where ρ is the mass density, S is the entropy density, and p is the pressure. It was shown in Morrison and Greene [1980] that this system, as well as its magnetohydrodynamic extension, admit a noncanonical Poisson formulation, that is, equation (1.1) can be written as ḟ = {f, h}, relative to a Hamiltonian function h. The study of the relativistic case was initiated in Bia lynicki-Birula, Hubbar...

Using a Poisson bracket representation, in 3D, of the Lie algebra sl(2), we first use highest weight representations to embed this into larger Lie algebras. These are then interpreted as symmetry and conformal symmetry algebras of the “kinetic energy”, related to the quadratic Casimir function. We then consider the potentials which can be added, whilst remaining integrable, leading to families ...

The purpose of this project is to show observations taken from the Iterative Proportional Scaling algorithm when used with data taken from Hierarchical LogLinear Models. We show with empirical proof that the difference between decomposable and non-decomposable graph models used is not exceedingly different. For the purpose of this project we looked at the properties of the two, three, and four ...

The covariant Boltzmann equation for a relativistic gas mixture is used to formulate a theory of relativistic irreversible thermodynamics. The modified moment method is applied to derive various evolution equations for macroscopic variables from the covariant Boltzmann equation. The method rigorously yields the entropy differential which is not an exact differential if

We apply Hardy-Littlewood’s Tauberian theorem to obtain an estimate on the harmonic expansion of a complex measure on the unit sphere, using a monotonicity property for positive harmonic functions. Let Bn = {x ∈ Rn : |x| < 1}, n ≥ 2 be the unit ball in Rn and Sn−1 = ∂Bn be the unit sphere. From a monotonicity property, we obtain a precise asymptotic for the spherical harmonic expansion of a com...

Count models are a subset of discrete response regression models. Count data are distributed as non-negative integers, are intrinsically heteroskedastic, right skewed, and have a variance that increases with the mean. Example count data include such situations as length of hospital stay, the number of a certain species of fish per defined area in the ocean, the number of lights displayed by fir...

The classical theory of transport processes is based on the Boltzmann transport equation. The equation can be derived simply by defining a distribution function and inspecting its time derivative. From this equation, many important results can be derived. In addition to some of the textbook results from the Boltzmann transport equation, it is still being used in many contemporary research proje...

We consider a bivariate Poisson model that is based on the lognormal heterogeneity model. Two recent applications have used this model. We suggest that the correlation estimated in their model frameworks is an ambiguous measure of the correlation of the variables of interest, and may substantially overstate it. We conclude with a detailed application of the proposed method using the data employ...

The classical integer valued first-order autoregressive (INA- R(1)) model has been defined on the basis of Poisson innovations. This model has Poisson marginal distribution and is suitable for modeling equidispersed count data. In this paper, we introduce an modification of the INAR(1) model with geometric innovations (INARG(1)) for model- ing overdispersed count data. We discuss some structu...