In this thesis the cosmological constant is investigated from two points of view. First, we study the influence of a time-dependent cosmological constant on the late-time expansion of the universe. Thereby, we consider several combinations of scaling laws motivated by renormalisation group running and different choices for the interpretation of the renormalisation scale. Apart from well known s...

Computations in geographic space are necessarily based on discrete versions of space, but much of the existing work on the foundations of GIS assumes a continuous infinitely divisible space. This is true both of quantitative approaches, using R, and qualitative approaches using systems such as the Region-Connection Calculus (RCC). This paper shows how the RCC can be modified so as to permit dis...

We prove that the free Fock space F(R+;C), which is very commonly used in Free Probability Theory, is the continuous free product of copies of the space C2. We describe an explicit embeding and approximation of this continuous free product structure by means of a discrete-time approximation: the free toy Fock space, a countable free product of copies of C2. We show that the basic creation, anni...

A Dowker space (that is, a normal space that is not countably metacompact) is constructed which is also screenable and the countable union of discrete subspaces. The construction and proofs are easy modifications of the ones for Balogh’s screenable Dowker space [B1]. Balogh’s example is presented alongside the modification in a new exposition with several new results common to the two spaces, i...

These notes develop the modern theory of martingale pricing in a discrete-time, discrete-space framework. This theory is also important for the modern theory of portfolio optimization as the problems of pricing and portfolio optimization are now recognized as being intimately related. We choose to work in a discrete-time and discrete-space environment as this will allow us to quickly develop re...

The Lorentz symmetry and the space and time translational symmetry are fundamental symmetries of nature. Crystals are themanifestation of the continuous space translational symmetry being spontaneously broken into a discrete one.We argue that, following the space translational symmetry, the continuous Lorentz symmetry should also be broken into a discrete one, which further implies that the con...

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed metho...

This paper presents two meta-heuristic algorithms to solve an extended portfolio selection model. The extended model is based on the Markowitz's Model, aiming to minimize investment risk in a specified level of return. In order to get the Markowitz model close to the real conditions, different constraints were embedded on the model which resulted in a discrete and non-convex solution space. ...

 In this paper we study the relative entropy rate between a homogeneous Markov chain and a hidden Markov chain defined by observing the output of a discrete stochastic channel whose input is the finite state space homogeneous stationary Markov chain. For this purpose, we obtain the relative entropy between two finite subsequences of above mentioned chains with the help of the definition of...