Yvonne Lai, a junior in mathematics, has helped extend a recent mathematical proof of the "double bubble conjecture" to four dimensions.
In a March address to the Undergraduate Mathematics Conference at the Rose-Hulman Institute of Technology, mathematicians from Williams College, Stanford University and the University of Granada announced their proof that the familiar double soap bubble is indeed the optimal shape for enclosing and separating two chambers of air.
In a postscript, a group of undergraduates from Stanford, Williams and MIT including Ms. Lai extended the theorem to four-dimensional bubbles. Working last summer at Williams, they found a way to extend the proof to 4-space and certain cases in 5-space and above. Their work was part of the Research Experiences for Undergraduates sponsored by the National Science Foundation and Williams College. The group's paper on their work is awaiting publication.
METALS FOUND IN BOSTON HARBOR
Caroline Tuit, a graduate student in the MIT/Woods Hole Oceanographic Institution Joint Program, is co-author of a study that reveals high levels of platinum and palladium in Boston Harbor surface sediments. The researchers say the most likely source of these metals is the use of catalytic converters in cars, as well as industrial waste entering the harbor through the sewage system.
Although the chemical behavior and possible toxicity of platinum and palladium in the marine environment are largely unknown, scientists do know that simple platinum compounds, among them the cancer drug cisplatin, can diffuse into the cell membrane, bind to DNA and prevent cell replication.
"Toxicity studies on these metals were conducted at levels much higher than those seen in these sediments, but given the widespread dispersal of [platinum and palladium] to the environment and the potential for accumulation within marine organisms, known as bioaccumulation, there may be long-term toxicological and ecological effects. At this point, we simply do not have the data to determine whether these levels are dangerous," Ms. Tuit said.
The study was published online in Environmental Science and Technology (an American Chemical Society journal, at http://pubs.acs.org/journals/esthag>) on February 2. Funding was provided by the Massachusetts Water Resource Authority, the US Geological Survey and a Mellon Independent Study Award from WHOI.
A version of this article appeared in MIT Tech Talk on April 26, 2000.