Study of transient photoconductivity of GaN epilayer grown by metalorganic chemical vapor deposition

Received: 24 March 1998/Accepted: 10 July 1998     

Topological representation of posets

There is a canonical imbedding of a poset into a complete Boolean lattice and hence into a Boolean lattice. This gives it a representation as a collection of clopen sets of a Boolean space. There are reflective functions from a category of distributive posets to the subcategories of distributive and Boolean lattices and consequently a topological dual equivalence that extends the Stone duality of Boolean lattices.Presented by B. Jonsson.     

Some comments on the hazard gradient

For random variables T₁,…,T_n, the gradient of $\text{R(t) = ?log}\text{P}\text{{T}{}_1\text{> t}{}_1\text{,…,T}{}_{\mathrm{n}}\text{> t}{}_{\mathrm{n}}\text{}}$ is called the hazard gradient. Some properties of this multivariate version of the hazard rate are demonstrated, and some examples are given to show the usefulness of the hazard gradient in characterizing distributions or families of distributions.     

Quasi-monotone mappings on θn-continua

A continuous function f from a continuum X onto a continuum Y is quasi-monotone if, for every subcontinuum M of Y with nonvoid interior, f^-1(M) has a finite number of components each of which is mapped onto M by f. A θ_n-continuum is one that no subcontinuum separates into more than n components. It is known that if f is quasi-monotone and X is a θ₁-continuum, then Y is a θ₁-continuum or a θ₂-continuum that is irreducible between two points. Examples are given to show that this cannot be generalized to a θ_n-continuum and n + 1 points for any n >1, but it is proved that if f is quasi-monotone and X is a θ_n-continuum, then Y is a θ_n-continuum or a θ_n+1-continuum that is the union of n + 2 continua H,S₁,S₂,…,S_n+1, whe for each i, S_i is the closure of a component of Y H, S_i is irreducible from some point P_i to H, and H is irreducible about its boundary. Some theorems and examples are given concerning the preservation of decomposition elements by a quasi-monotone map defined on a θ_n-continuum that admits a monotone, upper-semicontinuous decomposition onto a finite graph.     

Representations for eigenfunctions of expected value operators in the Wishart distribution

Recent articles by Kushner and Meisner (1980) and Kushner, Lebow and Meisner (1981) have posed the problem of characterising the ‘EP’ functions f(S) for which Ef(S) for which E(f(S)) = λ_nf(Σ) for some λ_n ? $\text{R}$, whenever the m × m matrix S has the Wishart distribution W(m, n, Σ). In this article we obtain integral representations for all nonnegative EP functions. It is also shown that any bounded EP function is harmonic, and that EP polynomials may be used to approximate the functions in certain L^p spaces.     

Molecular structures of inorganic compounds of low volatility: I. Salts of oxygen acids of the type M2XO4

We report an electron diffraction study of the molecular structure of gaseous cesium and thallium sulphates and cesium molybdate and tungstate. The average structure found for the M₂XO₄ molecules is described by a model (symmetry D_2d) in which the metal atoms bridge two edges of an XO₄ tetrahedron to form two 4-membered mutually perpendicular planar MO₂X rings.The data lead to conclusions on the complex nature of intramolecular motion. This motion may roughly correspond to great displacements of metal atoms on the surface of an imaginary sphere described near the tetrahedral acid residue.     

L-spaces and S-spaces in P(ω)

We show that CH implies that $\text{P}\text{(ω)}$, when equipped with the Vietoris topology, has a subspace which is an L-space and a subspace which is an S-space. This is an immediate consequence of the following purely combinatorial result: CH implies the existence of an ω₁-sequence 〈x_α: α < ω₁〉 in $\text{P}\text{(ω)}$ such that (1) if α<β<ω₁, then $\text{X}{}_{\mathrm{\beta }}\text{?}{}^1\text{X}{}_{\mathrm{\alpha }}$; (2) if I ?ω₁ is unaccountable, then there are distinct α, β ∈ I with X_β ?X_α.     

A generalized hypergreedy algorithm for weighted perfect matching

We give a generalization of the hypergreedy algorithm for minimum weight perfect matching on a complete edge weighted graph whose weights satisfy the triangle inequality. With a modified version of this algorithm we obtain a logn-approximate perfect matching heuristic for points in the Euclidean plane, inO(n log² n) time.This research was supported in part by the DIMACS Grant No. NSF-STC88-09648.This research was supported in part by the NSF under Grant No. CCR 88-07518.     

Relatively pseudocomplemented semilattices amalgamate strongly

Letk be any finite or infinite cardinal andS _ω the symmetric group of denumerable infinite degree. It is shown that fori<k ifG _i is thei-th row of a matrix whose columns are allk-termed sequences of elements ofS _ω in each of which all but a finite number of terms are equal to the identity ofS _ω thenG _i 's (withG _i ⁻¹ 's defined in an obvious way and with coordinatewise multiplication amongG _i 's andG _i ⁻¹'s) generate the Free Group onk free generatorsG _i . Analogously, Free Abelian and other types of free groups are also constructed. Presented by L. Fuchs.     

The rational line partitions every self-dense metrisable space

In the present note we shall prove that a metrisable space can be partitioned by the rational line if that space is self-dense. This gives an affirmative answer to a question raised by Rankston-McGovern [1].