This paper is devoted to integrability conditions for systems of linear difference and differential equations with difference parameters. It is shown that such a system is difference isomonodromic if and only if it is difference isomonodromic with respect to each parameter separately. Due to this result, it is no longer necessary to solve non-linear difference equations to verify isomonodromici...

In temporal specialization, the database designer restricts the relationship between the valid t ime-stamp (recording when something is true in the reality being modeled) and the transaction t ime-stamp (recording when a fact is stored in the database). An example is a retroactive temporal event relation, where the event must have occurred before it was stored, i.e., the valid t ime-stamp is re...

Remark 1 In this text, we always work between 0 and 1 with 1/2 playing the rôle of the midpoint. A simple rescaling allows to work between −1 and 1 with 0 playing the rôle of a midpoint. • A valued relation T is said to be reflexive if T (x, x) = 1, for all x ∈ X. A valued relation T on X such that T (x, y) ∈ {0, 1}, for all x, y ∈ X, is said to be crisp. As is usual, we write x T y instead of ...

It has been developed a C++ program that generates random fuzzy relations of a given dimension and computes their T-transitive closure (that contains the initial relation) and the new T-transitivized relation (that is contained in the initial relation) for the t-norms minimum, product and Lukasiewicz. It has been computed several distances between both transitive closure and transitivized relat...

Energy dissipation in a nonequilibrium steady state is studied in driven quantum Langevin systems. We analyze a characteristic function that generates energy dissipation flow to thermal environment. This function gives a general formula for the average rate of energy dissipation using an autocorrelation function for the system variable. This leads to a general expression of the equality that co...

For theoretical fuzzy control it is a well known strategy to transform a system of control rules into a system of relation equations. Because these systems of relation equations are not always solvable, solvability criteria and approximate solutions have been discussed. We reconsider some of the results in this field and extend them using more recent results on t-norm based fuzzy logics and on ...

This paper surveys some recent results on the existence and multiplicity of periodic solutions of nonlinear difference equations of the first order under Ambrosetti-Prodi or Landesman-Lazer type conditions.