ACCELERATING UNIVERSE WITH MODIFIED FRIEDMANN EQUATION

In this paper we propose a specific modification for Friedmann equation which leads during the matter-dominated era to a Cardassian type model, with the usual two undetermined parameters but with an important difference however, the usual parameter B which is constant in the Cardassian model becomes a function of time in this model. We found that although the model leads to acceleration at recent epoch. The acceleration values are more moderate than in the usual Cardassian model because B(t) is a reducing function of time. The model further leads to an increase in the abundance of light element during nucleosynthesis. We use the difference between the predicted and measured values of big bang nucleosynthesis of helium to obtain a value for n and B(t).

The behaviour of the likelihood function for ARMA models

The paper deals with some properties of the (Gaussian) likelihood function for multivariable ARMA models. Its behaviour at the boundary of the parameter space is described; its continuity properties as well as the question of the existence of a maximum are discussed. We have not been able to show in general the existence of the maximum over the usual parameter spaces. However, the maximum always exists over a suitably enlarged parameter space (given that the data are non-degenerate), which includes parameters corresponding to processes with discrete spectral components.

The behaviour of the likelihood function for ARMA models

The paper deals with some properties of the (Gaussian) likelihood function for multivariable ARMA models. Its behaviour at the boundary of the parameter space is described; its continuity properties as well as the question of the existence of a maximum are discussed. We have not been able to show in general the existence of the maximum over the usual parameter spaces. However, the maximum always exists over a suitably enlarged parameter space (given that the data are non-degenerate), which includes parameters corresponding to processes with discrete spectral components.

The Extrapolation of Families of Curves by Recurrence Relations, With Application to Creep-Rupture Data

A method using finite-difference recurrence relations is presented for direct extrapolation of families of curves. The method is illustrated by applications to creep-rupture data for several materials and it is shown that good results can be obtained without the necessity for any of the usual parameter concepts.

Continuously infinite matrices and the algebraic theory of Fredholm's equation

In this note the theory of the integral equation is reduced to elementary matrix algebra. The Fredholm theorems are proved without the introduction of the usual parameter λ and without using the properties of the resolvent considered as an analytic function of the complex variable λ. There is an exact correspondence between the properties of the equation (1) and the properties of a finite linear system. Here the proofs of these properties are also in extact correspondence with the same for the elementary case.