A notion of “radially monotone” cut paths is introduced as an effective choice for finding a non-overlapping edge-unfolding of a convex polyhedron. These paths have the property that the two sides of the cut avoid overlap locally as the cut is infinitesimally opened by the curvature at the vertices along the path. It is shown that a class of planar, triangulated convex domains always have a rad...

We show that whenever A is a monotone σ-complete dimension group, then A+ ∪ {∞} is countably equationally compact, and we show how this property can supply the necessary amount of completeness in several kinds of problems. In particular, if A is a countable dimension group and E is a monotone σ-complete dimension group, then the ordered group of all relatively bounded homomorphisms from A to E ...

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

This thesis is a pedagogical exposition of adequacy for recursive program schemes in the monotone frame. Adequacy relates the operational and denotational meanings of a term; it states that for any term of base type, the operational and denotational meanings are identical. Adequacy is typically proved in the continuous frame. This is a pedagogically questionable step; in order to prove adequacy...

Drawing on recent results in the industrial organization literature (Carvajal et al. 2013), we derive non-parametric tests of the tragedy of the commons. Our approach allows group output to be any arbitrarily concave, differentiable function of total inputs and for individual exploiters of the resource to have any arbitrary convex, differentiable cost of supplying inputs. We show that observed ...

In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are logconcave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a...

In standard property testing, the task is to distinguish between objects that have a property P and those that are ε-far from P , for some ε > 0. In this setting, it is perfectly acceptable for the tester to provide a negative answer for every input object that does not satisfy P . This implies that property testing in and of itself cannot be expected to yield any information whatsoever about t...

Let P be a monotone increasing graph property, let G = (V,E) be a graph, and let q be a positive integer. In this paper, we study the (1 : q) Maker-Breaker game, played on the edges of G, in which Maker’s goal is to build a graph that satisfies the property P . It is clear that in order for Maker to have a chance of winning, G itself must satisfy P . We prove that if G satisfies P in some stron...

A numerical method is developed for fire spread simulation modelling. The two dimensional surface model presented takes into account moisture content, radiation, wind and slope effects, which are by far the most important mechanisms in fire spread. We consider the combustion of a porous solid, where the energy conservation equation is applied. The influence of moisture content and eventually he...