Extractions: Source University Of Georgia Date Print this page Email to friend It's not as famous as Fermat's Last Theorem. In fact, the math problem, which has not had a correct solution since it was proposed in the 1960s, doesn't even have a name. But a new, elegant solution for the unnamed 40-year old problem has intrigued scientists enough to be published in a two-part paper in one of the world's top math journals. Related News Stories Purdue Mathematician Claims Proof For Riemann Hypothesis (June 9, 2004) A Purdue University mathematician claims to have proven the Riemann hypothesis, often dubbed the greatest unsolved problem in ... full story UF Psychologists: Computer Anxiety New Illness Of High-Tech Age (July 31, 1998) full story Mental Math Dependant On Language, Researchers Find (October 16, 2001) full story Mathematicians Prove Double Soap Bubble Had It Right (March 20, 2000)
As últimas Do Mundo Da Matemática Here we announce a proof HMRR of the general double bubble conjecture in R3,using stability See also Frank Morgan double bubble conjecture Proved http://www.mat.uc.pt/~jaimecs/ult/ult.html
Extractions: Paul Erdos morreu dia 20/9/96 -1 is now the Largest Known Prime December 6, 2001 > Michael Cameron, a 20 year-old volunteer in a worldwide research project called the Great Internet Mersenne Prime Search (GIMPS) , has discovered the largest known prime number using his PC and software by George Woltman and Entropia, Inc.
Kempner Colloquium Abstracts (Spring 2004) Title Proof of the double bubble conjecture Speaker Frank Morgan AffiliationWilliams College Time 230pm, Friday, April 2 Location EDUC 220 Abstract http://euclid.colorado.edu/~rmg/kempner/S04/abstracts.html
Extractions: Over the past twenty years, wavelets have gained popularity as bases for transforms used in image and signal processing. This talk will begin with a brief introduction to how wavelets arise naturally in this context. We will then show how the tools of abstract harmonic analysis and spectral multiplicity theory can be used to build and classify wavelets. In particular, we present results from joint work with L. Baggett, P. Jorgensen, H. Medina and J. Packer that extend the classical techniques of Mallat and Meyer to construct wavelets using generalized multi-resolution analyses and generalized filters. The dynamics of opinion transformation is modeled by a neural network with a nonnegative matrix of connections. Noise is introduced at each site, and the limit of the stationary distributions of the resulting Markov chains as the noise goes to zero is taken as an indication of what configurations will be seen. An algorithm for computing this limit is given, and a number of examples are worked out. Some of the mathematical ideas developed, such as visible states, time scales, and a calculus of indexed probabilities, are of independent interest.
Stanford University Geometric Analysis Seminar 1999-2000 Abstract The double bubble conjecture states that the leastarea way to encloseand separate 2 given volumes in R^3 is the standard double bubble , http://math.stanford.edu/~moore/ga-sem99-00.html
Extractions: Abstract: Shape from shading is the study of how to determine a 3-D surface from a 2-D picture of the surface (plus as minimal an amount of additional information as possible.) When the picture has discontinuities (i.e., a bright part of the picture borders a darker part), difficulties arise in determining existence, uniqueness, and a method of computation for the solution of the underlying PDE describing the surface. We will explain a method of resolving these questions involving a control theory representation for the PDE, which will also allow us to answer larger questions about much more general first order PDEs with discontinuous flux/Hamiltonian functions.
WPI Department Of Mathematical Sciences - 1999-2000 Events In both talks, he described recent results on the double bubble conjecture, whichsays that the familiar double soap bubble is the leastarea way to enclose http://www.wpi.edu/Academics/Depts/Math/News/Events/9900.html
Extractions: Department of Mathematical Sciences About WPI Related Sites more photos. Marcus Sarkis , and a team composed of Jovanna Baptista, Larissa Gilbreath, and Robert Jaeger received the CIMS MQP Award for their project "Pricing a Waiver of Premium Upon Disability," advised by Ann Wiedie and sponsored by John Hancock Insurance Company . Other participating teams and their projects were Andre Freeman and Matthew Lavoie, "Comparing Heuristics for the Traveling Salesman Problem," advised by Brigitte Servatius , and Elizabeth Hogan and Nicholas Allgaier, "Credibility Analysis for Automobile Cession Strategies," advised by Arthur Heinricher and sponsored by Premier Insurance of Massaschusetts. Jonathan Moussa and Matt Shaw were recognized for their strong performance on the Putnam exam, and two teams composed of Brian Ball, Jonathan Moussa, and James Stickney and Jon Kennedy, Will Kennerly, and Casey Richardson, respectively, were recognized for honors received in the COMAP 2000 Mathematical Contest in Modeling. See news item Undergraduates score in Math Modeling, Putnam competitions
WPI Department Of Mathematical Sciences - Colloquia 1999-2000 The double bubble conjecture says that the familiar double soap bubble, Student Talk News on the double bubble conjecture, including work by http://www.wpi.edu/Academics/Depts/Math/News/Colloquia/9900.html
