Algebraic Structure of Discrete Zero Curvature Equations and Master Symmetries of Discrete Evolution Equations

An algebraic structure related to discrete zero curvature equations is established. It is used to give an approach for generating master symmetries of first degree for systems of discrete evolution equations and an answer to why there exist such master symmetries. The key of the theory is to generate nonisospectral flows $(\lambda_t=\lambda ^l, l\ge0)$ from the discrete spectral problem associated with a given system of discrete evolution equations. Three examples are given.Comment: 24 pages, LaTex, revise

Economic dynamics with financial fragility and mean-field interaction: a model

Following the statistical mechanics methodology, firstly introduced in macroeconomics by Aoki [1996,2002], we provide some insights to the well known works of Greenwald and Stiglitz [1990, 1993]. Specifically, we reach analytically a closed form solution of their models overcoming the aggregation problem. The key idea is to represent the economy as an evolving complex system, composed by heterogeneous interacting agents, that can partitioned into a space of macroscopic states. This meso level of aggregation permits to adopt mean field interaction modeling and master equation techniques.Comment: APFA6 proceeding

Designing an online part-time Master of Philosophy with Problem Oriented Engineering

The paper reports on the application of Problem Oriented Engineering (POE) to the design of a highly innovative post-graduate research programme for the Open University, UK, a world leader in supported distance higher education. The new programme, to be launched in October 2009, is a part-time Master of Philosophy (MPhil) to be delivered entirely at a distance, supported by a blend of synchronous, asynchronous and immersive internet and web technologies. POE is a framework for engineering design under development at the Open University. After a brief description of the project and the task at hand, the paper discusses the overall engineering approach taken, key aspects of product design, the mapping between requirements and technology, and the development of one key technological component

Conditional quantum dynamics with several observers

We consider several observers who monitor different parts of the environment of a single quantum system and use their data to deduce its state. We derive a set of conditional stochastic master equations that describe the evolution of the density matrices each observer ascribes to the system under the Markov approximation, and show that this problem can be reduced to the case of a single "super-observer", who has access to all the acquired data. The key problem - consistency of the sets of data acquired by different observers - is then reduced to the probability that a given combination of data sets will be ever detected by the "super-observer". The resulting conditional master equations are applied to several physical examples: homodyne detection of phonons in quantum Brownian motion, photo-detection and homodyne detection of resonance fluorescence from a two-level atom. We introduce {\it relative purity} to quantify the correlations between the information about the system gathered by different observers from their measurements of the environment. We find that observers gain the most information about the state of the system and they agree the most about it when they measure the environment observables with eigenstates most closely correlated with the optimally predictable {\it pointer basis} of the system.Comment: Updated version: new title and contents. 22 pages, 8 figure

A sustainable tourism development in Alacati, Turkey : (Re)invention of public space with clean energy

Although there is an increasing recognition of the impacts of climate change on communities, residents often resist changing their lifestyle to reduce the effects of the problem. By using a landscape architectural design medium, this paper argues that public space, when designed as an ecological system, has the capacity to create social and environmental change and to increase the quality of the human environment. At the same time, this ecological system can engage residents, enrich the local economy, and increase the social network. Through methods of design, research and case study analysis, an alternative master plan is proposed for a sustainable tourism development in Alacati, Turkey. Our master plan uses local geographical, economic and social information within a sustainable landscape architectural design scheme that addresses the key issues of ecology, employment, public space and community cohesion. A preliminary community empowerment model (CEM) is proposed to manage the designs. The designs address: the coexistence of local agricultural and sustainable energy generation; state of the art water management; and the functional and sustainable social and economic interrelationship of inhabitants, NGOs, and local government