Telescoping columns

An extendable column is described which consists of several axially elongated rigid structural sections nested within one another. Each section includes a number of rotatably attached screws running along its length. The next inner section includes threaded lugs oriented to threadingly engage the screws. The column is extended or retracted upon rotation of the screws. The screws of each section are selectively rotated by a motor and an engagement mechanism

Partition regularity without the columns property

A finite or infinite matrix A with rational entries is called partition regular if whenever the natural numbers are finitely coloured there is a monochromatic vector x with Ax=0. Many of the classical theorems of Ramsey Theory may naturally be interpreted as assertions that particular matrices are partition regular. In the finite case, Rado proved that a matrix is partition regular if and only it satisfies a computable condition known as the columns property. The first requirement of the columns property is that some set of columns sums to zero. In the infinite case, much less is known. There are many examples of matrices with the columns property that are not partition regular, but until now all known examples of partition regular matrices did have the columns property. Our main aim in this paper is to show that, perhaps surprisingly, there are infinite partition regular matrices without the columns property --- in fact, having no set of columns summing to zero. We also make a conjecture that if a partition regular matrix (say with integer coefficients) has bounded row sums then it must have the columns property, and prove a first step towards this.Comment: 13 page

Hydrodynamics of photoionized columns in the Eagle Nebula, M 16

We present hydrodynamical simulations of the formation, structure and evolution of photoionized columns, with parameters based on those observed in the Eagle Nebula. On the basis of these simulations we argue that there is no unequivocal evidence that the dense neutral clumps at heads of the columns were cores in the pre-existing molecular cloud. In our simulations, a variety of initial conditions leads to the formation and maintenance of near-equilibrium columns. Therefore, it is likely that narrow columns will often occur in regions with large-scale inhomogeneities, but that observations of such columns can tell us little about the processes by which they formed. The manner in which the columns in our simulations develop suggests that their evolution may result in extended sequences of radiation-induced star formation.Comment: 12 pages, 9 figures, Latex, MN macros, in press with MNRA

Nano and Micro indentation studies of bulk zirconia and EB PVD TBCs

In order to model the erosion of a material it is necessary to know the material properties of both the impacting particles as well as the target. In the case of electron beam (EB) physical vapour deposited(PVD) thermal barrier coatings (TBCs) the properties of the columns as opposed to the coating as a whole are important. This is due to the fact that discrete erosion events are on a similar scale as the size of the individual columns. Thus nano* and micro* indentation were used to determine the hardness and the Young"s modulus of the columns. However, care had to be taken to ensure that it was the hardness of the columns that was being measured and not the coating as a whole. This paper discusses the differences in the results obtained when using the two different tests and relates them to the interactions between the indent and the columns of the EB PVD TBC microstructure. It was found that individual columns had a hardness of 14 GPa measured using nano indentation, while the hardness of the coating, using micro indentation decreased from 13 to 2.4 GPa as the indentation load increased from 0.1 to 3N. This decrease in hardness was attributed to the interaction between the indenter and a number of adjacent columns and the ability of the columns to move laterally under indentation

ROSAT X-ray sources in the field of the LMC I.Total LMC gas from the background AGN spectral fits

We analyzed a sample of 26 background X-ray sources in a ~60 square degree field of the Large Magellanic Cloud observed with the ROSAT PSPC. The sample has been selected from previously classified and optically identified X-ray sources. In addition pointlike and spectrally hard sources with at least 100 to 200 observed counts have been used for the analysis. We performed X-ray spectral fitting and derived total hydrogen absorbing column densities due to LMC gas in the range 10^20 - 2. 10^21 cm^-2. We compared these columns with the HI columns derived from a 21-cm Parkes survey of the LMC. For 7 optically identified sources we find, within the uncertainties derived from the X-ray spectral fit, agreement for both columns. For further 19 sources we constrain the LMC columns from the X-ray spectral fit assuming that the powerlaw photon index is that of AGN type spectra. We derive for 20 sources gas columns which are within the uncertainties in agreement with the HI columns. We derive for two background sources (RX J0536.9-6913 and RX J0547.0-7040) hydrogen absorbing column densities due to LMC gas, which are in excess to the HI columns. These sources - located in regions of large (~3. 10^21 cm^-2) LMC HI column densities - could be seen through additional gas which may be warm and diffuse, cold or molecular. For 10 sources we derive upper limits for the gas columns additional to HI and constrain the molecular mass fraction to <(30-140)%.Comment: Accepted by A&

Asymptotics for incidence matrix classes

We define {\em incidence matrices} to be zero-one matrices with no zero rows or columns. A classification of incidence matrices is considered for which conditions of symmetry by transposition, having no repeated rows/columns, or identification by permutation of rows/columns are imposed. We find asymptotics and relationships for the number of matrices with $n$ ones in these classes as $n\to\infty$.Comment: updated and slightly expanded versio