Macroscopic limit of the Becker-D\"oring equation via gradient flows

This work considers gradient structures for the Becker-D\"oring equation and its macroscopic limits. The result of Niethammer [17] is extended to prove the convergence not only for solutions of the Becker-D\"oring equation towards the Lifshitz-Slyozov-Wagner equation of coarsening, but also the convergence of the associated gradient structures. We establish the gradient structure of the nonlocal coarsening equation rigorously and show continuous dependence on the initial data within this framework. Further, on the considered time scale the small cluster distribution of the Becker--D\"oring equation follows a quasistationary distribution dictated by the monomer concentration

Meet Mr. Everyman: Everyone His Own Interpreter

In 1931, Carl Becker, president of the American Historical Association, the largest professional organization of historians, gave a speech in which he tried to distill history to its very essence. In that address, “Everyman His Own Historian,” Becker declared that history reduced to its lowest terms was the “memory of things said and done.” Using that simple definition, Becker argued that everyone, no matter whether they had professional training or expertise, was in some way, at some point in time, an historian. Everyone at some time in their lives did as a historian does – asks a question about the past and researches it, using evidence to come up with the most logical conclusion. [excerpt

A generalization of the Becker model in linear viscoelasticity: Creep, relaxation and internal friction

We present a new rheological model depending on a real parameter $\nu \in [0,1]$ that reduces to the Maxwell body for $\nu=0$ and to the Becker body for $\nu=1$. The corresponding creep law is expressed in an integral form in which the exponential function of the Becker model is replaced and generalized by a Mittag-Leffler function of order $\nu$. Then, the corresponding non-dimensional creep function and its rate are studied as functions of time for different values of $\nu$ in order to visualize the transition from the classical Maxwell body to the Becker body. Based on the hereditary theory of linear viscoelasticity, we also approximate the relaxation function by solving numerically a Volterra integral equation of the second kind. In turn, the relaxation function is shown versus time for different values of $\nu$ to visualize again the transition from the classical Maxwell body to the Becker body. Furthermore, we provide a full characterization of the new model by computing, in addition to the creep and relaxation functions, the so-called specific dissipation $Q^{-1}$ as a function of frequency, which is of particularly relevance for geophysical applicationsComment: 18 pages, 8 figures. arXiv admin note: text overlap with arXiv:1701.0306

The Behavioral Economics of Crime and Punishment

The Becker proposition (BP) is one of the founding pillars of the modern literature on Law and Economics. It states that it is optimal to impose the severest possible punishment (to maintain effective deterrence) at the lowest possible probability (to economize on enforcement costs). The BP is not consistent with the evidence. This is known as the Becker paradox. Using evidence from a wide range of phenomena we show that none of the proposed explanations for the Becker paradox are satisfactory. The BP has largely been considered within an expected utility framework. We clarify the Becker proposition and its welfare implications under expected utility. We show that BP also holds under rank dependent expected utility and cumulative prospect theory, the two main alternatives to expected utility. al-Nowaihi and Dhami (2010a) recently propose composite cumulative prospect theory that combines prospect theory with cumulative prospect theory. Under plausible conditions CCP is able to resolve the Becker paradox. Our article opens the way for incorporating non-expected utility theories into an economic analysis of criminal activity.Behavioral economics; Illegal activity; Expected utility theory; Rank dependent expected utility; Prospect theory; Prelec and composite Prelec probability weighting functions; Composite cumulative prospect theory; Punishment functions

1. Carl Becker on Progress

The first selection was written by Carl L. Becker (1873-1945), for many years professor of history at Cornell University (1917-1941), and one of the most highly respected members of his profession. One of his particular interests was the Enlightenment, about which he wrote a famous book: The Heavenly City of the Eighteenth Century Philosophers (1932). But while he clung to his fascination with the Enlightenment, Becker was in revolt against the scientific history which it had largely fostered. The ideal of scientific history, he thought, was noble enough, but unattainable and useless. Influenced by pragmatism, Becker asked the question: Can there by anything like objectively written history? Is the raw material from which it is to be derived a string of pure facts that the historian himself so deeply involved in his own cultural milieu that he reads into the past his own presuppositions (whether he wants to or not) and to a considerable extent finds what he wants there, both facts and interpretations? [excerpt