Fortran IV trent-surface program for the IBM 360 model 40 computer

A Fortran IV trend surface program with polynomial contouring and residual plotting has been adapted to the University of Alaska IBM 360 Model 40 Computer. The program will compute equations of polynomials of the first through sixth degree, measures of the goodness of fit of the surfaces, tabulate original data, x y coordinates and corresponding residuals for each surface; contour each polynomial, and plot original values and residuals for each surface computed

The dynamics and evolution of clusters of galaxies

Research was undertaken to produce a coherent picture of the formation and evolution of large-scale structures in the universe. The program is divided into projects which examine four areas: the relationship between individual galaxies and their environment; the structure and evolution of individual rich clusters of galaxies; the nature of superclusters; and the large-scale distribution of individual galaxies. A brief review of results in each area is provided

Optimal control of a leaking qubit

Physical implementations of quantum bits can contain coherent transitions to energetically close non-qubit states. In particular, for anharmonic oscillator systems such as the superconducting phase qubit and the transmon a two-level approximation is insufficient. We apply optimal control theory to the envelope of a resonant Rabi pulse in a qubit in the presence of a single, weakly off-resonant leakage level. The gate error of a spin flip operation reduces by orders of magnitude compared to simple pulse shapes. Near-perfect gates can be achieved for any pulse duration longer than an intrinsic limit given by the nonlinearity. The pulses can be understood as composite sequences that refocus the leakage transition. We also discuss ways to improve the pulse shapes.Comment: 4 pages, 2 figure

Generalization of a theorem of Fleck, Hedetniemi and Oehmke on δ∗-semigroups of automata

AbstractA solution to a conjecture of Fleck, Hedetniemi and Oehmke [4] on δ∗-semigroups of automata is presented. This also generalizes a result in [1]

r-tuple colorings of uniquely colorable graphs

AbstractAn r-tuple coloring of a graph is one in which r colors are assigned to each point of the graph so that the sets of colors assigned to adjacent points are always disjoint. We investigate the question of whether a uniquely n-colorable graph can receive an r-tuple coloring with fewer than nr colors. We show that this cannot happen for n=3 and r=2 and that for a given n and r to establish the conjecture that no uniquely n-colorable graph can receive an r-tuple coloring from fewer than nr colors it suffices to prove it for on a finite set of uniquely n-colorable graphs

Optimization of a neutrino factory oscillation experiment

We discuss the optimization of a neutrino factory experiment for neutrino oscillation physics in terms of muon energy, baselines, and oscillation channels (gold, silver, platinum). In addition, we study the impact and requirements for detector technology improvements, and we compare the results to beta beams. We find that the optimized neutrino factory has two baselines, one at about 3000 to 5000km, the other at about 7500km (``magic'' baseline). The threshold and energy resolution of the golden channel detector have the most promising optimization potential. This, in turn, could be used to lower the muon energy from about 50GeV to about 20GeV. Furthermore, the inclusion of electron neutrino appearance with charge identification (platinum channel) could help for large values of \sin^2 2 \theta_{13}. Though tau neutrino appearance with charge identification (silver channel) helps, in principle, to resolve degeneracies for intermediate \sin^2 2 \theta_{13}, we find that alternative strategies may be more feasible in this parameter range. As far as matter density uncertainties are concerned, we demonstrate that their impact can be reduced by the combination of different baselines and channels. Finally, in comparison to beta beams and other alternative technologies, we clearly can establish a superior performance for a neutrino factory in the case \sin^2 2 \theta_{13} < 0.01.Comment: 51 pages, 25 figures, 6 tables, references corrected, final version to appear in Phys. Rev.