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

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

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

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