Modified mixed Tsirelson spaces

We study the modified and boundedly modified mixed Tsirelson spaces $T_M[({\cal F}_{k_n},\theta_n)_{n=1}^{\infty }]$ and $T_{M(s)}[({\cal F}_{k_n},\theta_n)_{n=1}^{\infty }]$ respectively, defined by a subsequence $({\cal F}_{k_n})$ of the sequence of Schreier families $({\cal F}_n)$. These are reflexive asymptotic $\ell_1$ spaces with an unconditio- nal basis $(e_i)_i$ having the property that every sequence $\{ x_i\}_{i=1}^n$ of normalized disjointly supported vectors contained in $\langle e_i\rangle_{i=n}^{\infty }$ is equivalent to the basis of $\ell_1^n$. We show that if $\lim\theta_n^{1/n}=1$ then the space $T[({\cal F}_n,\theta_n) _{n=1}^{\infty }]$ and its modified variations are totally incomparable by proving that $c_0$ is finitely disjointly representable in every block subspace of $T[({\cal F}_n, \theta_n)_{n=1}^{\infty }]$. Next, we present an example of a boundedly modified mixed Tsirelson space $X_{M(1),u}$ which is arbitrarily distortable. Finally, we construct a variation of the space $X_{M(1),u}$ which is hereditarily indecomposable

Finite size effects on measures of critical exponents in d=3 O(N) models

We study the critical properties of three-dimensional O(N) models, for N=2,3,4. Parameterizing the leading corrections-to-scaling for the $\eta$ exponent, we obtain a reliable infinite volume extrapolation, incompatible with previous Monte Carlo values, but in agreement with $\epsilon$-expansions. We also measure the critical exponent related with the tensorial magnetization as well as the $\nu$ exponents and critical couplings.Comment: 12 pages, 2 postscript figure

A PMT-Block test bench

The front-end electronics of the ATLAS hadronic calorimeter (Tile Cal) is housed in a unit, called {\it PMT-Block}. The PMT-Block is a compact instrument comprising a light mixer, a PMT together with its divider and a {\it 3-in-1} card, which provides shaping, amplification and integration for the signals. This instrument needs to be qualified before being assembled on the detector. A PMT-Block test bench has been developed for this purpose. This test bench is a system which allows fast, albeit accurate enough, measurements of the main properties of a complete PMT-Block. The system, both hardware and software, and the protocol used for the PMT-Blocks characterisation are described in detail in this report. The results obtained in the test of about 10000 PMT-Blocks needed for the instrumentation of the ATLAS (LHC-CERN) hadronic Tile Calorimeter are also reported.Comment: 23 pages, 10 figure