Azafullerene C59N in Donor–Acceptor Dyads: Synthetic Approaches and Properties

Energy conversion schemes have attracted considerable attention in recent years. A large amount of research effort has focused on fullerenes, particularly C₆₀ and its derivatives, as suitable electron acceptors, owing to their outstanding properties. In this context, C₅₉N‐based donor–acceptor systems have lately attracted attention, owing to their exceptional energy‐and electron‐transfer properties. As a result, chemical derivatization of C₅₉N plays an important role in the realization of the aforementioned systems. The current Minireview aims to familiarize researchers with the main aspects of azafullerene synthesis, chemistry, and photophysical properties, while it mainly focuses on the synthetic methodologies employed for as well as on energy conversion schemes of azafullerene‐based donor–acceptor systems.     

One‐Pot Transformation of Simple Furans into 4‐Hydroxy‐2‐cyclopentenones in Water

A highly efficient one‐pot transformation of readily accessible furans into 4‐hydroxy‐2‐cyclopentenones in H₂O, using singlet oxygen as oxidant, has been developed.     

Torus Knot Polynomials and Susy Wilson Loops

We give, using an explicit expression obtained in (Jones V, Ann Math 126:335, 1987), a basic hypergeometric representation of the HOMFLY polynomial of (n, m) torus knots, and present a number of equivalent expressions, all related by Heine’s transformations. Using this result, the \({ (m, n) \leftrightarrow (n, m)}\) symmetry and the leading polynomial at large N are explicit. We show the latter to be the Wilson loop of 2d Yang–Mills theory on the plane. In addition, after taking one winding to infinity, it becomes the Wilson loop in the zero instanton sector of the 2d Yang–Mills theory, which is known to give averages of Wilson loops in \({\mathcal{N}}\) = 4 SYM theory. We also give, using matrix models, an interpretation of the HOMFLY polynomial and the corresponding Jones–Rosso representation in terms of q-harmonic oscillators.     

Investment strategies and compensation of a mean–variance optimizing fund manager

This paper introduces a general continuous-time mathematical framework for solution of dynamic mean–variance control problems. We obtain theoretical results for two classes of functionals: the first one depends on the whole trajectory of the controlled process and the second one is based on its terminal-time value. These results enable the development of numerical methods for mean–variance problems for a pre-determined risk-aversion coefficient. We apply them to study optimal trading strategies pursued by fund managers in response to various types of compensation schemes. In particular, we examine the effects of continuous monitoring and scheme’s symmetry on trading behavior and fund performance.