A variational problem for three fluids in which gravitational and surface tension forces are in equilibrium is studied using sets of finite perimeter and functions of bounded variation. Existence theorems are proven which imply the existence of an axisymmetric floating drop. This problem has been studied previously as a free boundary problem for axisymmetric capillary surfaces by Elcrat, Neel a...

by Dune Nixon : '"The Albany State booters broke their three game'losing streak Saturday with a decisive 4-1 win over Brooklyn College. The Great Danes, led by high-scoring Maurice Tsododo, really seemed to jell in this one. All phases of their game came around at once and resulted in an almost complete domination of the Brooklyn eleven. As the game got under way it looked as if Albany might be...

Sequence-to-sequence (Seq2Seq) models with attention have excelled at tasks which involve generating natural language sentences such as machine translation, image captioning and speech recognition. Performance has further been improved by leveraging unlabeled data, often in the form of a language model. In this work, we present the Cold Fusion method, which leverages a pre-trained language mode...

We present new complexity results on answer set checking for nonground programs under a variety of syntactic restrictions. For several of these problems, the kind of representation of the answer set to be checked is important. In particular, we consider set-based and bitmap-based representations, which are popular in implementations of Answer Set Programming systems. Furthermore, we present new...

We show that a set of graphs has bounded tree-width or bounded path-width if and only if the corresponding set of line graphs has bounded clique-width or bounded linear clique-width, respectively. This relationship implies some interesting algorithmic properties and re-proves already known results in a very simpleway. It also shows that theminimization problem forNLC-width isNP-complete. © 2007...

In this paper X denotes a set. Let L be a lattice. Note that Poset(L) has l.u.b.’s and g.l.b.’s. Let L be an upper-bounded lattice. One can verify that Poset(L) is upper-bounded. Let L be a lower-bounded lattice. One can verify that Poset(L) is lower-bounded. Let L be a complete lattice. Note that Poset(L) is complete. Let X be a set. Then X is an order in X . Let X be a set. The functor 〈X ,⊆〉...

Let Z and X be Banach spaces, U ⊂ Z an open convex set and f : U → X a mapping. We say that f is a delta-convex mapping (d. c. mapping) if there exists a continuous convex function h on U such that y ◦ f + h is a continuous convex function for each y ∈ Y , ‖y∗‖ = 1. We say that f : U → X is locally d. c. if for each x ∈ U there exists an open convex U ′ such that x ∈ U ′ ⊂ U and f |U ′ is d. c....

This paper starts with a study of the minimum of the Rényi divergence subject to a fixed (or minimal) value of the total variation distance. Relying on the solution of this minimization problem, we determine the exact region of the points ( D(Q||P1), D(Q||P2) ) where P1 and P2 are any probability distributions whose total variation distance is not below a fixed value, and the probability distri...