We will show that if X is a tree-complete subspace of ∞ , which contains c 0 , then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming. 1. Introduction. It is known that ∞ has an equivalent strictly convex renorming [2]; however, by a result due to Lindenstrauss, it cannot be equivalently renormed in locally u...

We present an extension of System F with call-by-name exceptions. The type system is enriched with two syntactic constructs: a union type A ? ∪{ε} for programs of type A whose execution may raise the exception ε at top level, and a corruption type A{ε} for programs that may raise the exception ε in any evaluation context (not necessarily at top level). We present the syntax and reduction rules ...

Let X be a non-locally convex F-space (complete metric linear space) whose dual X' separates the points of X. Then it is known that X possesses a closed subspace N which fails to be weakly closed (see [3]), or, equivalently, such that the quotient space XIN does not have a point separating dual. However the question has also been raised by Duren, Romberg and Shields [2] of whether X possesses a...

Weakly median graphs, being defined by interval conditions and forbidden induced subgraphs, generalize quasi-median graphs as well as pseudo-median graphs. It is shown that finite weakly median graphs can be decomposed with respect to gated amalgamation and Cartesian multiplication into 5-wheels, induced subgraphs of hyperoctahedra (alias cocktail party graphs), and 2-connected bridged graphs n...

The Banach space E has the weakly compact approximation property (W.A.P. for short) if there is a constant C < ∞ so that for any weakly compact set D ⊂ E and ε > 0 there is a weakly compact operator V : E → E satisfying supx∈D ‖x − V x‖ < ε and ‖V ‖ ≤ C. We give several examples of Banach spaces both with and without this approximation property. Our main results demonstrate that the James-type ...

We study some questions concerning the structure of the set of spreading models of a separable infinite-dimensional Banach space X. In particular we give an example of a reflexive X so that all spreading models of X contain l1 but none of them is isomorphic to l1. We also prove that for any countable set C of spreading models generated by weakly null sequences there is a spreading model generat...

We construct an explicit family of linear rank-metric codes over any field Fh that enables efficient list decoding up to a fraction ρ of errors in the rank metric with a rate of 1−ρ−ε, for any desired ρ ∈ (0, 1) and ε > 0. Previously, a Monte Carlo construction of such codes was known, but this is in fact the first explicit construction of positive rate rank-metric codes for list decoding beyon...

Given n line segments in the plane, do they form the edge set of a weakly simple polygon; that is, can the segment endpoints be perturbed by at most ε, for any ε > 0, to obtain a simple polygon? While the analogous question for simple polygons can easily be answered in O(n logn) time, we show that it is NP-complete for weakly simple polygons. We give O(n)-time algorithms in two special cases: w...

We investigate the thermal stability of helical hydrophobic oligomers using a three-dimensional, water-explicit lattice model and the Wang-Landau Monte Carlo method. The degree of oligomer helicity is controlled by the parameter ε(mm) < 0, which mimics monomer-monomer hydrogen bond interactions leading to the formation of helical turns in atomistic proteins. We vary |ε(mm)| between 0 and 4.5 kc...

CG, SYMMLQ, and MINRES are Krylóv subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This underst...