We construct a family of 2א1 trees of size א1 and no uncountable branches that in a certain way codes all ω1sequences of infinite subsets of ω. This coding allows us to conclude that in the presence of the club guessing between א1 and א0, these trees are pairwise very different. In such circumstances we can also conclude that the universality number of the ordered class of trees of size א1 with...

This article is devoted to two different generalizations of projective Boolean algebras: openly generated Boolean algebras and tightly σ-filtered Boolean algebras. We show that for every uncountable regular cardinal κ there are 2 pairwise non-isomorphic openly generated Boolean algebras of size κ > א1 provided there is an almost free non-free abelian group of size κ. The openly generated Boolea...

Let φ be a function that maps any non-empty subset A of R to a non-empty subset φ(A) of R. A φ-cover of a set T = {T1, T2, . . . , Tm} of pairwise non-crossing trees in the plane is a set of pairwise disjoint connected regions such that 1. each tree Ti is contained in some region of the cover, 2. each region of the cover is either (a) φ(Ti) for some i, or (b) φ(A ∪B), where A and B are construc...

Analytic formulas are developed for various types of power and error rates of some closed testing procedures. The formulas involve non-convex regions that may be integrated with high, pre-specified accuracy using available software. The non-convex regions are represented as a union of hyper-rectangles. These regions are transformed to the unit hypercube, then summed, to create an expression for...

This paper describes a series of experiments in using logistic regression machine learning as a method for entity resolution. From these experiments the authors concluded that when a supervised ML algorithm is trained to classify a pair of entity references as linked or not linked pair, the evaluation of the model’s performance should take into account the transitive closure of its pairwise lin...

An infinite countable Steiner triple system is called universal if any countable Steiner triple system can be embedded into it. The main result of this paper is the proof of non-existence of a universal Steiner triple system. The fact is proven by constructing a family S of size 2 of infinite countable Steiner triple systems so that no finite Steiner triple system can be embedded into any of th...

Memory effects are often introduced during coarse-graining of a complex dynamical system. In particular, a generalized Langevin equation (GLE) for the coarse-grained (CG) system arises in the context of Mori-Zwanzig formalism. Upon a pairwise decomposition, GLE can be reformulated into its pairwise version, i.e., non-Markovian dissipative particle dynamics (DPD). GLE models the dynamics of a si...

The far-infrared vibration-rotation spectrum of the out-of-plane DC1 bending band of Ar2-DC1 is observed around 36.0cm -1. The experimental bending frequency, rotational constants and hyperfine coupling constants are compared with the results of calculations employing both pairwise-additive and non-additive interaction potentials. As found previously for Ar2-HC1, there are substantial discrepan...