Pattern Count on Multiply Restricted Permutations

Previous work has studied the pattern count on singly restricted permutations. In this work, we focus on patterns of length 3 in multiply restricted permutations, especially for double and triple pattern-avoiding permutations. We derive explicit formulae or generating functions for various occurrences of length 3 patterns on multiply restricted permutations, as well as some combinatorial interpretations for non-trivial pattern relationships.Comment: 23 pages, 2 figure

Production of oxygen from lunar ilmenite

The overall objective of this project was to develop a novel carbothermal reduction process for production of oxygen from lunar ilmenite. The specific objective was to use a reaction sequence in which a wide variety of carbonaceous compounds (including carbonaceous wastes) can be used as reducing agents. During the first phase, two reactor systems were designed, constructed, and operated to study the reaction fundamental important in this process. One system is a small fluidized bed, and the other is a thermo-gravimetric reactor system. Preliminary experiments on synthetic ilmenite are conducted to study the effect of carbon type, carbon loading, temperature, and gas flow rate. Results indicate that a reaction path based on carbon gasification can be used to promote the overall kinetics. A unique temperature and concentration-programmed reaction procedure was being developed for rapid parametric study of the process

NeIII/OII as an oxygen abundance indicator in the HII regions and HII galaxies

To calibrate the relationship between Ne3O2 (Ne3O2 = log(\neiii$\lambda3869$/\oii$\lambda3727$)) and oxygen abundances, we present a sample of $\sim$3000 \hii galaxies from the Sloan Digital Sky Survey (SDSS) data release four. They are associated with a sample from the literature intended to enlarge the oxygen abundance region. We calculated the electron temperatures ($T_e$) of 210 galaxies in the SDSS sample with the direct method, and $T_e$ of the other 2960 galaxies in SDSS sample calculated with an empirical method. Then, we use a linear least-square fitting to calibrate the Ne3O2 oxygen abundance indicator. It is found that the Ne3O2 estimator follows a linear relation with \zoh\ that holds for the whole abundance range covered by the sample, from approximately 7.0 to 9.0. The best linear relationship between the Ne3O2 and the oxygen abundance is calibrated. The dispersion between oxygen abundance and Ne3O2 index in the metal rich galaxies may come partly from the moderate depletion of oxygen onto grains. The $Ne3O2$ method has the virtue of being single-valued and not affected by internal reddening. As a result, the $Ne3O2$ method can be a good metallicity indicator in the \hii regions and \hii galaxies, especially in high-redshift galaxies.Comment: 7 pages, 6 figures. A&A accepte