In this note we consider residual-based a posteriori error estimation for finite element approximations of the transport equation. For the discretization we use piecewise affine continuous or discontinuous finite elements and symmetric stabilization of interior penalty type. The lowest order discontinuous Galerkin method using piecewise constant approximation is included as a special case. The ...

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for a qualitative behaviour of a class of li...

Piecewise behavioral models are commonly adopted for modeling and linearization of RF power amplifiers (PAs) that exhibit strong amplitude-dependent nonlinear distortion characteristics, as global polynomial approximations tend to underperform in such scenarios. In this article, we consider a new piecewise model PAs based on the mixture experts (ME) approach, which builds probabilistic allows d...

We study the finite element approximation of the stationary Stokes equations in the velocitypressure formulation using continuous piecewise quadratic functions for velocity and discontinuous piecewise linear functions for pressure. For some meshes this method is unstable, even after spurious pressure modes are removed. For other meshes there are spurious local pressure modes, but once they are ...

A linearization technique is developed for multi-objective multi-quadratic 0-1 programming problems with linear and quadratic constraints to reduce it to multi-objective linear mixed 0-1 programming problems. The method proposed in this paper needs only O (kn) additional continuous variables where k is the number of quadratic constraints and n is the number of initial 0-1 variables.

Managing shelf space is critical for retailers to attract customers and to optimize profit. This paper develops a shelf space allocation optimization model that explicitly incorporates essential in-store costs and considers spaceand cross-elasticities. We propose a piecewise linearization technique for approximating the complicated nonlinear model that relaxes the nonconvex optimization problem...

denotes the greatest integer function, and x−1, x0 are given real numbers. Since 1980’s differential equations with piecewise constant arguments have attracted great deal of attention of researchers in mathematical and some of the others fields in science. Piecewise constant systems exist in a widely expanded areas such as biomedicine, chemistry, mechanical engineering, physics, etc. These kind...

In many cases, complex system behaviors are naturally modeled as nonlinear differential equations. However, these equations are often hard to analyze because of “stiffness” in their numerical behavior and the difficulty in generating and interpreting higher order phenomena. Engineers often reduce model complexity by transforming the nonlinear systems to piecewise linear models about operating p...

Mendelian randomization, the use of genetic variants as instrumental variables (IV), can test for and estimate the causal effect of an exposure on an outcome. Most IV methods assume that the function relating the exposure to the expected value of the outcome (the exposure-outcome relationship) is linear. However, in practice, this assumption may not hold. Indeed, often the primary question of i...