Extractions: Abstract: Current status data, also called interval censored data, Case 1, contains only information whether a failure happened or not at a random monitoring time. This type of data arise commonly in many studies of epidemiology, biomedicine, demography and reliability. While in its univariate setting, the estimation of the failure time distribution has been studied extensively, there has not been much research in the bivariate setting. When there are two failure times, say for example, development of hytertension and cardiovasular disease, we would like to study the relationship between them. Nonparametric estimation of the joint failure time distribution is not possible because of nonidentifiablity. A semiparametric approach as proposed to study the association between the two failure time variables. Nonparametric testing for the independence between two failure time variables is also explored. Peter Mueller,Institute of Statistics and Decision Sciences Duke University, October 8 1999
Elsevier.com - Geometric Measure Theory Soap Bubble Clusters. Proof of double bubble conjecture. The Hexagonal Honeycomband Kelvin Conjectures. Immiscible Fluids and Crystals. http://www.elsevier.com/wps/product/cws_home/675494
Extractions: Home Site map Regional Sites Advanced Product Search ... Geometric Measure Theory Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book related information Submit your book proposal Other books in same subject area About Elsevier Select your view GEOMETRIC MEASURE THEORY Geometric measure theory has become increasingly essential to geometry as well as numerous and varied physical applications. The third edition of this leading text/reference introduces the theory, the framework for the study of crystal growth, clusters of soap bubbles, and similar structures involving minimization of energy. Over the past thirty years, this theory has contributed to major advances in geometry and analysis including, for example, the original proof of the positive mass conjecture in cosmology. This third edition of Geometric Measure Theory: A Beginner's Guide presents, for the first time in print, the proofs of the double bubble and the hexagonal honeycomb conjectures. Four new chapters lead the reader through treatments of the Weaire-Phelan counterexample of Kelvin's conjecture, Almgren's optimal isoperimetric inequality, and immiscible fluids and crystals. The abundant illustrations, examples, exercises, and solutions in this book will enhance its reputation as the most accessible introduction to the subject.
CSU- Fresno Math Department Colloquia will speak on Double Bubbles Minimize at 4105pm in Science 145. proved lastyear the double bubble conjecture which answered a question that had http://zimmer.csufresno.edu/~cleary/colloq/oldcolloq.html
Extractions: The Math Department Colloquia are a series of talks intended for a general audience. Everyone is encouraged to attend and the talks are directed at people who have a reasonable comprehension of the topics in undergraduate mathematics. Come meet our undergraduates, graduate students and faculty as well as our distinguished guest speakers. Colloquia from 1996-1997 academic year: Rescheduled: Monday, May 5, 3pm Dr. Joel Hass from the UC Davis Department of Mathematics at 4:10-5pm in Science 145. There will be refreshments beforehand. Abstract: Dr. Hass will be speaking about the mathematical models of soap films and bubbles, which are modeled by minimal surfaces and constant mean curvature surfaces respectively. Dr. Hass, with his collaborator Roger Schlafly, proved last year the "Double Bubble Conjecture" which answered a question that had been first asked 2000 years ago and had been studied by many great mathematicians throughout history. He will be speaking about some of the innovative techniques used in this important work and will have some computer graphics as well as soap bubbles to illustrate the ideas. Monday April 21 3:10pm in Science 145: Sean Cleary , from the CSU -Fresno Mathematics Department will show the 20 minute video Not Knot , produced by the Geometry Center at the University of Minnesota. There will be a short explanatory talk in conjuntion with the video presentation. "Not Knot" is a computer-generated video which illustrates some important ideas from knot theory and hyperbolic geometry.
Notes From The Lab - MIT News Office Yvonne Lai, a junior in mathematics, has helped extend a recent mathematicalproof of the double bubble conjecture to four dimensions. http://web.mit.edu/newsoffice/2000/labnotes-0426.html
Extractions: April 26, 2000 FOUR-DIMENSIONAL PROOF 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.
Abstract For Frank Morgan's Colloquium Soap Bubble Geometry. Frank Morgan Department of Mathematics and Ros of thedouble bubble conjecture, in which undergraduates have played an important http://dept.physics.upenn.edu/colloquium/abstract_morgan.html
Extractions: Soap bubbles are round, and more complicated soap bubble clusters and other materials have other beautiful shapes. They apparently try to minimize surface area or energy. Are their shapes really the best possible? The presentation will include demonstrations and a description of the recent proof with Hutchings, Ritore', and Ros of the Double Bubble Conjecture, in which undergraduates have played an important role.
