23,209 research outputs found
On the intersection of free subgroups in free products of groups
Let (G_i | i in I) be a family of groups, let F be a free group, and let G =
F *(*I G_i), the free product of F and all the G_i. Let FF denote the set of
all finitely generated subgroups H of G which have the property that, for each
g in G and each i in I, H \cap G_i^{g} = {1}. By the Kurosh Subgroup Theorem,
every element of FF is a free group. For each free group H, the reduced rank of
H is defined as r(H) = max{rank(H) -1, 0} in \naturals \cup {\infty} \subseteq
[0,\infty]. To avoid the vacuous case, we make the additional assumption that
FF contains a non-cyclic group, and we define sigma := sup{r(H\cap
K)/(r(H)r(K)) : H, K in FF and r(H)r(K) \ne 0}, sigma in [1,\infty]. We are
interested in precise bounds for sigma. In the special case where I is empty,
Hanna Neumann proved that sigma in [1,2], and conjectured that sigma = 1;
almost fifty years later, this interval has not been reduced. With the
understanding that \infty/(\infty -2) = 1, we define theta := max{|L|/(|L|-2) :
L is a subgroup of G and |L| > 2}, theta in [1,3]. Generalizing Hanna Neumann's
theorem, we prove that sigma in [theta, 2 theta], and, moreover, sigma = 2
theta if G has 2-torsion. Since sigma is finite, FF is closed under finite
intersections. Generalizing Hanna Neumann's conjecture, we conjecture that
sigma = theta whenever G does not have 2-torsion.Comment: 28 pages, no figure
Measurement of the total energy of an isolated system by an internal observer
We consider the situation in which an observer internal to an isolated system
wants to measure the total energy of the isolated system (this includes his own
energy, that of the measuring device and clocks used, etc...). We show that he
can do this in an arbitrarily short time, as measured by his own clock. This
measurement is not subjected to a time-energy uncertainty relation. The
properties of such measurements are discussed in detail with particular
emphasis on the relation between the duration of the measurement as measured by
internal clocks versus external clocks.Comment: 7 pages, 1 figur
Is MS1054-03 an exceptional cluster? A new investigation of ROSAT/HRI X-ray data
We reanalyzed the ROSAT/HRI observation of MS1054-03, optimizing the channel
HRI selection and including a new exposure of 68 ksec. From a wavelet analysis
of the HRI image we identify the main cluster component and find evidence for
substructure in the west, which might either be a group of galaxies falling
onto the cluster or a foreground source. Our 1-D and 2-D analysis of the data
show that the cluster can be fitted well by a classical betamodel centered only
20arcsec away from the central cD galaxy. The core radius and beta values
derived from the spherical model(beta = 0.96_-0.22^+0.48) and the elliptical
model (beta = 0.73+/-0.18) are consistent. We derived the gas mass and total
mass of the cluster from the betamodel fit and the previously published ASCA
temperature (12.3^{+3.1}_{-2.2} keV). The gas mass fraction at the virial
radius is fgas = (14[-3,+2.5]+/-3)% for Omega_0=1, where the errors in brackets
come from the uncertainty on the temperature and the remaining errors from the
HRI imaging data. The gas mass fraction computed for the best fit ASCA
temperature is significantly lower than found for nearby hot clusters,
fgas=20.1pm 1.6%. This local value can be matched if the actual virial
temperature of MS1054-032 were close to the lower ASCA limit (~10keV) with an
even lower value of 8 keV giving the best agreement. Such a bias between the
virial and measured temperature could be due to the presence of shock waves in
the intracluster medium stemming from recent mergers. Another possibility, that
reconciles a high temperature with the local gas mass fraction, is the
existence of a non zero cosmological constant.Comment: 12 pages, 5 figures, accepted for publication in Ap
Back action of graphene charge detectors on graphene and carbon nanotube quantum dots
We report on devices based on graphene charge detectors (CDs) capacitively
coupled to graphene and carbon nanotube quantum dots (QDs). We focus on back
action effects of the CD on the probed QD. A strong influence of the bias
voltage applied to the CD on the current through the QD is observed. Depending
on the charge state of the QD the current through the QD can either strongly
increase or completely reverse as a response to the applied voltage on the CD.
To describe the observed behavior we employ two simple models based on single
electron transport in QDs with asymmetrically broadened energy distributions of
the source and the drain leads. The models successfully explain the back action
effects. The extracted distribution broadening shows a linear dependency on the
bias voltage applied to the CD. We discuss possible mechanisms mediating the
energy transfer between the CD and QD and give an explanation for the origin of
the observed asymmetry.Comment: 6 pages, 4 figure
Solution Structures of \u3cem\u3eMycobacterium tuberculosis\u3c/em\u3e Thioredoxin C and Models of Intact Thioredoxin System Suggest New Approaches to Inhibitor and Drug Design
Here, we report the NMR solution structures of Mycobacterium tuberculosis (M. tuberculosis) thioredoxin C in both oxidized and reduced states, with discussion of structural changes that occur in going between redox states. The NMR solution structure of the oxidized TrxC corresponds closely to that of the crystal structure, except in the C-terminal region. It appears that crystal packing effects have caused an artifactual shift in the α4 helix in the previously reported crystal structure, compared with the solution structure. On the basis of these TrxC structures, chemical shift mapping, a previously reported crystal structure of the M. tuberculosis thioredoxin reductase (not bound to a Trx) and structures for intermediates in the E. coli thioredoxin catalytic cycle, we have modeled the complete M. tuberculosis thioredoxin system for the various steps in the catalytic cycle. These structures and models reveal pockets at the TrxR/TrxC interface in various steps in the catalytic cycle, which can be targeted in the design of uncompetitive inhibitors as potential anti-mycobacterial agents, or as chemical genetic probes of function
Effect of Al on the sharpness of the MgSiO_3 perovskite to post-perovskite phase transition
By means of static ab-initio computations we investigate the influence of Al on the recently discovered perovskite to post-perovskite phase transition in MgSiO_3. We examine three substitution mechanisms for Al in the two structures: MgSi → AlAl; SiSiO → AlAl□; and Si → AlH. The substitutions introducing oxygen vacancies (highly unfavorable, energetically) and water (favorable) both lower the 0 Kelvin transition pressure, whereas charge coupled substitution increases it relative to 105 GPa for pure MgSiO_3. From the transition pressures for 0, 6.25, and 100 mol% charge coupled Al_2O_3 incorporation and simple solution theories, we estimate the phase diagram of Al-bearing MgSiO_3 at low Al concentrations. Assuming the Clapeyron slope is independent of Al concentration, we find the perovskite-to-post-perovskite transition region to span 127–140 GPa, at 6.25 mol% Al_2O_3. When the upper pressure limit is bounded by the core-mantle boundary, the phase coexistence region has width 150 km
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