One Upper Estimate on the Number of Limit Cycles of Even Degree Li\'enard Equations in the Focus Case

We give an explicit upper bound for a number of limit cycles of the Li\'enard equation $\dot{x}=y-F(x)$, $\dot{y}=-x$ of even degree in the case its unique singular point $(0,0)$ is a focus.Comment: 10 pages, 1 figur

Non-Fermi-liquid phases in the two-band Hubbard model: Finite-temperature exact diagonalization study of Hund's rule coupling

The two-band Hubbard model involving subbands of different widths is investigated via finite-temperature exact diagonalization (ED) and dynamical mean field theory (DMFT). In contrast to the quantum Monte Carlo (QMC) method which at low temperatures includes only Ising-like exchange interactions to avoid sign problems, ED permits a treatment of Hund's exchange and other onsite Coulomb interactions on the same footing. The role of finite-size effects caused by the limited number of bath levels in this scheme is studied by analyzing the low-frequency behavior of the subband self-energies as a function of temperature, and by comparing with numerical renormalization group (NRG) results for an effective one-band model. For half-filled, non-hybridizing bands, the metallic and insulating phases are separated by an intermediate mixed phase with an insulating narrow and a bad-metallic wide subband. The wide band in this phase exhibits different degrees of non-Fermi-liquid behavior, depending on the treatment of exchange interactions. Whereas for complete Hund's coupling, infinite lifetime is found at the Fermi level, in the absence of spin-flip and pair-exchange, this lifetime becomes finite. Excellent agreement is obtained both with new NRG and previous QMC/DMFT calculations. These results suggest that-finite temperature ED/DMFT might be a useful scheme for realistic multi-band materials.Comment: 15 pages, 17 figure

Problem-based leadership: nurturing managers during turbulent times

Purpose – The paper explores problem-based learning (PBL) as a useful methodology in leadership development during turbulent times. It identifies several pertinent action points for managers to lead through problems while understanding their capacity to empower themselves and others to face challenges at work. Design/methodology/approach – Broad concepts of PBL are used to distil the characteristics of this methodology and how they might be applicable to leadership development. An actual case of PBL in leadership education and training is employed to illustrate the processes of problem solving and reflective action-taking. Findings – When confronted by problems, managers should adopt a learning-oriented mindset and draw on the strengths of others to generate immediate solutions for experimentation. In doing so, they need to accept failure as a prerequisite for creative tensions to be generated and applied in messy circumstances. Until they think out of the box, they will continue to solve problems in tried-and-tested ways obstructing the emergence of revolutionary solutions. Practical implications – In order for managers to make an impact on organizational process and improvement, they need to focus on the action and learn components of PBL. They should be given the space to listen to their own “voice” and internalize the “voice” of others through reflection and dialogue. They should also be recognized for their courage and boldness in confronting problems even if more problems are generated in the process. It is facing the goliath that managers truly grow to become real leaders. Originality/value – Although the concept of PBL has been around for a long while, its applicability to leadership development has not been sufficiently explored in both theory and practice. This paper brings another dimension to the common idea of problem solving where solution seeking is not an end it itself. At best, it is a means to discovering the potential of true leadership in those whose mindset is focused on learning and reflective decision-making

Do you want to bet? The prevalence of problem gambling amongst athletes in the UK

This presentation was given as part of the 2011 London Workshop on Problem Gambling: Theory and (Best) Practice by Dr Daniel Rhind from the Sports Sciences subject area at Brunel University. The workshop was organised by Professor Fernand Gobet and Dr Marvin Schiller and hosted by Brunel University on the 13th September 2011

A solution for Europe's banking problem

Nicolas Véron and Adam Posen believe Europe should build new long term European joint-action to face the likely high rising number of insolvent banks on the continent. The authors propose on the one hand, a centralised triage and restructuring process of bad European banks lead by a new temporary European Institution, a European Bank Support Authority (EBSA), and on the other hand, long-term EU Institutions dedicated to the completion of an integrated market.

Connes' embedding problem and Tsirelson's problem

We show that Tsirelson's problem concerning the set of quantum correlations and Connes' embedding problem on finite approximations in von Neumann algebras (known to be equivalent to Kirchberg's QWEP conjecture) are essentially equivalent. Specifically, Tsirelson's problem asks whether the set of bipartite quantum correlations generated between tensor product separated systems is the same as the set of correlations between commuting C*-algebras. Connes' embedding problem asks whether any separable II$_1$ factor is a subfactor of the ultrapower of the hyperfinite II$_1$ factor. We show that an affirmative answer to Connes' question implies a positive answer to Tsirelson's. Conversely, a positve answer to a matrix valued version of Tsirelson's problem implies a positive one to Connes' problem