Zeros of the Möbius function of permutations

We show that if a permutation \pi contains two intervals of length 2, where one interval is an ascent and the other a descent, then the Möbius function \mu[1,\pi] of the interval [1,\pi] is zero. As a consequence, we prove that the proportion of permutations of length $\textit{n}$ with principal Möbius function equal to zero is asymptotically bounded below by (1\ -\ \sfrac{1}{e)^2} \geq 0.3995. This is the first result determining the value of \mu\left[1,\pi\right] for an asymptotically positive proportion of permutations \pi. We further establish other general conditions on a permutation \pi that ensure \mu\left[1,\pi\right]\ =\ 0, including the occurrence in \pi of any interval of the form \alpha\oplus\ 1\ \oplus\ \beta

Epidemiologic and clinical updates on impulse control disorders: a critical review

The article reviews the current knowledge about the impulse control disorders (ICDs) with specific emphasis on epidemiological and pharmacological advances. In addition to the traditional ICDs present in the DSM-IV—pathological gambling, trichotillomania, kleptomania, pyromania and intermittent explosive disorder—a brief description of the new proposed ICDs—compulsive–impulsive (C–I) Internet usage disorder, C–I sexual behaviors, C–I skin picking and C–I shopping—is provided. Specifically, the article summarizes the phenomenology, epidemiology and comorbidity of the ICDs. Particular attention is paid to the relationship between ICDs and obsessive–compulsive disorder (OCD). Finally, current pharmacological options for treating ICDs are presented and discussed

Accounting: A General Commentary on an Empirical Science

Many researchers have questioned the view of accounting as a science. Some maintain that it is a service activity rather than a science, yet others entertain the view that it is an art or merely a technology. While it is true that accounting provides a service and is a technology (a methodology for recording and reporting), that fact does not prevent accounting from being a science. Based upon the structure and knowledge base of the discipline, this paper presents the case for accounting as an empirical science

Alexander, Callisthenes and the Sources of the Nile

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