We consider an infinite horizon production planning problem with non-stationary, convex production and inventory costs. Backlogging is allowed unlike related previous work and inventory cost is interpreted as backlogging cost when inventory is negative. We create finite horizon truncations of the infinite horizon problem and employ classic results on convex production planning to derive a close...

The zero-temperature random-field Ising model is solved analytically for magnetization versus external field for a bilayered Bethe lattice. The mechanisms of infinite avalanches which are observed for small values of disorder are established. The effects of variable interlayer interaction strengths on infinite avalanches are investigated. The spin-field correlation length is calculated and its ...

The Kolmogorov complexity function of an infinite word ξ maps a natural number to the complexity K(ξ n) of the n-length prefix of ξ. We investigate the maximally achievable complexity function if ξ is taken from a constructively describable set of infinite words. Here we are interested in linear upper bounds where the slope is the Hausdorff dimension of the set. As sets we consider Π1-definable...

We study abelian repetitions in partial words, or sequences that may contain some unknown positions or holes. First, we look at the avoidance of abelian pth powers in infinite partial words, where p > 2, extending recent results regarding the case where p = 2. We investigate, for a given p, the smallest alphabet size needed to construct an infinite partial word with finitely or infinitely many ...

A pair of graphs (Hb,Hr) is highly Ramsey-infinite if there is some constant c such that for large enough n there are at least 2cn 2 non-isomorphic graphs on n or fewer vertices that are minimal with respect to the property that when their edges are coloured blue or red, there is necessarily a blue copy of Hb or a red copy of Hr. We show that a pair of 3-connected graphs is highly Ramsey-infini...

An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain at most Θ(n) distinct factors, and there exist words of length n containing Θ(n) distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length n grow...

This paper presents some examples of ill-behaved central paths in convex optimization. Some contain infinitely many fixed length central segments; others manifest oscillations with infinite variation. These central paths can be encountered even for infinitely differentiable data.

The use of classical logic for some combinatorial proofs, as it is the case with Ramsey’s theorem, can be localized in the Infinite Pigeonhole (IPH) principle, stating that any infinite sequence which is finitely colored has an infinite monochromatic subsequence. Since in general there is no computable functional producing such an infinite subsequence, we consider a Π2-corollary, proving the cl...

Partial words are sequences over a finite alphabet that may contain wildcard symbols, called holes, which match or are compatible with all letters; partial words without holes are said to be full words (or simply words). Given an infinite partial word w, the number of distinct full words over the alphabet that are compatible with factors of w of length n, called subwords of w, refers to a measu...

In this paper we investigate local-to-global phenomena for a new family of complexity functions of infinite words indexed by k ∈ N1∪{+∞} where N1 denotes the set of positive integers. Two finite words u and v in A∗ are said to be k-abelian equivalent if for all x ∈ A∗ of length less than or equal to k, the number of occurrences of x in u is equal to the number of occurrences of x in v. This def...