At Carnegie Mellon University in 2011, numerical approximations of incompressible fluid with specific density and viscosity approximate hydrocarbon reservoirs. Hydrocarbon reservoirs, detected with ultraviolet lasers, can be differentiated from water, oil and gas at varied temperatures and pressures. Nuclear magnetic resonance helps researchers distinguish ethane, propane, methane, carbon dioxide and nitrogen by viscosity, diffusion rate, density, pressure and hydrogen index. Seismic readings, 50 meters apart, help the United States Geological Survey map the three-dimensional geometry of petroleum or hydrocarbon reservoirs. The USGS also maps the locations of aquifers, reservoirs of water, which can undermine mining operations by filling the mineshaft with water.
Applied mathematics, statistics and bio-statistics at Old Dominion University yield analytical and numerical approximations, probability and statistical inference in oceanography and meteorology. Approximations in applied mathematics explain biological, geological, ecological, business, banking and medical statistics. The American Society of Mechanical Engineering on the University of California Los Angeles campus researches robotic microsurgery in USC's Advanced Surgical and Interventional Technology classroom. Motors, 1.5 mm long, are used in minimally invasive medical microsurgery. Since 1979, the Carnegie Mellon Robotics Institute has created robots equipped with sensors, data and algorithms to explore uncertain areas and transmit data to researchers.
Strategies for success include resiliency. Successful enterprise requires recognizing opportunities and strategic marketing. Daily monitoring of profit and loss with the ability to change direction if profits or stock prices fall, is a necessary characteristic of a successful resilient business. Financial markets are approximated by theoretical models for decision making. Network analysis of projected sales yield production information for management. For example, network analysis of seasonal summer sales tells merchants when they must receive delivery of merchandise, how much they iare likely to sell and the number in their inventory. Basic mathematical approximations tell merchants when to order more of an inventoried part.
Actuarial science is based on probabilistic approximations of age and mortality factors, but actuarial ages are usually given in years and half-years, with no months or days considered. Mortality rates are based on diverse aggregate sums, not mixed factors in unique individuals. Financial and insurance actuarial models consider collections of contracts or policies. Investors approximations are based on a portfolio of investments. Central tendency is an approximation of distribution. Statistical models of pension plans, risk estimation and modeling of investment options. The "Journal of Financial and Actuarial Statistics" addresses mortality adjustment factors, time-trend regression adjustments and simulation of stochastic models.