Measurement of the proton structure functionF2 from the 1993 HERA data

The ZEUS detector has been used to measure the proton structure functionF ₂. During 1993 HERA collided 26.7 GeV electrons on 820 GeV protons. The data sample corresponds to an integrated luminosity of 0.54 pb^–1, representing a twenty fold increase in statistics compared to that of 1992. Results are presented for 7Q ²<>⁴ GeV² andx values as low as 3×10^–4. The rapid rise inF ₂ asx decreases observed previously is now studied in greater detail and persists forQ ² values up to 500 GeV².supported by Worldlab, Lausanne, Switzerland     

Zwillingskonvergenzgebiete für Kettenbrüche 1+K(a n /1), deren eines die Kreisscheibe ∣a 2n−1∣≦ϱ2 ist

Ohne ZusammenfassungThis research was supported by the United States Air Force under Contract No. AF 49 (638)-100 monitored by the AF Office of Scientific Research of the Air Research and Development Command.     

An asymptotically tight bound on the adaptable chromatic number

The adaptable chromatic number of a multigraph G, denoted χ_a(G), is the smallest integer k such that every edge labeling, τ, of G from [k] = {1, 2, …, k} permits a vertex coloring, σ, of G from [k] such that no edge e = uv has τ(e) = σ(u) = σ(v). Hell and Zhu proved that for any multigraph G with maximum degree Δ, the adaptable chromatic number is at most . We strengthen this to the asymptotically best possible bound of for any ?>0. © 2012 Wiley Periodicals, Inc. J Graph Theory     

Limit periodic Schur algorithms,the case 441-1441-1441-1

We show that if a function bounded in the unit disk gives rise to a limit periodic Schur algorithm with ||=1, d _n ,< then the function can be continued analytically to a meromorphic function in the entire plane except, possibly, for an essential singularity at z=–1. The lpS provides a very good approximation to the function.This research was supported in part by the US National Science Foundation under Grant DMS-9103141.