Results 271 to 280 of about 143,405 (309)
Some of the next articles are maybe not open access.
A NOTE ON THE PARTITION FUNCTION
Universal Journal of Mathematics and Mathematical Sciences, 2020Summary: The purpose of this note is to establish an identity of the partition function. Theorem. Let \(p(n)\) be the partition function, and suppose \(d(n, a_k)\) is the number of partitions where \(a_k\) appears at least one time, then \(d(n, a_k) = p(n - a_k)\).
Phúc, Đặng Võ, Nawaz, Shahid
openaire +2 more sources
The partition functions of methanol
Journal of Molecular Spectroscopy, 1990Presentation d'une methode pour le calcul de fonctions de partition du methanol, basee sur une formulation extremement simplifiee et neanmoins ...
M. Dang Nhu +2 more
openaire +3 more sources
ON THE PARITY OF PARTITION FUNCTIONS
International Journal of Mathematics, 2003Let S denote a subset of the positive integers, and let pS(n) be the associated partition function, that is, pS(n) denotes the number of partitions of the positive integer n into parts taken from S. Thus, if S is the set of positive integers, then pS(n) is the ordinary partition function p(n).
Berndt, Bruce C. +2 more
openaire +1 more source
CRANK 0 PARTITIONS AND THE PARITY OF THE PARTITION FUNCTION
International Journal of Number Theory, 2011A well-known problem regarding the integer partition function p(n) is the parity problem, how often is p(n) even or odd? Motivated by this problem, we obtain the following results: (1) A generating function for the number of crank 0 partitions of n. (2) An involution on the crank 0 partitions whose fixed points are called invariant partitions.
openaire +1 more source
Partition function from the Green function
Journal of Physics A: Mathematical and General, 1984The partition function in quantum statistical mechanics can be expressed as an energy integral of exp(- beta E) times the discontinuity of the Green function. A Monte Carlo approach for its evaluation which is not based on path integral representation is suggested. The fermion problem is avoided in the sense that all integrands are positive.
Avishai, Y., Richert, J.
openaire +2 more sources
2016
This chapter explores the concept of a partition function introduced by the Boltzmann distribution, which is the central mathematical concept of the treatment of statistical thermodynamics. It focuses on how to interpret the partition function and how to calculate it in a number of simple cases.
Peter Atkins +2 more
openaire +1 more source
This chapter explores the concept of a partition function introduced by the Boltzmann distribution, which is the central mathematical concept of the treatment of statistical thermodynamics. It focuses on how to interpret the partition function and how to calculate it in a number of simple cases.
Peter Atkins +2 more
openaire +1 more source
2010
The main purpose of this chapter is to discuss the theory of Dahmen–Micchelli describing the difference equations that are satisfied by the quasipolynomials that describe the partition function \(\mathcal{T}_X\) on the big cells. These equations allow also us to develop possible recursive algorithms.
Corrado De Concini, Claudio Procesi
openaire +1 more source
The main purpose of this chapter is to discuss the theory of Dahmen–Micchelli describing the difference equations that are satisfied by the quasipolynomials that describe the partition function \(\mathcal{T}_X\) on the big cells. These equations allow also us to develop possible recursive algorithms.
Corrado De Concini, Claudio Procesi
openaire +1 more source
2009
Abstract This chapter introduces the partition function, which encodes all the information concerning the states of a system and their thermal occupation. Topics discussed include writing down the partition function, obtaining the functions of state, and combining partition functions.
Stephen J. Blundell +1 more
openaire +1 more source
Abstract This chapter introduces the partition function, which encodes all the information concerning the states of a system and their thermal occupation. Topics discussed include writing down the partition function, obtaining the functions of state, and combining partition functions.
Stephen J. Blundell +1 more
openaire +1 more source
On the Expansion of the Partition Function in a Series
The Annals of Mathematics, 19431. A geometric property of the Farey series, discovered by L. R. Ford (1) is used in this note for the construction of a new path of integration to replace the circle carrying the Farey dissection, first introduced by Hardy and Ramanujan in their classical paper (2).
openaire +2 more sources
On the Asymptotics of the Binary Partition Function
Mathematical Notes, 2004For integers \(k\), \(d\geq 2\), let \(b(d,k)\) denote the number of partitions of \(k\) into powers of 2 wherein no part is repeated more than \(d-1\) times. The asymptotic behaviour of \(b(\infty,k)\) as \(k\to\infty\) was studied by numerous authors, see a paper by \textit{B. Reznick} [in: Analytic Number Theory (Allerton Park, IL, 1989), Prog. Math.
openaire +2 more sources