Cwikel’s bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrödinger operators with operator-valued potentials. We recover Cwikel’s bound for the Lieb–Thirring constant L0,3 which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the ...

For confining potentials of the form q(r) = r+ p(r), where p(r) decays rapidly and is smooth for r > 0, it is proved that q(r) can be uniquely recovered from the data {Ej , sj}∀j=1,2,3..... Here Ej are energies of bound states and sj are the values u ′ j(0), where uj(r) are the normalized eigenfunctions, ∫∞ 0 u 2 jdr = 0. An algorithm is given for finding q(r) from the knowledge of few first da...

We describe a small, non-intrusive extension to the declarative modelling language Zinc that allows users to define model-specific search. This is achieved by providing a number of generic search patterns that take Zinc user-defined functions as parameters. We show the generality of the approach by using it to implement three very different kinds of search: backtracking search, branch-and-bound...

We consider a simple and well-known category of alternating games (also known as sequential data structures) and several categories derived from it. In each case, we present an extension of Plotkin’s language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types. The quest for such languages results in a novel selection of language primitives for...

A tree pattern is a structured pattern known as a term in formal logic, and a tree pattern language is the set of trees which are the ground instances of a tree pattern. In this paper, we deal with the class of tree languages whose language is de ned as a union of at most k tree pattern languages, where k is an arbitrary xed positive number. In particular, we present a polynomial time algorithm...

A large number of metal deposits are initially extracted via surface methods, but then transition underground without necessarily ceasing to operate above ground. Currently, most mine operators schedule the open pit and underground operations independently and then merge the two, creating a myopic solution. We present a methodology to maximize the NPV for an entire metal deposit by determining ...

Contraction Consistent Stochastic Choice Correspondence We model a general choice environment via probabilistic choice correspondences, with (possibly) incomplete domain and infinite universal set of alternatives. We offer a consistency restriction regarding choice when the feasible set contracts. This condition, ‘contraction consistency’, subsumes earlier notions such as Chernoff’s Condition, ...

We consider a simple and well-known category of alternating games (also known as sequential data structures) and several categories derived from it. In each case, we present an extension of Plotkin’s language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types. The quest for such languages results in a novel selection of language primitives for...

We show that to every recursive total continuous functional Φ there is a representative Ψ of Φ in the hierearchy of partial continuous functionals such that Ψ is S1 − S9 computable over the hierarchy of partial continuous functionals. Equivalently, the representative Ψ will be PCF -definable over the partial continuous functionals, where PCF is Plotkin’s programming language for computable func...