Automated preparation of carbon-11 ethanol and carbon-11 butanol for human studies using positron emission tomography

An automated continuous flow process has been developed for the synthesis of¹¹C-ethanol and¹¹C-butanol. These alcohols were synthesized via the same route. The reaction of¹¹CO₂ with methylmagnesium bromide or with n-propylmagnesium chloride, followed by a lithium aluminum hydride reduction and hydrolysis produced respectively¹¹C-ethanol and¹¹C-butanol. Preparation can be completed in 25 min. In each case the radiochemical purity, as determined by high pressure liquid chromatography /HPLC/ was greater than 98%. Biological quality control shows that the products are suitable for human use. The process has been completely automated to limit radiation exposure to personnel, reduce preparation time, and increase reproducibility.     

Limit Consistent Solutions in Noncooperative Games

Strong and limit consistency in finite noncooperative games are studied. A solution is called strongly consistent if it is both consistent and conversely consistent (Ref. 1). We provide sufficient conditions on one-person behavior such that a strongly consistent solution is nonempty. We introduce limit consistency for normal form games and extensive form games. Roughly, this means that the solution can be approximated by strongly consistent solutions. We then show that the perfect and proper equilibrium correspondences in normal form games, as well as the weakly perfect and sequential equilibrium correspondences for extensive form games, are limit consistent.     

Benzylic Functionalization of Anthrones via the Asymmetric Ring Opening of Oxabicycles Utilizing a Fourth‐Generation Rhodium Catalytic System

While anthrones exist as privileged scaffolds in bioactive molecules, the enantioselective functionalization of anthrones is surprisingly scarce in the literature, with no asymmetric transition metal catalyzed example to date. Herein, we report the first asymmetric transition metal catalyzed benzylic functionalization of anthrones through the rhodium(I) catalyzed desymmetrization of oxabicycles. As previously developed rhodium(I) systems were found to be unsuitable for this substrate, a new robust fourth‐generation [Rh(cod)OH]₂ based catalytic system was developed to address synthetic challenges in this protocol.     

Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

Phase and Interfacial Tension Behavior of Certain Model Gas Condensates: Measurements and Modeling

This contribution reports on the phase and interfacial tension behavior of some model high-temperature–high-pressure gas condensates. On the one hand these types of gas condensate are becoming a subject of major interest for the oil industry, while on the other their phase and interfacial tension behavior have not been very well studied. For two different model gas condensates, both composed of the three n-alkanes, methane, butane, and decane, experimental results on their fluid phase behavior have been obtained in the temperature region 270 < T (K) < 490 and up to pressures as high as 24 MPa. Also, critical points of the two mixtures have been determined experimentally. Both mixtures show an extended retrograde region. Using the Peng–Robinson equation of state, the phase behavior of the two mixtures was modeled. In addition, the interfacial tension behavior of the model gas condensates was modeled. For that purpose, the Cahn–Hilliard theory was applied in combination with the Peng–Robinson equation of state. Satisfactory results were obtained.