Counting joints with multiplicities

Let $\mathfrak{L}$ be a collection of $L$ lines in $\R^3$ and $J$ the set of joints formed by $\mathfrak{L}$, i.e. the set of points each of which lies in at least 3 non-coplanar lines of $\mathfrak{L}$. It is known that $|J| \lesssim L^{3/2}$ (first proved by Guth and Katz). For each joint $x \in J$, let the multiplicity $N(x)$ of $x$ be the number of triples of non-coplanar lines through $x$. We prove here that $\sum_{x \in J}N(x)^{1/2} \lesssim L^{3/2}$, while in the last section we extend this result to real algebraic curves of uniformly bounded degree in $\R^3$, as well as to curves in $\R^3$ parametrised by real polynomials of uniformly bounded degree.Comment: More details in section 4. Typos corrected. The main results are unchange

Recent QCD results from OPAL

Some recent QCD results from the OPAL Collaboration are summarized. In particular: a test of color reconnection models and a search for glueballs using gluon jets with a rapidity gap; a study of unbiased gluon jet properties using a new technique called jet boost algorithm; a measurement of the strong coupling constant from radiative events.Comment: 5 pages, 2 figures. Invited talk at the XIIth International Workshop on Deep-Inelastic Scattering DIS2004, 14-18 April 2004, Strbske Pleso, Slovakia; OPAL-CR52

Comment on "Metallization of Fluid Nitrogen and the Mott Transition in Highly Compressed Low-Z Fluids"

A comment on ``Metallization of Fluid Nitrogen and the Mott Transition in Highly Compressed Low-Z Fluids'' by Chau et al, Phys. Rev. Lett. 90, 245501 (2003).Comment: Submitted to PR

The BTeV RICH Front End Electronics

We report on the design and testing of novel mixed analog and digital front end ASICs custom made for the single photon detectors considered for the BTeV RICH system. The key features are reviewed, as well as results achieved using electronics bench tests and beam studies.Comment: 7 pages, 4 figures, talk given at the 5th International Workshop on Ring Imaging Cherenkov Counters (RICH2004