Considered are linear algebraic systems of equations and/or inequalities involving linear dependencies between interval-valued parameters. The goal is to characterize weak and strong solvability of such systems. Since any parametric interval equation is equivalent to a system of parametric interval inequalities, the focus is on the latter. We discuss an algorithmic procedure for characterizing ...

The interval-Newton approach provides the power to solve nonlinear equation solving and global optimization problems with complete mathematical and computational certainty. The primary drawback to this approach is that computation time requirements may become quite high. In this paper, a strategy for using linear programming (LP) techniques to improve computational efficiency is considered. In ...

it is known that a stochastic dierential equation (sde) induces two probabilisticobjects, namely a diusion process and a stochastic ow. while the diusion process isdetermined by the in nitesimal mean and variance given by the coecients of the sde,this is not the case for the stochastic ow induced by the sde. in order to characterize thestochastic ow uniquely the in nitesimal covariance give...

One-third of the people with an age over twenty have some signs of degenerated discs. However, in most of the patients the mere presence of degenerative discs is not a problem leading to pain, neurological compression, or other symptoms. This paper presents an interval type-2 fuzzy hybrid rule-based system to diagnose the abnormal degenerated discs where pain variables are represented by interv...

The general deterministic recombination equation in continuous time is analysed for various lattices, with special emphasis on the lattice of interval (or ordered) partitions. Based on the recently constructed [4] general solution for the lattice of all partitions, the corresponding solution for interval partitions is derived and analysed in detail. We focus our attention on the recursive struc...

Let q(x, t) satisfy the Dirichlet initial-boundary value problem for the nonlinear Schrödinger equation on the finite interval, 0 < x < L, with q 0 (x) = q(x, 0), g 0 (t) = q(0, t), f 0 (t) = q(L, t). Let g 1 (t) and f 1 (t) denote the unknown boundary values q x (0, t) and q x (L, t), respectively. We first show that these unknown functions can be expressed in terms of the given initial and bo...

We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex k-plane. This Riemann-Hilbert problem has explicit (x, t)-dependence and it involves certain functions of k referred to as “spectral functions”. Some of these functions are defined in terms of t...

Timed Petri Nets (also called Duration Petri Nets, DPNs) [7, 8] are a commonly used class for modeling formally complex technical systems as embedded real time systems, for instance in aeronautics. Engineers stated that intervals allowing some variable duration of events would be a more realistic view, so Interval-Timed Petri Nets (ITPNs) have been proposed as generalizations in [2]. Hierarchic...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...