Sum-free sets and Ramsey numbers

In this note we obtain new lower bounds for the Ramsey numbers R(5, 5) and R(5, 6). The method is based on computational results of partitioning the integers into sum-free sets. We obtain R(5, 5)?42 and R(5, 6)?53.     

Selenium-sulfur analogs. Mass spectrometric comparison of substituted selenazoles and thiazoles

The electron impact mass spectra of a series of thiazoles and selenazoles were compared. No major differences in the mass spectral behavior between the sulfur and selenium containing compounds were observed. Isotopic labelling with deuterium permitted deconvolution of ion peaks of identical mass and composition, but arising from different fragmentation pathways.     

A combined OH/acetone planar laser-induced fluorescence imaging technique for visualizing combusting flows

A combined OH/acetone planar laser-induced fluorescence (PLIF) imaging technique that provides simultaneous visualizations of regions of unburned fuel and of combustion in a reacting flow is described. OH marks the location of chemical reaction and of combustion products, and acetone vapor, which is seeded into the fuel stream, marks unburned fuel. A single pulse from an ultraviolet laser is used to simultaneously excite both the OH and acetone, and the fluorescence from each is detected on separate cameras. Acetone spectroscopy and chemistry are reviewed to provide a basis for interpreting acetone fluorescence signals in high-temperature combusting environments. The imaging technique is applied to two nonpremixed turbulent reacting flows to assess the utility of the technique for visualizing the instantaneous flow structure and to illustrate the dependence of the interpretation of the acetone PLIF images on the flow conditions.Support was provided for this work by the Air Force Office of Scientific Research, Aerospace Sciences Directorate, with Julian Tishkoff as Technical Monitor, and is gratefully acknowledged. The contributions of Mr. T. C. Island in operating the supersonic flow facility are also greatly appreciated.     

Two-line planar fluorescence for temporally resolved temperature imaging in a reacting supersonic flow over a body

An instantaneous temperature imaging technique for chemically reacting, supersonic flows over bodies is described and demonstrated in a H₂/O₂/Ar shock tube flow (M=1.3, 0.7 atm, 1760K freestream). Based on a planar fluorescence measurement, the approach uses a two-line rotational population ratio to infer temperature. The measured 2-d temperature profiles qualitatively match the expected flowfield structure around the blunt body, and the temperature increase across the bow shock in a single-shot measurement agrees within 5–10% of the prediction of a 1-d shock analysis. The significant systematic error sources for the technique are detailed, and the random error effects associated with shot-noise-limited fluorescence images are statistically analyzed to identify transitions which minimize the temperature errors for instantaneous and average measurements. Even for average temperature measurements, the analysis predicts errors which can be as large as 5–10% when noisy fluorescence images are used in conjunction with low temperature sensitivity. In general, temperature errors can be reduced by increasing sensitivity, i.e., the energy separation of the two rotational levels, until the fluorescence shot-noise rises to a value of 30–50% within the temperature range of interest.     

On a combinatorial problem in geometry

Denote by g(n) the cardinality of a minimal subset C of an n × n square array of lattice points which does not contain the vertices of a square with sides parallel to the axes, but which is such that the addition of any new point to C forces the appearance of such a square. It is proved that g(n) < n^α for some α < 2.     

The attractor—basin portrait of a cellular automaton

Local space-time structures, such as domains and the intervening dislocations, dominate a wide class of cellular automaton (CA) behavior. For such spatially-extended dynamics regular domains, vicinities, and attractors are introduced as organizing principles to identify the discretized analogs of attractors, basins, and separatrices: structures used in classifying dissipative continuous-state dynamical systems. We describe the attractor-basin portrait of nonlinear elementary CA rule 18, whose global dynamics is largely determined by a single regular attracting domain. The latter's basin is analyzed in terms of subbasin and portal structures associated with particle annihilation. The conclusion is that the computational complexity of such CA is more apparent than real. Transducer machines are constructed that automatically identify domain and dislocation structures in space-time, count the number of dislocations in a spatial pattern, and implement an isomorphism between rule 18 and rule 90. We use a transducer to trace dislocation trajectories, and confirm that in rule 18, isolated dislocation trajectories, as well as a dislocation gas, agree extremely well with the classical model of annihilating diffusive particles. The CA efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space-time.