finding the most appropriate governing equation under different environmental conditions is the most important step for both designing sorption systems and pollutant transport modeling. in this study, the second order model based on the sorbent concentration is theoretically and experimentally investigated. a circular flume was used for the sorption of cadmium by zeolite to simulate the natural...

A method for identifying a piecewise-linear approximation to the nonlinear forces acting on a system is presented and demonstrated using response data from a micro cantilever beam. It is based on the Restoring Force Surface (RFS) method by Masri and Caughey, which is very attractive when initially testing a nonlinear system because it does not require the user to postulate a form for the nonlin...

Trapezoid maps are a kind of continuous and piecewise linear maps with a flat top. By the conjugacy relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an extension method, we construct all homeomorphic solutions of conjugacy equation φ ◦ f = g ◦ φ for some non-monotone continuous maps f and g. Secondly, using an iterative construction method a...

We introduce a novel computational method for a Mumford–Shah functional, which decomposes a given image into smooth regions separated by closed curves. Casting this as a shape optimization problem, we develop a gradient descent approach at the continuous level that yields nonlinear PDE flows. We propose time discretizations that linearize the problem and space discretization by continuous piece...

Abstract We consider a nonconvex mixed-integer nonlinear programming (MINLP) model proposed by Goldberg et al. (Comput Optim Appl 58:523–541, 2014. 10.1007/s10589-014-9647-y ) for piecewise linear function fitting. show that this MINLP is incomplete and can result in curve not the graph of function, because it misses set necessary constraints. provide two counterexamples to illustrate effect, p...

In this paper an approximate innovation method is introduced for the estimation of diffusion processes given a set of discrete and noisy observations of some of their components. The method is based on a recent extension of Local Linearization filters to the general case of continuous-discrete state space models with multiplicative noise. This filtering method provides adequate approximations f...