Olympics Legacy: the London Olympics 2012

The reasons for proposing a London 2012 bid are outlined in the light of London city planning over the past sixty years. The processes influencing the bid for the London 2012 Olympics are investigated in respect of the lessons from Barcelona and Sydney. The role of environmental and landscape improvement is examined and the importance of legacy is described and analysed. The cost of Olympiads since Sydney 2000 are described and compared. Then progress of the London 2012 Olympics development is described relative to regeneration of East London. Finally the effects of current proposals to cut back the costs of the 2012 Olympics are considered. Olympic Games play significant roles in host city’s economy as well as other outcomes such as tourism, culture, unemployment, infrastructure. However the economy can never describe the whole picture of Olympic Games’ gainnings, it is one of the most significant sign before, during and after the event. All of the expenditures have different values at different legacy levels. Although post election budget cut-backs in the United Kingdom have placed a question mark on the costs; the proposed urban legacy make the city beautiful and London East End livable

Self-scaled barrier functions on symmetric cones and their classification

Self-scaled barrier functions on self-scaled cones were introduced through a set of axioms in 1994 by Y.E. Nesterov and M.J. Todd as a tool for the construction of long-step interior point algorithms. This paper provides firm foundation for these objects by exhibiting their symmetry properties, their intimate ties with the symmetry groups of their domains of definition, and subsequently their decomposition into irreducible parts and algebraic classification theory. In a first part we recall the characterisation of the family of self-scaled cones as the set of symmetric cones and develop a primal-dual symmetric viewpoint on self-scaled barriers, results that were first discovered by the second author. We then show in a short, simple proof that any pointed, convex cone decomposes into a direct sum of irreducible components in a unique way, a result which can also be of independent interest. We then show that any self-scaled barrier function decomposes in an essentially unique way into a direct sum of self-scaled barriers defined on the irreducible components of the underlying symmetric cone. Finally, we present a complete algebraic classification of self-scaled barrier functions using the correspondence between symmetric cones and Euclidean Jordan algebras.Comment: 17 page

A necessary condition for generic rigidity of bar-and-joint frameworks in dd-space

A graph $G=(V,E)$ is $d$-sparse if each subset $X\subseteq V$ with $|X|\geq d$ induces at most $d|X|-{{d+1}\choose{2}}$ edges in $G$. Maxwell showed in 1864 that a necessary condition for a generic bar-and-joint framework with at least $d+1$ vertices to be rigid in ${\mathbb R}^d$ is that $G$ should have a $d$-sparse subgraph with $d|X|-{{d+1}\choose{2}}$ edges. This necessary condition is also sufficient when $d=1,2$ but not when $d\geq 3$. Cheng and Sitharam strengthened Maxwell's condition by showing that every maximal $d$-sparse subgraph of $G$ should have $d|X|-{{d+1}\choose{2}}$ edges when $d=3$. We extend their result to all $d\leq 11$.Comment: There was an error in the proof of Theorem 3.3(b) in version 1 of this paper. A weaker statement was proved in version 2 and then used to derive the main result Theorem 4.1 when $d\leq 5$. The proof technique was subsequently refined in collaboration with Hakan Guler to extend this result to all $d\leq 11$ in Theorem 3.3 of version

Modelling the Daily Currency in Circulation in Turkey

The main focus of this paper is to model the daily series of currency in circulation in Turkey. The currency in circulation is one of the most significant factors influencing the liquidity of the Turkish banking system. Therefore, the amount of currency in circulation has to be forecasted as accurately as possible. The currency in circulation displays an increasing long-term trend and strong seasonal factors which can be forecasted. This paper introduces the ARIMA-based approach to model seasonality in daily time series and evaluates the forecasting performance of the model. The results indicate that the forecasting performance of the model is better than the expert judgments both in the short-term and the long-term.Currency in circulation, Liquidity management, Time series models, Seasonality