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

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

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

Unexpected reemergence of von Neumann theorem

Is is shown here that the "simple test of quantumness for a single system" of arXiv:0704.1962 (for a recent experimental realization see arXiv:0804.1646) has exactly the same relation to the discussion of to the problem of describing the quantum system via a classical probabilistic scheme (that is in terms of hidden variables, or within a realistic theory) as the von Neumann theorem (1932). The latter one was shown by Bell (1966) to stem from an assumption that the hidden variable values for a sum of two non-commuting observables (which is an observable too) have to be, for each individual system, equal to sums of eigenvalues of the two operators. One cannot find a physical justification for such an assumption to hold for non-commeasurable variables. On the positive side. the criterion may be useful in rejecting models which are based on stochastic classical fields. Nevertheless the example used by the Authors has a classical optical realization

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

Measurement of the proton light response of various LAB based scintillators and its implication for supernova neutrino detection via neutrino-proton scattering

The proton light output function in electron-equivalent energy of various scintillators based on linear alkylbenzene (LAB) has been measured in the energy range from 1 MeV to 17.15 MeV for the first time. The measurement was performed at the Physikalisch-Technische Bundesanstalt (PTB) using a neutron beam with continuous energy distribution. The proton light output data is extracted from proton recoil spectra originating from neutron-proton scattering in the scintillator. The functional behavior of the proton light output is described succesfully by Birks' law with a Birks constant kB between (0.0094 +/- 0.0002) cm/MeV and (0.0098 +/- 0.0003) cm/MeV for the different LAB solutions. The constant C, parameterizing the quadratic term in the generalized Birks law, is consistent with zero for all investigated scintillators with an upper limit (95% CL) of about 10^{-7} cm^2/MeV^2. The resulting quenching factors are especially important for future planned supernova neutrino detection based on the elastic scattering of neutrinos on protons. The impact of proton quenching on the supernova event yield from neutrino-proton scattering is discussed.Comment: 12 pages, 17 figures, 4 tables, updated version for publication in Eur.Phys.J.