Temperature and Solvent Effects on the Europium(III)-catalyzed Hydrolysis of Bis-(nitrophenyl) Phosphate

The hydrolysis of bis-(nitrophenyl) phosphate (BNPP) as model for secondary phosphate esters is analyzed at six different concentrations of Eu(III) ions and four temperatures between 303 and 343 K. Eyring plots yield activation enthalpy parameters which with, e.g. [Eu 3+ ] between 0.40 and 10.0 mM drop from 130 to 74 kJ mol m 1 , respectively, with a relatively small drop in the opposing entropy contributions. The observed saturation profiles allow for the first time to evaluate the influence of j H and j S separately on the Michaelis-Menten values K M and k cat , showing that the catalytic metal-ion effects are largely due to changes in k cat and dominated by favorable j H changes. Preliminary studies of the solvent influence show a surprising difference between water mixtures with either ethanol or DMSO. With, e.g. 40% ethanol, one observes a doubling of the rate constant, with 40% DMSO an almost 10-fold rate decrease. In both cases, a linear correlation with the solvent polarity parameter E T is found.     

Amine-Directed Palladium-Catalyzed C−H Halogenation of Phenylalanine Derivatives

An efficient primary-amine-directed, palladium-catalyzed C−H halogenation (X=I, Br, Cl) of phenylalanine derivatives is reported on a range of quaternary amino acid (AA) derivatives thanks to suitable conditions employing trifluoroacetic acid as additive. The extension of this original native functionality-directed ortho-selective halogenation was even demonstrated with the more challenging native phenylalanine as tertiary AA.     

The shadow of a collapsing dark star

The shadow of a black hole is usually calculated, either analytically or numerically, on the assumption that the black hole is eternal, i.e., that it has existed for all time. Here we ask the question of how this shadow comes about in the course of time when a black hole is formed by gravitational collapse. To that end we consider a star that is spherically symmetric, dark and non-transparent and we assume that it begins, at some instant of time, to collapse in free fall like a ball of dust. We analytically calculate the dependence on time of the angular radius of the shadow, first for a static observer who is watching the collapse from a certain distance and then for an observer who is falling towards the centre following the collapsing star.     

Crime and punishment: Does it pay to punish?

Crime is the result of a rational distinctive balance between the benefits and costs of an illegal act. This idea was proposed by Becker more than forty years ago (Becker (1968) [1]). In this paper, we simulate a simple artificial society, in which agents earn fixed wages and can augment (or lose) wealth as a result of a successful (or not) act of crime. The probability of apprehension depends on the gravity of the crime, and the punishment takes the form of imprisonment and fines. We study the costs of the law enforcement system required for keeping crime within acceptable limits, and compare it with the harm produced by crime. A sharp phase transition is observed as a function of the probability of punishment, and this transition exhibits a clear hysteresis effect, suggesting that the cost of reversing a deteriorated situation might be much higher than that of maintaining a relatively low level of delinquency. Besides, we analyze economic consequences that arise from crimes under different scenarios of criminal activity and probabilities of apprehension.