Blocking and invasion for reaction–diffusion equations in periodic media

We investigate the large time behavior of solutions of reaction–diffusion equations with general reaction terms in periodic media. We first derive some conditions which guarantee that solutions with compactly supported initial data invade the domain. In particular, we relate such solutions with front-like solutions such as pulsating traveling fronts. Next, we focus on the homogeneous bistable equation set in a domain with periodic holes, and specifically on the cases where fronts are not known to exist. We show how the geometry of the domain can block or allow invasion. We finally exhibit a periodic domain on which the propagation takes place in an asymmetric fashion, in the sense that the invasion occurs in a direction but is blocked in the opposite one.     

Wermer Examples and Currents

We give the first examples of positive closed currents T in ${{\mathbb C}^2}We give the first examples of positive closed currents T in \mathbb C²{{\mathbb C}^2} with continuous potentials, T ùT = 0{T \wedge T = 0}, and whose supports do not contain any holomorphic disk. This gives in particular an affirmative answer to a question of Forn?ss and Levenberg. We actually construct examples with potential of class C ^1,α for all α < 1. This regularity is expected to be essentially optimal.     

No-arbitrage and optimal investment with possibly non-concave utilities: a measure theoretical approach

We consider a discrete-time financial market model with finite time horizon and investors with utility functions defined on the non-negative half-line. We allow these functions to be random, non-concave and non-smooth. We use a dynamic programming framework together with measurable selection arguments to establish both the characterisation of the no-arbitrage property for such markets and the existence of an optimal portfolio strategy for such investors.     

Metal Linkage Effects on Ultrafast Energy Transfer

We report the preparation of several new porphyrin homodimers bridged by a platinum(II) ion in which very intense electronic communication through the coordination link occurs. Moreover, the synthesis of a new porphyrin dyad and its photophysical properties are reported. This dyad exhibits the fastest singlet energy transfer ever reported for synthetic systems between a zinc(II) porphyrin and a porphyrin free base. This extremely fast transfer (～100 femtoseconds) is in the same range as the fastest one measured in natural systems. This feature is due to the platinum(II) linker, which allows for strong MO couplings between the two porphyrin units as experimentally supported by electrochemistry and corroborated by DFT computations.     

Asymmetric Hydroxylative Phenol Dearomatization Promoted by Chiral Binaphthylic and Biphenylic Iodanes

The long‐standing quest for chiral hypervalent organoiodine compounds (i.e., iodanes) as metal‐free reagents for asymmetric synthesis continues. Although remarkable progress has recently been made in organoiodine‐catalyzed reactions using a terminal oxidant in stoichiometric amounts, there is still a significant need for “flaskable” chiral iodane reagents. Herein, we describe the synthesis of new iodobinaphthyls and iodobiphenyls, their successful and selective DMDO‐mediated oxidation into either λ³‐ or λ⁵‐iodanes, and the evaluation of their capacity to promote asymmetric hydroxylative phenol dearomatization (HPD) reactions. Most notably, a C₂‐symmetrical biphenylic λ⁵‐iodane promoted the HPD‐induced conversion of the monoterpene thymol into the corresponding ortho‐quinol‐based [4+2] cyclodimer (i.e., bis(thymol)) with enantiomeric excesses of up to 94 %.