We analyze the problem of packing squares in an online fashion: Given a semi-infinite strip of width 1 and an unknown sequence of squares of side length in [0, 1] that arrive from above, one at a time. The objective is to pack these items as they arrive, minimizing the resulting height. Just like in the classical game of Tetris, each square must be moved along a collision-free path to its final...

Coordinate, plural and predicative constructions of noun phrases are common and highly productive in natural languages. They are also related in intricate ways: conjunctive coordination is one of the simple means to form plural NP’s from singular ones; many coordinate and plural NP’s appear naturally in predicative positions. Any theory of grammar and semantic interpretation should account for ...

We present a simple, two dimensional example of a ”cat” – a body with zero angular momentum that can rotate itself with no external forces. This model is used to explain why this problem is known to be a gauge theory and to illustrate the importance of non-commutative operators. We will also show a comparison between the free-space ”cat” in Newtonian mechanics and the same problem in Aristoteli...

Starting from infinitely many supercompact cardinals, we force a model of ZFC where אω2+1 satisfies simultaneously a strong principle of reflection, called ∆-reflection, and a version of the square principle, denoted (אω2+1). Thus we show that אω2+1 can satisfy simultaneously a strong reflection principle and an anti-reflection principle.

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We present a technique for destroying stationary subsets of Pκκ using partial square sequences. We combine this method with Gitik’s poset for changing the cofinality of a cardinal without adding bounded sets to prove a variety of consistency results concerning saturated ideals and the set S(κ, κ+). In this paper we continue our study of consistency results concerning the set S(κ, κ) = {a ∈ Pκκ ...

Let Q0 denote the rational numbers expanded to a meadow by totalizing inversion such that 0 = 0. Q0 can be expanded by a total sign function s that extracts the sign of a rational number. In this paper we discuss an extension Q0(s, √ ) of the signed rationals in which every number has a unique square root.

Considerations regarding predication in ordinary language as well as the ontology of relations suggest a refinement of the Ontological Square, a conceptual scheme used in many foundational ontologies and which consists of particular substrates as well as their types on the one hand and particular attributes as well as their types on the other hand. First, the distinction between particulars and...

INTRODUCTION Lead exposure in children remains a significant public health issue, although many advances have been made. The Mid-Appalachia area (Kentucky, New York, Ohio, Pennsylvania, and West Virginia) is 89-91% rural with a population density of 16-21 people/km2 (41-54 people/mi2). Mid-Appalachia has significant health disparities including concerns for the consequences of greater lead expo...