Existence of solution for fractional Langevin equation: Variational approach

We consider the Dirichlet problem for the fractional Langevin equation with two fractional order derivatives \begin{align*} -{_{0}}D_{t}^{\alpha}(_{0}D_{t}^{\alpha}u(t)) &= f(t,u(t), {_{0}}D_{t}^{\alpha}u(t)), \quad t\in [0,1],\\ u(0) &= u(1) = 0. \end{align*} The existence of a nontrivial solution is stated through an iterative method based on mountain pass techniques

Anonymity in Large Societies

In a social choice model with an infinite number of agents, there may occur "equal size" coalitions that a preference aggregation rule should treat in the same manner. We introduce an axiom of equal treatment with respect to a measure of coalition size and explore its interaction with common axioms of social choice. We show that, provided the measure space is sufficiently rich in coalitions of the same measure, the new axiom is the natural extension of the concept of anonymity, and in particular plays a similar role in the characterization of preference aggregation rules.

2D sigma models and differential Poisson algebras

We construct a two-dimensional topological sigma model whose target space is endowed with a Poisson algebra for differential forms. The model consists of an equal number of bosonic and fermionic fields of worldsheet form degrees zero and one. The action is built using exterior products and derivatives, without any reference to any worldsheet metric, and is of the covariant Hamiltonian form. The equations of motion define a universally Cartan integrable system. In addition to gauge symmetries, the model has one rigid nilpotent supersymmetry corresponding to the target space de Rham operator. The rigid and local symmetries of the action, respectively, are equivalent to the Poisson bracket being compatible with the de Rham operator and obeying graded Jacobi identities. We propose that perturbative quantization of the model yields a covariantized differential star product algebra of Kontsevich type. We comment on the resemblance to the topological A model.Comment: 20 page

On the Merit of the Legacy of Failed Olympic Bids

Olympic legacy has become a dominant theme within the Olympic Movement. For decades, legacy concerns were confined to the hosting of the Olympic Games. However, these concerns have been recently extended to the bidding process itself. Cities bidding for the Olympic Games are now required to identify their legacy regardless of the outcome of their bids. This paper explores the merits of extending legacy discourse in case bids failed. It contends that the extension of legacy discourse into failed bids, at least as typically articulated in Olympic circles, is problematic. It also contends that failed bids should be seen themselves as a form of legacy worth recognizing and protecting

Morally Incompatible? An Analysis of the Relationship Between Competitive Sport and International Relations at the Olympic Games

The Olympic Games are a multinational and multisport event with unparalleled global allure. As athletes from more than 200 countries convene to compete, they are guided by the “Fundamental Principles of Olympism,” which call for a mutually acceptable quest for excellence through challenge. Critics of Olympism claim the zero-sum nature of competitive challenge promotes extreme patriotism and international animosity rather than cooperative spirit. In light of this criticism and the resilience of the Olympic Games, this paper considers the proposition that athletic competition is incompatible with the goals of the Games, but ultimately rejects that view and provides two policy recommendations to allow the Olympic Games to realize their full potential as a global assembling event

Stymied Expectations Buenos Aires\u27 Persistent Efforts to Host Olympic Games

Argentine elites have shown interest in hosting the Olympic Games in Buenos Aires at various times during the twentieth century. Expressions of interest intensified after the creation of a stable national Olympic bureaucracy in the 1920s. The last concerted effort was the bid for the 2004 Olympics. Argentine Olympic officials have perceived the efforts to bring the Olympic Games to Buenos Aires as an important aspect of their role as promoters of the Olympic Movement. Despite this perception, the history and status of these efforts remain unclear. This article explores the failed attempts to host the Olympic Games in Argentina\u27s capital. in doing so, it ascertains how many times Buenos Aires actually bid and clarifies the logic, conditions, and forces behind these efforts. This article shows that these efforts have served as a terrain in and through which Argentines have imagined their collective identity

The Youth Olympic Games, Their Programs, and Olympism

The Youth Olympic Games were inaugurated by the International Olympic Committee in Singapore in 2010. Their scale was nothing short of impressive. Focused around a vision to inspire young people to participate in sport and learn about the values of Olympism, the YOG implemented an extensive Cultural and Educational Program and an innovative Competitive Program. This paper evaluates both these programs and the extent to which they embody and advance Olympism. It identifies strengths as well as potential areas of improvements. This paper argues that the YOG demonstrate that alternate Olympic scenarios, ones that are more sensible to Olympism, are not only desirable but also possible