Related papers: The partition function of the unit interval
Interferences in multi-path systems for single and multiple particles are theoretically analyzed. A holistic method is presented, which allows to construct the unitary transition matrix describing interferometers for any port number d and…
We define a fractional Ito stochastic integral with respect to a randomly scaled fractional Brownian motion via an $S$-transform approach. We investigate the properties of this stochastic integral, prove the Ito formula for functions of…
We derive expressions for the partition function p(n), with n in the form 7k+a, as (k+1)-dimensional determinants.
Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
Quark distribution and spectator functions are estimated in a diquark spectator model. The representation of the functions in terms of non-local operators together with the rather simple model allow estimates for the yet experimentally…
In the Super-Transition-Array statistical method for the computation of radiative opacity of hot dense matter, the moments of the absorption or emission features involve partition functions with reduced degeneracies, occurring through the…
The Hermite-Birkhoff interpolation problem of a function given on arbitrarily distributed points on the sphere and other manifolds is considered. Each proposed interpolant is expressed as a linear combination of basis functions, the…
In this article, we impose a new class of fractional analytic functions in the open unit disk. By considering this class, we define a fractional operator, which is generalized Salagean and Ruscheweyh differential operators. Moreover, by…
The first-order Euler-Maclaurin formula relates the sum of the values of a smooth function on an interval of integers with its integral on the same interval on $\mathbb R$. We formulate here the analogue for functions that are just of…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…
In this paper we determine the region of variability for spirallike funcions with respect to a boundary point. In the final section we graphically illustrate the region of variability for several sets of parameters.
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
We study certain weighted area integral means of analytic functions in the unit disc. We relate the growth of these means to the property of being mean H\"older continuous with respect to the Bergman space norm. In contrast with earlier…
In this article, we illustrate the asymptotic behaviour of exponential functions of nabla fractional calculus. For this purpose, we propose a novel matrix technique to compute these functions numerically.
Based on discrete truncated powers, the beautiful Popoviciu's formulation for restricted integer partition function is generalized. An explicit formulation for two dimensional multivariate truncated power functions is presented. Therefore,…
We study a new simple quadrature rule based on integrating a $C^1$ quadratic spline quasi-interpolant on a bounded interval. We give nodes and weights for uniform and non-uniform partitions. We also give error estimates for smooth functions…
A new and efficient algorithm is presented for the calculation of the partition function in the $S=\pm 1$ Ising model. As an example, we use the algorithm to obtain the thermal dependence of the magnetic spin susceptibility of an Ising…
Functions of several quaternion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the $\tilde \partial $-equations are studied. Moreover, quaternion Stein manifolds are…
We show that the unitary operator on a separable Hilbert space is a parametrization of any conditional probability measure in a standard measure space. We propose unitary inference, a generalization of Bayesian inference. We study…