On estimator efficiency in stochastic processes

It is shown, under mild regularity conditions on the random information matrix, that the maximum likelihood estimator is efficient in the sense of having asymptotically maximum probability of concentration about the true parameter value. In the case of a single parameter, the conditions are improvements of those used by Heyde (1978). The proof is based on the idea of maximum probability estimators introduced by Weiss and Wolfowitz (1967).     

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.     

Probabilistic metric spaces constructed from stationary Markov chains

Cumulative transition density functions of stationary Markov chains are shown to sausfy the Menger triangle inequality under thet-normT = Prod.     

The fundamental duality of partially ordered sets

The representation of partially ordered sets by subsets of some set such that specified joins (meets) are taken to unions (intersections) suggests two categories, that of partially ordered sets with specified joins and meets, and that of sets equipped with suitable collections of subsets, and adjoint contravariant functors between them. This, in turn, induces a duality including, among several others, the two Stone Dualities and that between spatial locales and sober spaces.     

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.     

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.     

Self-adjunctions and matrices

It is shown that the multiplicative monoids of Temperley-Lieb algebras are isomorphic to monoids of endomorphisms in categories where an endofunctor is adjoint to itself. Such a self-adjunction is found in a category whose arrows are matrices, and the functor adjoint to itself is based on the Kronecker product of matrices. This self-adjunction underlies the orthogonal group case of Brauer's representation of the Brauer centralizer algebras.     

Photoreflectance study of energy level structure of self-assembled InAs/GaAs quantum dots emitting at 1.3 μm

Photoreflectance and photoluminescence measurements were performed on the ensemble of self assembled InAs/GaAs quantum dots designed to emit at 1.3 μm. As many as six QDs-related optical transitions were observed in PR spectra, the energies of which were confirmed by high-excitation PL results. Numerical calculations allowed estimating the average size of the dots, which is larger than for standard InAs/GaAs QDs. This result is in agreement with structural data. Additionally, the energy level structure for such QDs was derived and compared with the electronic structure of standard InAs/GaAs dots. It was shown that the energy level structure of such large dots qualifies them for the active region of a laser emitting at 1.3 μm.     

Der Verband der zusammenhängenden Untergruppen einer kommutativen algebraischen Gruppe

We classify the connected commutative algebraic groups having as lattice of connected closed subgroups a projective space and determine the coordinate fields of these projective spaces. Furthermore we determine the not necessarily commutative connected algebraic groups with a distributive or boolean lattice of connected closed subgroups.

Received: 3 December 2004