Modules with irrational slope over tubular algebras

Let $A$ be a tubular algebra and let $r$ be a positive irrational. Let ${\mathcal D}_r$ be the definable subcategory of $A$-modules of slope $r$. Then the width of the lattice of pp formulas for ${\mathcal D}_r$ is $\infty$. It follows that if $A$ is countable then there is a superdecomposable pure-injective module of slope $r$.Comment: minor corrections/improvements to argument

Peak finding through Scan Statistics

We discuss the conditions under which Scan Statistics can be fruitfully implemented to signal a departure from the underlying probability model that describes the experimental data. It is shown that local perturbations (``bumps'' or ``excesses'' of events) are better dealt within this framework and, in general, tests based on these statistics provide a powerful and unbiased alternative to the traditional techniques related with the chi2 and Kolmogorov distributions. Approximate formulas for the computation of Scan Statistics in the range of interest for high energy and nuclear physics applications are also presented.Comment: 14 pages, 5 figures, to appear in Nucl.Instrum.Meth.

Search for the Cryptoexotic Member of the Baryon Antidecuplet 1/2+ in the Reactions pi- p --> pi- p and pi- p --> K L

The main goal of this proposal is the search for a narrow cryptoexotic nucleon resonance by scanning of the pi- p system invariant mass in the region (1610-1770) MeV with the detection of pi- p and K Lambda decays. The scan is supposed to be done by the variation of the incident pi- momentum and its measurement with the accuracy of up to +-0.1% (better than 1 MeV in terms of the invariant mass in the whole energy range) with a set of proportional chambers located in the first focus of the magnetooptical channel. High sensitivity of the method to the resonance under search is shown. The secondary particles scattered from a liquid hydrogen target are detected by sets of the wire drift chambers equipped with modern electronics. The time scale of the project is about 3 years. The budget estimate including manpower, the apparatus and operation cost, is about 40 million rubles. The beam time required is (4-6) two week runs on "high" (10 GeV/c) flattop of the ITEP proton synchrotron.Comment: 16 pages, 10 figures. v2: an acknowledge adde