On σ-Embedded and σ-n-Embedded Subgroups of Finite Groups

Siberian Mathematical Journal - Let G be a finite group, and let σ = {σi | i ∈ I} be a partition of the set of all primes ℙ and σ(G) = {σi | σi ∩...     

Cardinalities of σ-complete OML's

In this paper we show that the Comfort-Hager result on cardinalities of-complete Boolean algebras is also true for-complete OML's having a bound on the number of complements. Using the Kaplansky theorem on continuous geometries we get a result on modular ortho-lattices. We also get a result on cardinalities of saturated OML's.Presented by R. McKenzie.Supported by the NSF of Srbija through Math. Inst., Grant #401A.     

Geometries on σ-Hermitian matrices

Ring geometry and the geometry of matrices naturally meet at the ring R := K ^n×n of (n×n)-matrices with entries in a field K (not necessarily commutative). Our aim is to strengthen the interaction between these disciplines. Below we sketch some results from either side, even though not in their most general form, but in a way that is tailored to our needs.     

Characterization of residual σ-algebras

The behavior of residual -algebras is studied. For a probability space (, , P) a new topology is introduced on the set of all -subalgebras. Necessary and sufficient conditions for the independence of events from the final -algebra are obtained in terms of mixing.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1149–1152, August, 1992.     

The Infinite-dimensional σ-widthsof Besov Classes

Let (X(Rd), x) be a normed space of real functions on Rd. Let > 0 and P be theoperator in X(Rd) defined by P f(x) = x(x)f(x) (where (x) is the characteristic functionof the cube Id = [- , ]d). Let L be a subspace of X(Rd). Set P L= {P f: f L}. SupposeL is locally-finite dimensional, i.e., dim(P L,X) < for every > 0. Then the followingquantity is said to be the average dimension of L in X (in the sense of LED)(see [1]).Let > 0, and C be a centrally symmetric subset of X(Rd). The i…     

On σ-images of Metric Spaces

In this paper the relation between the σ-images of metrical spaces and spaces with σ-locally finite cs-network, or spaces with σ-locally finite cs^*-network, or spaces with σ-locally finite sequence neighborhood network, or spaces with σ-locally finite sequence open network are established by use of σ-mapping.     

Three theorems on σ-m-expandable spaces

Results concerning the connections between -m-expandability and compact-m-expandability, as well as the connections between -m-normality and compact-m-normality. Two problems are proposed.     

Metric and Complete Metric σ-Frames

A -frame is a lattice in which countable joins exist and binary meets distribute over countable joins. In this paper, the category MFrm, of metric -frames, is introduced, and it is shown to be equivalent to the category MLFrm _u, of metric Lindelöf frames.Finally, it is shown that the complete metric -frames are exactly the cozero parts of complete metric Lindelöf frames.     

ON σ-FINITE INTEGRALS ON C-ALGEBRAS

This paper considers positive Iinear functionals f defined on a dense -subalgebra, which is an analogue of the continuous functions with compact supports, of a C_*-algebra. L~1-spaces associated with f are studied. Also introduced is an analogue of the bounded Borel functions vanishing at infinity.     

A compactness property of Dedekind σ-completef-rings

We prove that Dedekind -completef-rings are boundedly countably atomic compact in the language (+, –, ·,, , ). This means that whenever is a countable set of atomic formulae with parameters from some Dedekind -completef-ringA every finite subsystem of which admits a solution in some fixed productK of bounded closed intervals ofA, then admits a solution inK.Presented by M. Henriksen.     

A Cantor-Bernstein Theorem for σ-Complete MV-Algebras

The Cantor-Bernstein theorem was extended to -complete boolean algebras by Sikorski and Tarski. Chang's MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Lukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.     

On σ-discrete borel mappings via quasi-metrics

Let X and Y be metrizable spaces. We show that, for a mapping f : X Y, there exists a quasi-metric X inducing the topology of X such that f regarded as a mapping from (X, max{, ^–1}) to Y is continuous if and only if f in the original topology of X is a -discrete map of Borel class 1. Further, we prove that, for every -discrete mapping f: X Y of Borel class + 1, there exists a compatible quasi-metric on X such that f : (X, max{, ^–1}) Y is of Borel class . We also investigate a more general situation when the range of the mapping under consideration is not necessarily metrizable. In passing, we obtain some results related to the behaviour of absolutely Borel sets and absolutely analytic spaces with respect to compatible quasi-metrics.     

Slice Sampling σ-Stable Poisson-Kingman Mixture Models

The article is concerned with the use of Markov chain Monte Carlo methods for posterior sampling in Bayesian nonparametric mixture models.In particular, we consider the problem of slice sampling mixture models for a large class of mixing measures generalizing the celebrated Dirichlet process. Such a class of measures, known in the literature as σ-stable Poisson-Kingman models, includes as special cases most of the discrete priors currently known in Bayesian nonparametrics, for example, the two-parameter Poisson-Dirichlet process and the normalized generalized Gamma process. The proposed approach is illustrated on some simulated data examples. This article has online supplementary material.