Isometric Representations of Totally Ordered Semigroups

Let S be a subsemigroup of an abelian torsion-free group G. If S is a positive cone of G, then all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic. Proved by Murphy, this statement generalized the well-known theorems of Coburn and Douglas. In this note we prove the reverse. If all C*-algebras generated by faithful isometrical non-unitary representations of S are canonically isomorphic, then S is a positive cone of G. Also we consider G = Z\times Z and prove that if S induces total order on G, then there exist at least two unitarily not equivalent irreducible isometrical representation of S. And if the order is lexicographical-product order, then all such representations are unitarily equivalent.Comment: February 21, 2012. Kazan, Russi

Lorentz violating electrodynamics

After summarizing the most interesting results in the calculation of synchrotron radiation in the Myers-Pospelov effective model for Lorentz invariance violating (LIV) electrodynamics, we present a general unified way of describing the radiation regime of LIV electrodynamics which include the following three different models : Gambini-Pullin, Ellis et al. and Myers-Pospelov. Such unification reduces to the standard approach of radiation in a dispersive and absortive (in general) medium with a given index of refraction. The formulation is presented up to second order in the LIV parameter and it is explicitly applied to the synchrotron radiation case.Comment: 11 pages, extended version of the talk given by L.F. Urrutia in the VI Mexican School: Approaches to Quantum Gravity, Playa del Carmen, Mexico, Nov. 2004. Minor chages in the text and added reference

Discovery of a Third Harmonic Cyclotron Resonance Scattering Feature in the X-ray Spectrum of 4U 0115+63

We have discovered a third harmonic cyclotron resonance scattering feature (CRSF) in observations of the recent outburst of 4U 0115+63 with the Rossi X-ray Timing Explorer (RXTE). The spectrum in a narrow pulse phase range shows CRSFs at 12.40+0.65/-0.35, 21.45+0.25/-0.38, and 33.56+0.70/-0.90 keV. With centroid energy ratios to the fundamental of 1.73+/-0.08 and 2.71+/-0.13, the CRSFs are not harmonically spaced. Strong variability of the continuum and CRSFs with pulse phase indicate a complex emission geometry near the neutron star polar cap. In addition, one RXTE observation, which spanned periastron passage, revealed a strong 2 mHz quasi-periodic oscillation (QPO). This is slower by two orders of magnitude than the beat-frequency QPO expected in this system and slower by a factor of more than 5 compared with other QPOs seen in accreting X-ray pulsars.Comment: To appear in The Astrophysical Journal Letters. 4 pages, 5 figures. Uses "emulateapj.sty". Revised version includes new figures and additions to the analysi

Diffuse Galactic Soft Gamma-Ray Emission

The Galactic diffuse soft gamma-ray (30-800 keV) emission has been measured from the Galactic Center by the HIREGS balloon-borne germanium spectrometer to determine the spectral characteristics and origin of the emission. The resulting Galactic diffuse continuum is found to agree well with a single power-law (plus positronium) over the entire energy range, consistent with RXTE and COMPTEL/CGRO observations at lower and higher energies, respectively. We find no evidence of spectral steepening below 200 keV, as has been reported in previous observations. The spatial distribution along the Galactic ridge is found to be nearly flat, with upper limits set on the longitudinal gradient, and with no evidence of an edge in the observed region. The soft gamma-ray diffuse spectrum is well modeled by inverse Compton scattering of interstellar radiation off of cosmic-ray electrons, minimizing the need to invoke inefficient nonthermal bremsstrahlung emission. The resulting power requirement is well within that provided by Galactic supernovae. We speculate that the measured spectrum provides the first direct constraints on the cosmic-ray electron spectrum below 300 MeV.Comment: 26 pages, 7 figure, submitted to Ap

Discovery of a Cyclotron Resonant Scattering Feature in the RXTE Spectrum of 4U 0352+309 (X Per)

