In this article we study a type of directed completion for posets and T0-spaces introduced by O. Wyler [Wy81] that we call the D-completion. The category D of monotone convergence spaces is a full reflective subcategory of the category of topological spaces and continuous maps, and the D-completion gives the reflection of a topological space into D, and as such exhibits a useful universal prope...

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results...

We consider the general class of strongly Fej er monotone map-pings and some of their basic properties. These properties are useful for a convergence theory of corresponding iterative methods which are widely used to solve convex problems. In part II the geometrical properties of these map-pings are studied. In particular the maximal of such mappings with respect to set inclusion of the images ...

This paper presents a simple chaotic circuit consisting of two capacitors, one linear two-port VCCS and one time-state-controlled impulsive switch. The impulsive switch causes rich chaotic and periodic behavior. The circuit dynamics can be simplified into a one-dimensional return map that is piecewise linear and piecewise monotone. Using the return map, we clarify parameter conditions for chaot...

This paper proposes a novel color correction scheme for image stitching where the color map transfer is modelled by a monotone Hermite cubic spline and smoothly propagated into the target image. A three-segments monotone cubic spline minimizing color distribution statistics and gradient differences with respect to both the source and target images is used. While the spline model can handle non-...

In this paper a theorem is discussed that unifies two lines of work in I/O monotone control systems. Under a generalized small gain hypothesis, it is shown that almost all solutions of closed loops of MIMO monotone systems are convergent, regardless of whether the feedback is positive or negative. This result is based on a topological argument showing that any monotonically decreasing n-dimensi...

Many computational problems related to probabilistic networks are complete for complexity classes that have few ’real world’ complete problems. For example, the decision variant of the inference problem (pr) is PP-complete, the map-problem is nppp-complete and deciding whether a network is monotone in mode or distribution is conppp-complete. We take a closer look at monotonicity; more specific,...

It is shown that a set-valued map M : R ⇒ R is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph. We also show that the conditions (iii) and (v) can be replace...

In the context of decision making under uncertainty, I formalize the concept of analogy: an Analogy between two decision problems is a mapping that transforms one problem into the other while preserving the problem’s structure. After identifying the basic structure of a decision problem, I introduce the concepts of Analogical Reasoning Operator and of Analogical Reasoning Preference. The former...

(1) some basic features to treat partially ordered sets; (2) the ability to enumerate, create, and display monotone and regular partitions of partially ordered sets; (3) the capability of constructing the lattices of partitions of a poset, and of doing some useful computations on these structures; (4) the possibility of computing products and coproducts in the category of partially ordered sets...