Abstract: The goal of this series of lectures is to present an overview of the theory of orbit equivalence, with a particular focus on the probability measure preserving actions of the free groups. I will start by giving the basis of the theory of orbit equivalence and explain the theory of cost. In particular, prove such statements as the induction formula and the computation of the cost of fr...

An effective technique for real-time differential orbit determination with GPS bias fixing is formulated. With this technique, only real-time GPS orbits and clocks are needed (available from the NASA Global Differential GPS System with 10–20 cm accuracy). The onboard, realtime orbital states of user satellites (few meters in accuracy) are used for orbit initialization and integration. An extend...

In this paper, we consider a continuous review perishable inventory system with a service facility having two heterogeneous servers, server 1 and server 2 , and the demands originate from a finite population of N sources. In such systems, the customers demand is satisfied only after some service is completed by any one of the two servers. Compared to most inventory models in which inventory is ...

A utility function is an important tool for representing a DM’s preference. We adjoin utility functions to multi-objective optimization problems. In current studies, usually one utility function is used for each objective function. Situations may arise for a goal to have multiple utility functions. Here, we consider a constrained multi-objective problem with each objective having multiple utili...

This paper deals with the transient analysis of batch arrival retrial queueing system with general retrial times, priority service, balking, second optional service, Bernoulli vacation, extended vacation, breakdown, delayed repair and stand by server. Here we assume that customers arrive in batches according to compound Poisson processes, where the blocked customers either with probability p jo...

The Open University, in collaboration with e2v technologies and XCAM Ltd, have been selected to fly an EO (Earth Observation) technology demonstrator and in-orbit radiation damage characterisation instrument on board the UK Space Agency’s UKube-1 pilot Cubesat programme. Cubesat payloads offer a unique opportunity to rapidly build and fly space hardware for minimal cost, providing easy access t...

We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding constrained minimization problem and establish existence, symmetry and uniqueness of the ground state solutions.

ORBIT is a MATLAB-based toolkit for black-box and grey-box modeling of non-linear dynamic systems. The model representation is based on multiple local models valid in di erent operating regimes that are being smoothly patched together into a global non-linear model. ORBIT is a computer-aided modeling environment that supports interactive development of regime based models on the basis of a mixt...