Extractions: The Greater Hudson Valley Mathematical Speakers Bureau, formed among liberal arts colleges in eastern New York, Connecticut and western Massachusetts, provides member institutions a source of undergraduate-level talks given by talented mathematicians residing at nearby colleges. In addition to providing interesting, accessible talks for undergraduates, the Bureau provides an opportunity for faculty members of neighboring colleges to interact and discuss common research or pedagogical interests. Current GHVMSB institutions: Bard College, Mount Holyoke College, Skidmore College, Sarah Lawrence College, Smith College, Trinity College, Union College, Vassar College and Williams College. If you have any questions or suggestions regarding the GHVMSB, please contact Dan King at Sarah Lawrence College (dking@mail.slc.edu). Please note: Edith Starr, GHVMSB co-organizer, of Vassar College is on sabbatical this year. Below is the GHVMSB's listing of available speakers and their talks for the 1998-00 academic year. Host institutions are encouraged to contact the speakers listed below directly to make specific arrangements regarding date and time of talk, directions for travel, equipment needs and honorarium amount.
Extractions: Science News e-LETTER. ... Week of Jan. 29, 2000; Vol. 157, No. 5 Ivars Peterson A proof of the double-bubble conjecture for the case in which the two bubbles' volumes are unequal appears within reach. References: Morgan, F. 2000. The double bubble conjecture. Abstracts of Papers Presented to the American Mathematical Society 21(January):129. Further Readings: Morgan, F. 2000. The Math Chat Book . Washington, D.C.: Mathematical Association of America. Peterson, I. 1995. Toil and trouble over double bubbles. Science News 148(Aug. 12):101. Sources: Michael Hutchings
MAA-NJ Spring 2001 Meeting double bubbles Proof and Prizes. Frank Morgan, Williams College. We ll reporton the 2000 proof of the double Soap bubble conjecture and http://orion.ramapo.edu/~ldant/old/rowan01/programs01.html
Extractions: The Mathematical Association of America New Jersey Section - Spring Meeting Rowan University,Glassboro, NJ Saturday,April 21, 2001 Main Lecture Hall - Bosshart 203 Registration and Coffee - Second floor Lobby Bosshart Hall Book Exhibits Welcome byRonald Czochor, Chairperson, Department of Mathematics, Rowan University Graph Products and Cannon Pairs Joseph Loeffler, The College of New Jersey Student Speaker Presider: Cathy Liebars, The College of New Jersey Effective 3-D Visualizations of High Level Mathematical Functions Bonita Saunders, National Institute of Standards and Technology Presider: Bonnie Gold, Monmouth University Remarks by Chair of MAA-NJ Judith Lenk, Ocean County College Intermission (Coffee and Book Exhibits) Concurrent Sessions Workshop on Active Learning , by Janet Caldwell, Rowan University Campbell Library Commons Room 126 MAA-NJ Contributed papers I Bosshart 118 MAA-NJ Contributed papers - II Bosshart 116 MAA-NJ Contributed papers - III Bosshart 129 MAA-NJ Contributed papers - IV Bosshart 236 Student Contributed papers - Bosshart 316 Lunch (Book Exhibits end at 1:30) and Discussion Tables Student Center Ballroom Mathematics as Empirical Science Doron Zeilberger, Temple University
Double Bubble Is No Trouble A major advance towards the twin prime conjecture The trouble was that,although the familiar double bubble configuration certainly satisfied all the http://pass.maths.org.uk/issue12/news/bubble/
Extractions: The search for the maths gene Plus... more news from the world of maths Explore the news archive Subscribe to our free newsletter Get the ... posters! September 2000 News A standard double bubble Four mathematicians have finally confirmed that the familiar double soap bubble is indeed the best way to enclose two separate volumes of air. In a double bubble, the joining surface bulges a little into the larger of the two bubbles. The three surfaces meet along a circle at 120 o If the two bubbles enclose the same volume, the separating surface is flat.
Bubbles For 2 areas, a standard double bubble is shortest (early 90s). To prove theplanar soap bubble conjecture for m =7 areas or the soap bubble conjecture http://mail2.sc.chula.ac.th/~wacharin/maths/bubbles.html
Double Bubbles Minimize - Hass, Schlatly (ResearchIndex) The proof of this conjecture was announced by Hass, Hutchings and 2.double bubble and torus bubble One first has to find categories of surfaces. http://citeseer.ifi.unizh.ch/hass98double.html
Extractions: Abstract: The classical isoperimetric inequality in R 3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 o . 1 Introduction Double, double, toil and trouble, Fire burn and cauldron bubble. Macbeth Act 4, Scene 1, Line 10 In this paper we find the unique surface of... (Update)
[math/0208120] Double Bubbles In The 3-torus double bubbles in the 3torus. Authors Miguel Carrión-Álvarez (UC Riverside),Joseph Corneli We present a conjecture, based on computational results, http://arxiv.org/abs/math.DG/0208120
Extractions: We present a conjecture, based on computational results, on the area minimizing way to enclose and separate two arbitrary volumes in the flat cubic 3-torus. For comparable small volumes, we prove that an area minimizing double bubble in the 3-torus is the standard double bubble from R^3. References and citations for this submission:
