Jets and Prompt Photons in Photoproduction at ZEUS

In the ZEUS experiment at HERA, photoproduction processes have been studied for photon-proton centre-of-mass energies in the range 100 < W_gamma p < 300 GeV and jet transverse energies extending to E_T^jet ~ 70 GeV. The data contribute to our understanding of QCD dynamics, and also provide new constraints on the photon's parton density.Comment: 7 pages, 12 figures, talk given at ICHEP'98, writeup also available at http://ppewww.ph.gla.ac.uk/preprints/98/05

Rapidity Gaps in Hard Photoproduction

Recent results obtained from studies of diffractive processes in hard photoproduction performed by the ZEUS collaboration using data delivered by HERA in 1993 and 1994 are presented. In particular, we have found that $(7 \pm 3)$\% of events with two jets at a pseudorapidity interval of 3.5 to 4 are inconsistent with a non-diffractive production mechanism. These events may be interpreted as arising due to the exchange of a colour singlet object of negative squared invariant mass ($-t$) around 40~GeV$^2$. We have also probed the structure of the exchanged colour singlet object in low--$t$ diffractive scattering. By comparing the results from photoproduction and electroproduction processes we find that between 30\% and 80\% of the momentum of the exchanged colour singlet object which is carried by partons is due to hard gluons.Comment: 13 pages. 13 postscript figures + 1 postscript preprint logo + 1 LaTeX file. Files tarred, gzipped and uuencoded into 1 file. Also available at http://ppewww.ph.gla.ac.uk/preprints/96/03

Equidistribution of Algebraic Numbers of Norm One in Quadratic Number Fields

Given a fixed quadratic extension K of Q, we consider the distribution of elements in K of norm 1 (denoted N). When K is an imaginary quadratic extension, N is naturally embedded in the unit circle in C and we show that it is equidistributed with respect to inclusion as ordered by the absolute Weil height. By Hilbert's Theorem 90, an element in N can be written as \alpha/\bar{\alpha} for some \alpha \in O_K, which yields another ordering of \mathcal N given by the minimal norm of the associated algebraic integers. When K is imaginary we also show that N is equidistributed in the unit circle under this norm ordering. When K is a real quadratic extension, we show that N is equidistributed with respect to norm, under the map \beta \mapsto \log| \beta | \bmod{\log | \epsilon^2 |} where \epsilon is a fundamental unit of O_K.Comment: 19 pages, 2 figures, comments welcome

A Primary Ecological Survey of Dardanelle Reservoir Prior to Nuclear Facility Effluent Discharge

A preliminary ecological survey of Dardanelle Reservoir during the construction phase of Arkansas Power and Light Company\u27s nuclear generating facility was conducted from January 1970 through June 1974. The reservoir is characterized by relatively shallow depths and a high flow-thru rate. A number of features were associated with these characteristics. The reservoir carried a great deal of suspended material and exhibited high turbidities throughout most of the year. Typical thermal stratification and oxygen depletion were only rarely observed. Many of the physico-chemical parameters exhibited relatively high values in comparison to other Arkansas lakes and reservoirs, but due to absence of prolonged periods of stratification and stagnation, they did not undergo the extreme fluctuations sometimes observed in other reservoirs. Plankton and benthic samples were collected at least nine times per year from ten stations. These stations were selected to include both shallow and deep locations and to include points both within and outside the projected area of thermal influence when the plant became operational. There were a great variety of forms in the phytoplankton with the diatoms making up a considerable portion. The level of turbidity appeared to dampen somewhat the extreme fluctuations sometimes found in bloom periods. In the zooplankton the rotifers Brachionus, Keratella, and Polyarthra predominated followed by the microcrustaceans Cyclops and Bosmina. Both the plankton and the benthic fauna showed great seasonal variation. The benthic fauna consisted primarily of Chironomidae, Oligochaeta, and Hexagenia with the Chironomidae predominating in the shallower depths and the Oligochaeta exhibiting increased abundance and importance in the deeper stations

The reciprocal Mahler ensembles of random polynomials

We consider the roots of uniformly chosen complex and real reciprocal polynomials of degree N whose Mahler measure is bounded by a constant. After a change of variables, this reduces to a generalization of Ginibre’s complex and real ensembles of random matrices where the weight function (on the eigenvalues of the matrices) is replaced by the exponentiated equilibrium potential of the interval [−2,2] on the real axis in the complex plane. In the complex (real) case, the random roots form a determinantal (Pfaffian) point process, and in both cases, the empirical measure on roots converges weakly to the arcsine distribution supported on [−2,2]. Outside this region, the kernels converge without scaling, implying among other things that there is a positive expected number of outliers away from [−2,2]. These kernels as well as the scaling limits for the kernels in the bulk (−2,2) and at the endpoints {−2,2} are presented. These kernels appear to be new, and we compare their behavior with related kernels which arise from the (non-reciprocal) Mahler measure ensemble of random polynomials as well as the classical Sine and Bessel kernels

Universality for ensembles of matrices with potential theoretic weights on domains with smooth boundary

We investigate a two-dimensional statistical model of N charged particles interacting via logarithmic repulsion in the presence of an oppositely charged compact region K whose charge density is determined by its equilibrium potential at an inverse temperature corresponding to \beta = 2. When the charge on the region, s, is greater than N, the particles accumulate in a neighborhood of the boundary of K, and form a determinantal point process on the complex plane. We investigate the scaling limit, as N \to \infty, of the associated kernel in the neighborhood of a point on the boundary under the assumption that the boundary is sufficiently smooth. We find that the limiting kernel depends on the limiting value of N/s, and prove universality for these kernels. That is, we show that, the scaled kernel in a neighborhood of a point \zeta \in \partial K can be succinctly expressed in terms of the scaled kernel for the closed unit disk, and the exterior conformal map which carries the complement K to the complement of the closed unit disk. When N / s \to 0 we recover the universal kernel discovered by Doron Lubinsky in Universality type limits for Bergman orthogonal polynomials, Comput. Methods Funct. Theory, 10:135-154, 2010.Comment: 25 pages, 11 figure