On a theorem by Treves

According to a theorem of Treves, the conserved functionals of the KdV equation vanish on each formal Laurent series 1/x^2 + u0 + u2 x^2 + u3 x^3 + >... . We propose a new, very simple geometrical proof for this statement.Comment: 7 page

On the Treves theorem for the AKNS equation

According to a theorem of Treves, the conserved functionals of the AKNS equation vanish on all pairs of formal Laurent series of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of B\"acklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same of our previous paper on the Treves theorem for the KdV, with some non trivial technical differences.Comment: LaTeX, 16 page

The vacuum polarization around an axionic stringy black hole

We consider the effect of vacuum polarization around the horizon of a 4 dimensional axionic stringy black hole. In the extreme degenerate limit ($Q_a=M$), the lower limit on the black hole mass for avoiding the polarization of the surrounding medium is $M\gg (10^{-15}\div 10^{-11})m_p$ ($m_p$ is the proton mass), according to the assumed value of the axion mass ($m_a\simeq (10^{-3}\div 10^{-6})~eV$). In this case, there are no upper bounds on the mass due to the absence of the thermal radiation by the black hole. In the nondegenerate (classically unstable) limit ($Q_a<M$), the black hole always polarizes the surrounding vacuum, unless the effective cosmological constant of the effective stringy action diverges.Comment: 7 pages, phyzzx.tex, ROM2F-92-3

A view of PKS 2155-304 with XMM-Newton Reflection Grating Spectrometers

We present the high resolution X-ray spectrum of the BL Lac object PKS 2155-304 taken with the RGS units onboard XMM-Newton in November 2000. We detect a OVII Kalpha resonant absorption line from warm/hot local gas at 21.59A (~4.5 sigma detection). The line profile is possibly double peaked. We do not confirm the strong 20.02 A absorption line seen with Chandra and interpreted as z~0.05 OVIII Kalpha. A 3sigma upper limit of 14 mA on the equivalent width is set. We also detect the ~23.5 A interstellar OI 1s-->2p line and derive a factor <=1.5 subsolar O/H ratio in the ISM along PKS 2155-304 line of sight.Comment: 13 pages, 5 figures, 3 tables, emulateapj style. Accepted by Ap

Some remarks on the GNS representations of topological ∗^*-algebras

After an appropriate restatement of the GNS construction for topological $^*$-algebras we prove that there exists an isomorphism among the set \cycl(A) of weakly continuous strongly cyclic $^*$-representations of a barreled dual-separable $^*$-algebra with unit $A$, the space \hilb_A(A^*) of the Hilbert spaces that are continuously embedded in $A^*$ and are $^*$-invariant under the dual left regular action of $A$ and the set of the corresponding reproducing kernels. We show that these isomorphisms are cone morphisms and we prove many interesting results that follow from this fact. We discuss how these results can be used to describe cyclic representations on more general inner product spaces.Comment: 34 pages. Minor changes. To appear in J. Math. Phys. 49 (4) Apr-0

VLT/FORS2 observations of the optical counterpart of the isolated neutron star RBS 1774

X-ray observations performed with ROSAT led to the discovery of a group (seven to date) of X-ray dim and radio-silent middle-aged isolated neutron stars (a.k.a. XDINSs), which are characterised by pure blackbody spectra (kT~40-100 eV), long X-ray pulsations (P=3-12 s), and appear to be endowed with relatively high magnetic fields, (B~10d13-14 G). RBS 1774 is one of the few XDINSs with a candidate optical counterpart, which we discovered with the VLT. We performed deep observations of RBS 1774 in the R band with the VLT to disentangle a non-thermal power-law spectrum from a Rayleigh-Jeans, whose contributions are expected to be very much different in the red part of the spectrum. We did not detect the RBS 1774 candidate counterpart down to a 3 sigma limiting magnitude of R~27. The constraint on its colour, (B-R)<0.6, rules out that it is a background object, positionally coincident with the X-ray source. Our R-band upper limit is consistent with the extrapolation of the B-band flux (assuming a 3 sigma uncertainty) for a set of power-laws F_nu ~nu^alpha with spectral indeces alpha<0.07. If the optical spectrum of RBS 1774 were non-thermal, its power-law slope would be very much unlike those of all isolated neutron stars with non-thermal optical emission, suggesting that it is most likely thermal. For instance, a Rayleigh-Jeans with temperature T_O = 11 eV, for an optically emitting radius r_O=15 km and a source distance d=150 pc, would be consistent with the optical measurements. The implied low distance is compatible with the 0.04 X-ray pulsed fraction if either the star spin axis is nearly aligned with the magnetic axis or with the line of sight, or it is slightly misaligned with respect to both the magnetic axis and the line of sight by 5-10 degreesComment: 8 pages, 8 postscript figures, accepted for publication in Astronomy & Astrophysic

Estimating probabilities from experimental frequencies

Estimating the probability distribution 'q' governing the behaviour of a certain variable by sampling its value a finite number of times most typically involves an error. Successive measurements allow the construction of a histogram, or frequency count 'f', of each of the possible outcomes. In this work, the probability that the true distribution be 'q', given that the frequency count 'f' was sampled, is studied. Such a probability may be written as a Gibbs distribution. A thermodynamic potential, which allows an easy evaluation of the mean Kullback-Leibler divergence between the true and measured distribution, is defined. For a large number of samples, the expectation value of any function of 'q' is expanded in powers of the inverse number of samples. As an example, the moments, the entropy and the mutual information are analyzed.Comment: 10 pages, 3 figures, to be published in Physical Review

Hardy-Carleman Type Inequalities for Dirac Operators

General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities are established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques

The Neutron Stars Census

The paucity of old isolated accreting neutron stars in ROSAT observations is used to derive a lower limit on the mean velocity of neutron stars at birth. The secular evolution of the population is simulated following the paths of a statistical sample of stars for different values of the initial kick velocity, drawn from an isotropic Gaussian distribution with mean velocity $0\leq < V>\leq 550$ ${\rm km s^{-1}}$. The spin--down, induced by dipole losses and the interaction with the ambient medium, is tracked together with the dynamical evolution in the Galactic potential, allowing for the determination of the fraction of stars which are, at present, in each of the four possible stages: Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc from the Sun, we infer a lower bound for the mean kick velocity, $\gtrsim 200-300$ ${\rm km s^{-1}},$ corresponding to a velocity dispersion $\sigma_V\gtrsim 125-190$ km s$^{-1}$. The same conclusion is reached for both a constant magnetic field ($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a timescale $\sim 10^9$ yr. Such high velocities are consistent with those derived from radio pulsar observations. Present results, moreover, constrain the fraction of low velocity stars, which could have escaped pulsar statistics, to less than 1%.Comment: 13 pages, 6 PostScript figures, accepted to Ap