can
be obtained in a rather easy and rapid way. This derivation is based on
heuristic arguments that are made rigorous by using van Trees inequalities. The
interrelation between the estimation of the purity and the direction of the
state is also discussed. In the general case we show that they correspond to
independent estimations whereas for the equatorial-plane states this is only
true asymptotically.Comment: 19 pages, no figure
Prefactorized subgroups in pairwise mutually permutable products
The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-012-0257-yWe continue here our study of pairwise mutually and pairwise totally permutable
products. We are looking for subgroups of the product in which the given factorization
induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized
Carter subgroup and a prefactorized system normalizer exist.Aless stringent property
have F-residual, F-projector and F-normalizer for any saturated formation F including the
supersoluble groups.The first and fourth authors have been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain).Ballester-Bolinches, A.; Beidleman, J.; Heineken, H.; Pedraza Aguilera, MC. (2013). Prefactorized subgroups in pairwise mutually permutable products. Annali di Matematica Pura ed Applicata. 192(6):1043-1057. https://doi.org/10.1007/s10231-012-0257-yS104310571926Amberg B., Franciosi S., de Giovanni F.: Products of Groups. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Pedraza-Aguilera, M.C., Pérez-Ramos, M.D.: Totally and Mutually Permutable Products of Finite Groups, Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 65–68. Cambridge University Press, Cambridge (1999)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: On finite products of totally permutable groups. Bull. Aust. Math. Soc. 53, 441–445 (1996)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: Finite groups which are products of pairwise totally permutable subgroups. Proc. Edinb. Math. Soc. 41, 567–572 (1998)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: On pairwise mutually permutable products. Forum Math. 21, 1081–1090 (2009)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: Local classes and pairwise mutually permutable products of finite groups. Documenta Math. 15, 255–265 (2010)Beidleman J.C., Heineken H.: Mutually permutable subgroups and group classes. Arch. Math. 85, 18–30 (2005)Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)Carocca A.: p-supersolvability of factorized groups. Hokkaido Math. J. 21, 395–403 (1992)Carocca, A., Maier, R.: Theorems of Kegel-Wielandt Type Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 195–201. Cambridge University Press, Cambridge, (1999)Doerk K., Hawkes T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Maier R., Schmid P.: The embedding of quasinormal subgroups in finite groups. Math. Z. 131, 269–272 (1973
Optimal path for a quantum teleportation protocol in entangled networks
Bellman's optimality principle has been of enormous importance in the
development of whole branches of applied mathematics, computer science, optimal
control theory, economics, decision making, and classical physics. Examples are
numerous: dynamic programming, Markov chains, stochastic dynamics, calculus of
variations, and the brachistochrone problem. Here we show that Bellman's
optimality principle is violated in a teleportation problem on a quantum
network. This implies that finding the optimal fidelity route for teleporting a
quantum state between two distant nodes on a quantum network with bi-partite
entanglement will be a tough problem and will require further investigation.Comment: 4 pages, 1 figure, RevTeX
Exoplanet HD 209458b : Evaporation strengthened
Following re-analysis of Hubble Space Telescope observations of primary
transits of the extrasolar planet HD209458b at Lyman-alpha, Ben-Jaffel (2007,
BJ007) claims that no sign of evaporation is observed. Here we show that, in
fact, this new analysis is consistent with the one of Vidal-Madjar et al.
(2003, VM003) and supports the detection of evaporation. The apparent
disagreement is mainly due to the disparate wavelength ranges that are used to
derive the transit absorption depth. VM003 derives a (15+/-4)% absorption depth
during transit over the core of the stellar Lyman-alpha line (from -130 km/s to
+100 km/s), and this result agrees with the (8.9+/-2.1)% absorption depth
reported by BJ007 from a slightly expanded dataset but over a larger wavelength
range (+/-200 km/s). These measurements agree also with the (5+/-2)% absorption
reported by Vidal-Madjar et al. (2004) over the whole Lyman-alpha line from
independent, lower-resolution data. We show that stellar Lyman-alpha
variability is unlikely to significantly affect those detections. The HI atoms
must necessarily have velocities above the escape velocities and/or be outside
the Roche lobe, given the lobe shape and orientation. Absorption by HI in
HD209458b's atmosphere has thus been detected with different datasets, and now
with independent analyses. All these results strengthen the concept of
evaporating hot-Jupiters, as well as the modelization of this phenomenon.Comment: To be published in ApJ
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