Improvement of mathematical models for vehicle handling. Volume 7: technical manual for the general simulation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 8: summary report. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 1: user's guide for the five degree of freedom models. Final report.

Mode of access: Internet.

Improvement of mathematical models for simulation of vehicle handling. Volume 2: programmers' guide for the five degree of freedom models. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 3: technical manual for the five-degree-of-freedom models. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for vehicle handling. Volume 4: users'guide for the general simulation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 5: programmers' guide for the vehicle model. Part I: documentation through subroutine IOUT. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 5: programmers' guide for the vehicle model. Part 2: documentation for subroutines PRTDIC through KNMTC. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Improvement of mathematical models for simulation of vehicle handling. Volume 5: programmers' guide for the vehicle model. Part 3: documentation for subroutines SLPCLC through OUTPUT and a double precision listing. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Applicability of two mathematical models to the batch settling of activated sludge.

"Supported by Federal Water Pollution Control Administration, U.S. Department of the Interior. Research project WP-01011."

Regional adjustments in grain production : a linear programming analysis : mathematical models, proofs, methods of data collection and estimation, and supplementary tables /

Cover title.

Summary report from Workshop on Two-Dimensional Mathematical Models for Use in Hydraulic Problems /

Mode of access: Internet.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

An integrated scheduling problem of PCB components on sequential pick-and-place machines:mathematical models and heuristic solutions

This paper formulates several mathematical models for determining the optimal sequence of component placements and assignment of component types to feeders simultaneously or the integrated scheduling problem for a type of surface mount technology placement machines, called the sequential pick-andplace (PAP) machine. A PAP machine has multiple stationary feeders storing components, a stationary working table holding a printed circuit board (PCB), and a movable placement head to pick up components from feeders and place them to a board. The objective of integrated problem is to minimize the total distance traveled by the placement head. Two integer nonlinear programming models are formulated first. Then, each of them is equivalently converted into an integer linear type. The models for the integrated problem are verified by two commercial packages. In addition, a hybrid genetic algorithm previously developed by the authors is adopted to solve the models. The algorithm not only generates the optimal solutions quickly for small-sized problems, but also outperforms the genetic algorithms developed by other researchers in terms of total traveling distance.