Fluoropropenoates as dienophiles in the Diels-Alder reaction

Several fluorinated alkenes were prepared from known ethyl (R)-2-fluoro-4,5-dihydroxyisopropylidine-2-pentenoate (1). The fluoroalkenoates were tested as dienophiles with several dienes and showed cycloaddition only with the very reactive diene, 1,3-diphenylisobenzofuran (5). Fluorobutenolide 2 reacted with 5 to produce the endo-syn adduct 9 in a highly stereoselective manner.     

Mechanistic Study of the Titanocene(III)‐Catalyzed Radical Arylation of Epoxides

An atom‐economical and catalytic arylation of epoxide‐derived radicals is described. The key step of the catalytic system is a sequential electron and proton transfer for the rearomatization of the radical σ‐complex and catalyst regeneration. Kinetic, computational, spectroscopic, and cyclovoltammetric investigations highlight the key issues of the reaction mechanism and catalyst stabilization by collidine hydrochloride. Studies employing radicophiles rule out the participation of cations as reactive intermediates.     

Cationic Titanocene(III) Complexes for Catalysis in Single‐Electron Steps

By exploiting solvent and anion effects, [Cp₂Ti]⁺ complexes for atom‐economical catalysis in single‐electron steps were developed and applied for the first time. These complexes constitute remarkably stable and active catalysts for radical arylations. The reaction kinetics and catalyst composition were studied by cyclic voltammetry and in situ IR spectroscopy.     

A Markov decision process model for equitable distribution of supplies under uncertainty

Many individuals suffering from food insecurity obtain assistance from governmental programs and nonprofit agencies such as food banks. Much of the food distributed by food banks come from donations which are received from various sources in uncertain quantities at random points in time. This paper presents a model that can assist food banks in distributing these uncertain supplies equitably and measure the performance of their distribution efforts. We formulate this decision problem as a discrete-time, discrete state Markov decision process that considers stochastic supply, deterministic demand and an equity-based objective. We investigate three different allocation rules and describe the optimal policy as a function of available inventory. We also provide county level estimates of unmet need and determine the probability distribution associated with the number of underserved counties. A numerical study is performed to show how the allocation policy and unmet need are impacted by uncertain supply and deterministic, time-varying demand. We also compare different allocation rules in terms of equity and effectiveness.