We have discovered a ~29 keV Cyclotron Resonant Scattering Feature (CRSF) in the X-Ray spectrum of 4U 0352+309 (X Per) using observations taken with the Rossi X-Ray Timing Explorer. 4U 0352+309 is a persistent low luminosity (L_x = 4.2x10^34 ergs/s) X-ray pulsar, with a 837 s period and which accretes material from the Be star X Per. The X-Ray spectrum, unusual when compared to brighter accreting pulsars, may be due to the low mass accretion rate and could be typical of the new class of persistent low luminosity Be/X-Ray binary pulsars. We attempted spectral fits with continuum models used historically for 4U 0352+309, and found that all were improved by the addition of a CRSF at ~29 keV. The model that best fit the observations is a combination of a 1.45+/-0.02 keV blackbody with a 5.4x10^8 cm^2 area, and a power-law with a 1.83+/-0.03 photon index modified by the CRSF. In these fits the CRSF energy is 28.6+1.5-1.7 keV, implying a magnetic field strength of 2.5(1+z)x10^12 G in the scattering region (where z is the gravitational redshift). Phase resolved analysis shows that the blackbody and cyclotron line energies are consistent with being constant through the pulse.Comment: 34 pages, 6 figures, 3 tables, Accepted by Ap

Implications of the γ\gamma-ray Polarization of GRB 021206

We compare two possible scenarios for the producing of high level of polarization within the prompt emission of a GRB: synchrotron emission from a relativistic jet with a uniform (in space and time) magnetic field and synchrotron emission from a jet with a random magnetic field in the plane of the shock. Somewhat surprisingly we find that both scenarios can produce a comparable level of polarization ($\sim 45-50$% for the uniform field and $\sim 30-35$% for a random field). Uniform time independent field most naturally arises by expansion of the field from the compact object. It requires a $10^{12}$G field at the source and a transport of the field as $\propto R^{-1}$. It {\it does not} imply Poynting flux domination of the energy of the wind. There is a serious difficulty however, within this scenario, accounting for particle acceleration (which requires random magnetic fields) both for Poynting flux and non-Poynting flux domination. Significant polarization can also arise from a random field provided that the observer is located within $1/\Gamma$ orientation from a narrow ($\theta_j \sim 1/\Gamma$) jet. While most jets are wider, the jet of GRB 021206 from which strong polarization was recently observed, was most likely very narrow. GRB 021206 is among the strongest bursts ever. Adopting the energy-angle relation we find an estimated angle of $<1/40$rad or even smaller. Thus, for this particular burst the required geometry is not unusual. We conclude that the RHESSI observations suggest that the prompt emission results from synchrotron radiation. However, in view of the comparable levels of polarizations predicted by both the random field and the homogeneous field scenarios these observations are insufficient to rule out or confirm either one.Comment: 14 pages, 4 figure

Testing a MultiTEP-based combination vaccine to reduce Aβ and tau pathology in Tau22/5xFAD bigenic mice.

BackgroundAlzheimer disease (AD) is characterized by the accumulation of beta-amyloid (Aβ) plaques and neurofibrillary tangles composed of hyperphosphorylated tau, which together lead to neurodegeneration and cognitive decline. Current therapeutic approaches have primarily aimed to reduce pathological aggregates of either Aβ or tau, yet phase 3 clinical trials of these approaches have thus far failed to delay disease progression in humans. Strong preclinical evidence indicates that these two abnormally aggregated proteins interact synergistically to drive downstream neurodegeneration. Therefore, combinatorial therapies that concurrently target both Aβ and tau might be needed for effective disease modification.MethodsA combinatorial vaccination approach was designed to concurrently target both Aβ and tau pathologies. Tau22/5xFAD (T5x) bigenic mice that develop both pathological Aβ and tau aggregates were injected intramuscularly with a mixture of two MultiTEP epitope vaccines: AV-1959R and AV-1980R, targeting Aβ and tau, respectively, and formulated in AdvaxCpG, a potent polysaccharide adjuvant. Antibody responses of vaccinated animals were measured by ELISA, and neuropathological changes were determined in brain homogenates of vaccinated and control mice using ELISA and Meso Scale Discovery (MSD) multiplex assays.ResultsT5x mice immunized with a mixture of Aβ- and tau-targeting vaccines generated high Aβ- and tau-specific antibody titers that recognized senile plaques and neurofibrillary tangles/neuropil threads in human AD brain sections. Production of these antibodies in turn led to significant reductions in the levels of soluble and insoluble total tau, and hyperphosphorylated tau as well as insoluble Aβ42, within the brains of bigenic T5x mice.ConclusionsAV-1959R and AV-1980R formulated with AdvaxCpG adjuvant are immunogenic and therapeutically potent vaccines that in combination can effectively reduce both of the hallmark pathologies of AD in bigenic mice. Taken together, these findings warrant further development of this vaccine technology for ultimate testing in human AD