in recent years, it has become increasingly important to incorporate explicit dynamics in economic analysis. these two tools that mathematicians have developed, differential equations and optimal control theory, are probably the most basic for economists to analyze dynamic problems. in this paper i will consider the linear differential equations on the plane (phase diagram) and elements of nonl...

Rooted in structural dynamics theory, three approximate procedures for estimating seismic demands for bridges crossing fault-rupture zones and deforming into their inelastic range are presented: modal pushover analysis �MPA�, linear dynamic analysis, and linear static analysis. These procedures estimate the total seismic demand by superposing peak values of quasi-static and dynamic parts. The p...

data envelopment analysis (dea) is a technique used to compare efficiency in various sectors such as hospitals, chain stores, and dealerships. it represents a set of linear programming techniques and uses deter-ministic data (inputs and outputs), in stable conditions. the dea technique cannot be used when there is data with indeterministic nature, or when there is an environment with dynamic co...