Jean Leray (1906-98): Master of applied mathematics
Article Abstract:
Jean Leray was born in 1906 and was educated at the Ecole Normale Superieure in Paris. Leray saw mathematics as a tool for modelling, and was inspired by problems im mechanics and physics. His studies of the Navier-Stokes equations were fundamental to fluid dynamics, and his 1934 paper on the Navier-Stokes equations was ahead of its time and remains unsurpassed. He was one of the main sources for the Bourbaki type of mathematics, and his energy estimates for partial differential equations were combined with ideas from algebraic topology.
Publication Name: Nature
Subject: Zoology and wildlife conservation
ISSN: 0028-0836
Year: 1999
User Contributions:
Comment about this article or add new information about this topic:
What you eat is how many you are
Article Abstract:
Decision-making can be cast into a mathematical model, and much has been built on the Homo oeconomicus. It is difficult to tell if an observed demand function is compatible with Homo oeconomicus, and solutions to the minimization problems must satisfy the Slutsky relations, a system of nonlinear partial differential equation. The Slutsky relations have been found to fail, but an experiment by M. Browning and P.A. Chiappori based on data from the Canadian Family Expenditure Survey, indicate that the Homo oeconomicus model is correct
Publication Name: Nature
Subject: Zoology and wildlife conservation
ISSN: 0028-0836
Year: 1997
User Contributions:
Comment about this article or add new information about this topic:
Agreeing on strategies
Article Abstract:
Philip J Reny's theorem introduces John F Nash's equilibria in situations where Nash's own result does not. Two examples are the game of timing (noisy duel), and an auction where bidders compete for a single indivisible prize. Nash equilibria are still achieved by brute calculation requiring that the agents have major computational power, or by trial and error, extending over generations. Reny's results significantly improve on Nash's work.
Publication Name: Nature
Subject: Zoology and wildlife conservation
ISSN: 0028-0836
Year: 1999
User Contributions:
Comment about this article or add new information about this topic:
- Abstracts: Secondary use of aspen cavities by tree-roosting big brown bats. Urban maternity-roost selection by bid brown bats in Colorado
- Abstracts: The eastern coyote. Searching for stately storks. In pursuit of wild dogs and wildness
- Abstracts: Design and results of a waterfowl breeding population survey for Wyoming. Evaluation of visibility correction factors for waterfowl surveys in Wyoming
- Abstracts: A spectacular summer for birds. Keeping an eye on eagles
- Abstracts: S-nitrosylation regulates apoptosis. Control of apoptosis and mitotic spindle checkpoint by survivin