Mathematicians Solve 140-Year-Old Boltzmann Equation
PHILADELPHIA –- Two University of Pennsylvania mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases. The study, part historical journey but mostly mathematical proof, was conducted by Philip T. Gressman and Robert M. Strain of Penn’s Department of Mathematics. The solution of the Boltzmann equation problem was published in the Proceedings of the National Academy of Sciences. Solutions of this equation, beyond current computational capabilities, describe the location of gas molecules probabilistically and predict the likelihood that a molecule will reside at any particular location and have a particular momentum at any given time in the future.
Developing Your Intuition For Math
Our initial exposure to an idea shapes our intuition. And our intuition impacts how much we enjoy a subject. What do I mean? Suppose we want to define a “cat”: Caveman definition: A furry animal with claws, teeth, a tail, 4 legs, that purrs when happy and hisses when angry…Evolutionary definition: Mammalian descendants of a certain species (F. catus), sharing certain characteristics…Modern definition: You call those definitions?
Mathematical Atlas: A gateway to Mathematics
Welcome! This is a collection of short articles designed to provide an introduction to the areas of modern mathematics and pointers to further information, as well as answers to some common (or not!) questions. The material is arranged in a hierarchy of disciplines, each with its own index page ("blue pages").
Online Speed Reading tools and software
Simply start by clicking on the Play button on the left. Reading is that one activity that we do every day but we don't really practice. Most people learn the basics of reading in kindergarten and never graduate to the next levels. You are probably using the same basic rudimental tools and techniques that you learned when you were 6.
Microparticles allow you to live without breathing
Although it may seem like science fiction, a Boston research group has developed a type of microparticles which can be injected directly into the bloodstream to oxygenate your body quickly … even if we could not breathe. An extraordinary advancement in medicine that could help to save millions of lives in a year. According to the doctors, this development would allow medical teams to keep patients alive 15 to 30 minutes even though they may have severe respiratory failure. A time for medical teams in which they could act without risk for a heart attack or permanent brain injury. The first tests in animals are completed with a success. They say that doctors are able to inject this liquid into a vein restoring blood oxygen levels , giving the animals who needed those extra minutes .
Jain's True Value of Pi
I will be releasing a new body of work that gives the True Value of Pi, based on the Harmonics of Phi (1.618033...
Prime numbers
Version for printing Prime numbers and their properties were first studied extensively by the ancient Greek mathematicians. The mathematicians of Pythagoras's school (500 BC to 300 BC) were interested in numbers for their mystical and numerological properties. They understood the idea of primality and were interested in perfect and amicable numbers.
Fibonacci in Nature
The Fibonacci numbers play a significant role in nature and in art and architecture. We will first use the rectangle to lead us to some interesting applications in these areas. We will construct a set of rectangles using the Fibonacci numbers 1, 1, 2, 3, 5, 8, 13, 21, and 34 which will lead us to a design found in nature. You will need a ruler, protractor, and compass. Start by drawing two, unit squares (0.5 cm is suggested) side by side. Next construct a 2-unit by 2-unit square on top of the two, unit squares.
Nerd Paradise : Divisibility Rules for Arbitrary Divisors
It's rather obvious when a number is divisible by 2 or 5, and some of you probably know how to tell if a number is divisible by 3, but it is possible to figure out the division 'rule' for any number. Here are the rules for 2 through 11... The last digit is divisible by 2. The sum of all the digits in the number is divisible by 3. The last 2 digits are divisible by 4. The last digit is 5 or 0.
