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partition function |
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partition function [pär′tish·ən ‚fəŋk·shən] (statistical mechanics) The integral, over the phase space of a system, of the exponential of (-E/kT), whereEis the energy of the system,kis Boltzmann's constant, andTis the temperature; from this function all the thermodynamic properties of the system can be derived. In quantum statistical mechanics, the sum over allowed states of the exponential of (-E/kT). Also known as sum of states; sum over states. How to thank TFD for its existence? Tell a friend about us, add a link to this page, add the site to iGoogle, or visit webmaster's page for free fun content. |
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| The idea that, starting with 4, the number of partitions for every fifth integer is a multiple of 5 can be expressed compactly in the following mathematical form, where p(n), called the partition function, is the number of partitions of an integer n; [equivalent] indicates congruence; and 0 (mod 5) means that the remainder after division by 5 must be 0. Jayce Getz, 18, a senior at Big Sky High School in Missoula, MT, was awarded the second place $75,000 scholarship for his mathematics project titled, "Extension of a Theorem of Kiming and Olsson for the Partition Function. An article by Erikkson on the partition function has been accepted by the International Journal of Mathematics and Mathematical Sciences. |
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