We introduce a generalization of the Stirling numbers called the V-Stirling numbers which are inspired by the symmetric function form of the p, q-binomial coefficients. A number of properties are derived, including recurrence relations, generating functions, orthogonality relations and convolution formulas. The results are used to derive properties of some special cases and provide alternative ...

By de Vries duality, the category of compact Hausdorff spaces is dually equivalent to the category of de Vries algebras (complete Boolean algebras endowed with a proximity-like relation). We provide an alternative “modal-like” duality by introducing the concept of a Gleason space, which is a pair (X,R), where X is an extremally disconnected compact Hausdorff space and R is an irreducible equiva...

In 1995, combined Medicare and Medicaid spending in the last year of life for dually eligible beneficiaries was more than $40,000 per beneficiary. Medicaid's share, primarily for long-term care (LTC), constituted about 40 percent of the total. Beneficiaries under age 65, Black persons, and individuals who died in a hospital had higher than average expenditures. The vast majority (86 percent) re...

Using Medicaid Analytic eXtract (MAX) claims files for 1999 and 2001, the authors describe patterns of prescription drug use and expenditures among dually eligible Medicare and Medicaid beneficiaries for all Medicaid full dually eligible beneficiaries and three important subgroups: (1) aged, (2) disabled, and (3) full-year nursing home residents. The analyses indicate great variation in use and...

In this paper we will generalize the representation theory developed for nite Tarski algebras given in [7]. We will introduce the notion of Tarski space as a generalization of the notion of dense Tarski set, and we will prove that the category of Tarski algebras with semi-homomorphisms is dually equivalent to the category of Tarski spaces with certain closed relations, called T -relations. By t...

Given a topological property (or a class) P, the class P∗ dual to P (with respect to neighbourhood assignments) consists of spaces X such that for any neighbourhood assignment {Ox : x ∈ X} there is Y ⊂ X with Y ∈ P and S {Ox : x ∈ Y } = X. The spaces from P∗ are called dually P. We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define D-sp...

It is shown that in an infinite-dimensional dually separated second category topological vector space X there does not exist a probability measure μ for which the kernel coincides with X. Moreover, we show that in “good” cases the kernel has the full measure if and only if it is finitedimensional. Also, the problem posed by S. Chevet [5, p. 69] is solved by proving that the annihilator of the k...

In [7] we introduced the category MKHaus of modal compact Hausdorff spaces, and showed these were concrete realizations of coalgebras for the Vietoris functor on compact Hausdorff spaces, much as modal spaces are coalgebras for the Vietoris functor on Stone spaces. Also in [7] we introduced the categories MKRFrm and MDV of modal compact regular frames, and modal de Vries algebras as algebraic c...

BACKGROUND Patients on dialysis have high rates of cardiovascular disease and are frequently treated with HMG-CoA reductase inhibitors. Given that these patients have insurance coverage for medications as well as regular contact with health care providers, differences by race in exposure to statins over time should be minimal among patients who are candidates for the drug. METHODS We created ...

The theory of graph games with ω-regular winning conditions is the foundation for modeling and synthesizing reactive processes. In the case of stochastic reactive processes, the corresponding stochastic graph games have three players, two of them (System and Environment) behaving adversarially, and the third (Uncertainty) behaving probabilistically. We consider two problems for stochastic graph...