A symmetric matrix is Robinsonian if its rows and columns can be simultaneously reordered in such a way that entries are monotone nondecreasing in rows and columns when moving toward the diagonal. The adjacency matrix of a graph is Robinsonian precisely when the graph is a unit interval graph, so that Robinsonian matrices form a matrix analogue of the class of unit interval graphs. Here we prov...

We consider a firm moving towards a stochastic final destination, to be chosen from a discrete set after a decision period. The decision period itself may be deterministic or stochastic. We assume the firm can move at variable innovation (R&D) speed associated with a monotone nondecreasing variable cost, and it can also stop and move anywhere. There is a fixed cost per time unit "carried" by th...

We introduce the concept of quasi-Lovász extension as being a mapping f : I → IR defined over a nonempty real interval I containing the origin, and which can be factorized as f(x1, . . . , xn) = L(φ(x1), . . . , φ(xn)), where L is the Lovász extension of a pseudo-Boolean function ψ : {0, 1} → IR (i.e., the function L : IR → IR whose restriction to each simplex of the standard triangulation of [...

In this paper we consider quasi-concave set functions defined on antimatroids. There are many equivalent axiomatizations of antimatroids, that may be separated into two categories: antimatroids defined as set systems and antimatroids defined as languages. An algorthmic characterization of antimatroids, that considers them as set systems, was given in [4]. This characterization is based on the i...

Minimax Rules Under Zero-One Loss In this paper, we obtain minimax and near-minimax nonrandomized decision rules under zeroone loss for a restricted location parameter of an absolutely continuous distribution. Two types of rules are addressed: monotone and nonmonotone. A complete-class theorem is proved for the monotone case. This theorem extends the previous work of Zeytinoglu and Mintz (1984)...

This paper presents several analytical results on global asymptotic stability (GAS) and global exponential stability (GES) for the equilibrium states of a general class of discrete-time recurrent neural networks (DTRNNS) with asymmetric connection weight matrices and globally Lipschitz continuous and monotone nondecreasing activation functions. A necessary and sufficient condition is formulated...

*Correspondence: [email protected] 3Department of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China Full list of author information is available at the end of the article Abstract In this paper, we introduce the concept of JS-quasi-contraction and prove some fixed point results for JS-quasi-contractions in complete metric spaces under the assumption that the ...

The monotone convergence theorem holds for the Riemann integral, provided (of course) it is assumed that the limit function is Riemann integrable. It might be thought, though, that this would be difficult to prove and inappropriate for an undergraduate course. In fact the identity is elementary: in the Lebesgue theory it is only the integrability of the limit function that is deep. This article...

Given the prime CNF representation φ of a monotone Boolean function f : {0, 1} 7→ {0, 1}, the dualization problem calls for finding the corresponding prime DNF representation ψ of f . A very simple method (called Berge multiplication [3, Page 52–53]) works by multiplying out the clauses of φ from left to right in some order, simplifying whenever possible using the absorption law. We show that f...