Non Symmetric Dirichlet Forms on Semifinite von Neumann Algebras

The theory of non symmetric Dirichlet forms is generalized to the non abelian setting, also establishing the natural correspondences among Dirichlet forms, sub-Markovian semigroups and sub-Markovian resolvents within this context. Examples of non symmetric Dirichlet forms given by derivations on Hilbert algebras are studied.Comment: 32 pages, plain TeX, Preprint Roma TOR VERGATA Nr.9-93-May 9

On the spectrum of the transfer operators of a one-parameter family with intermittency transition

We study the transfer operators for a family $F_r:[0,1] \to [0,1]$ depending on the parameter $r\in [0,1]$, which interpolates between the tent map and the Farey map. In particular, considering the action of the transfer operator on a suitable Hilbert space, we can define a family of infinite matrices associated to the operators and study their spectrum by numerical methods.Comment: 6 pages, 3 figure

Statistics of energy levels and zero temperature dynamics for deterministic spin models with glassy behaviour

We consider the zero-temperature dynamics for the infinite-range, non translation invariant one-dimensional spin model introduced by Marinari, Parisi and Ritort to generate glassy behaviour out of a deterministic interaction. It is shown that there can be a large number of metatastable (i.e., one-flip stable) states with very small overlap with the ground state but very close in energy to it, and that their total number increases exponentially with the size of the system.Comment: 25 pages, 8 figure

The correlation between soft and hard X-rays component in flares: from the Sun to the stars

In this work we study the correlation between the soft (1.6--12.4 keV, mostly thermal) and the hard (20--40 and 60--80 keV, mostly non-thermal) X-ray emission in solar flares up to the most energetic events, spanning about 4 orders of magnitude in peak flux, establishing a general scaling law and extending it to the most intense stellar flaring events observed to date. We used the data from the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) spacecraft, a NASA Small Explorer launched in February 2002. RHESSI has good spectral resolution (~1 keV in the X-ray range) and broad energy coverage (3 keV--20 MeV), which makes it well suited to distinguish the thermal from non-thermal emission in solar flares. Our study is based on the detailed analysis of 45 flares ranging from the GOES C-class, to the strongest X-class events, using the peak photon fluxes in the GOES 1.6--12.4 keV and in two bands selected from RHESSI data, i.e.20--40 keV and 60--80 keV. We find a significant correlation between the soft and hard peak X-ray fluxes spanning the complete sample studied. The resulting scaling law has been extrapolated to the case of the most intense stellar flares observed, comparing it with the stellar observations. Our results show that an extrapolation of the scaling law derived for solar flares to the most active stellar events is compatible with the available observations of intense stellar flares in hard X-rays.Comment: 9 pages, 10 figures. To be published in Astronomy and Astrophysic

A Probabilistic Model For The Distribution Of Authorships And A Measure Of The Degree Of Research Collaboration

The collaborative coefficient (CC), a measure that combines some of the merits of two earlier measures of research collaboration, is presented. This measure is used to compare the degrees of collaboration in the fields of engineering sciences, medical sciences, physical sciences, mathematical sciences, social sciences, and humanities. A theoretical model for the distribution of authorships is also developed. This model, the shifted Waring distribution, and 15 other discrete probability models are tested for goodness-of-fit against 96 data sets collected from the six fields listed above. The shifted inverse Gaussian-Poisson is found to be the best model. It is suggested that this model could be used in the estimation of the number of entries in an author index and in determining the maximum number of authors per paper to be included in an author index. A relationship is established between the parameters of this model and the collaborative coefficient

GEOMETRIC-PROPERTIES OF THE PRUNING FRONT

Monotonicity of the prunig front is proved for the Lozi map. A general expression for its Hausdorff dimension is also derived which takes into account multifractal fluctuations as wel

On the leading eigenvalue of transfer operators of the Farey map with real temperature

We study the spectral properties of a family of generalized transfer operators associated to the Farey map. We show that when acting on a suitable space of holomorphic functions, the operators are self-adjoint and the positive dominant eigenvalue can be approximated by means of the matrix expression of the operators.Comment: 9 pages, 3 figure

Cluster Approximation for the Farey Fraction Spin Chain

We consider the Farey fraction spin chain in an external field $h$. Utilising ideas from dynamical systems, the free energy of the model is derived by means of an effective cluster energy approximation. This approximation is valid for divergent cluster sizes, and hence appropriate for the discussion of the magnetizing transition. We calculate the phase boundaries and the scaling of the free energy. At $h=0$ we reproduce the rigorously known asymptotic temperature dependence of the free energy. For $h \ne 0$, our results are largely consistent with those found previously using mean field theory and renormalization group arguments.Comment: 17 pages, 3 figure