The classical Baker-Campbell-Hausdorff formula gives a recursive way to compute the Hausdorff series H = log(e X e Y) for non-commuting X, Y. Formally H lives in a completionˆL of the free Lie algebra L generated by X, Y. We prove that there are F, G ∈ [ ˆ L, ˆ L] such that H = e F Xe −F + e G Y e −G. We give a closed expression for H in the Lie algebra of formal vector fields on the line.

Since the early seventies, the development of the theoretical literature on contracts has been nothing short of explosive. The study of more and more sophisticated abstract models has gone hand in hand with the use of the tools of the theory to better understand many ...elds of economics, such as industrial organization, labor economics, taxation, insurance markets or the economics of banking. ...

In the high-energy limit, we compute the gauge-invariant three-parton forward clusters, which in the BFKL theory constitute the tree parts of the NNLO impact factors. In the triple collinear limit, we obtain the polarized double-splitting functions. For the unpolarized and the spin-correlated double-splitting functions, our results agree with the ones obtained by Campbell-Glover and Catani-Graz...

John H. Cochrane is the Sigmund E. Edelstone Professor of Finance in the Graduate School of Business at the University of Chicago, a consultant to the Federal Reserve Bank of Chicago, and a research associate at the National Bureau of Economic Research (NBER). The author thanks Andrea Eisfeldt for research assistance and David Marshall, John Campbell, and Robert Shiller for comments. The author...

Restricted growth functions (RGFs) avoiding the pattern 1212 are in natural bijection with noncrossing partitions. Motivated by recent work of Campbell et al., we study five classical statistics bk, ls, lb, rs and rb on 1212-avoiding RGFs. We show the equidistribution of (ls, rb, lb, bk) and (rb, ls, lb,bk) on 1212-avoiding RGFs by constructing a simple involution. To our surprise, this result ...

A new species of Phreodrilidae from Macquarie Harbour, Tasmania is described. Astacopsidrilus ostiensis sp. nov. is unique in possessing the combination of long, tightly folded atria, modified spermarhecal chaetae and ventral chaetae that are almost simple pointed. These are the first phreodrilids to be recorded from estuarine or intertidal habitats, other than two species collected from beache...

In this paper, we use a computer simulation to explore the effects of dynamic capabilities on the evolution of business processes. Dynamic capability is conceptualized as variation and selective retention (Campbell, 1965; Bickhard and Campbell, 2003) which governs the development and adaptation of business process. The model demonstrates that variation and selective retention of business proces...

A popular approach to monothematic delusions in the recent literature has been to argue that monothematic delusions involve broadly rational responses to highly unusual experiences. Campbell (2001) calls this the empiricist approach to monothematic delusions, and argues that it cannot account for the links between meaning and rationality. In place of empiricism, Campbell offers a rationalist ac...

Macroscopic and microscopic characteristics of the species included in the genus Arthrinium (Dematiaceaous Hyphomycete) have been described by several authors for some years, but the studies related to their ultrastructure as well as the first published articles on this subject were carried out by Campbell in 1975, and later by Cole and Samson in 1979. Since 1990, our research team has develope...

This paper compares the synchronicity of individual stock returns in different countries. For the US, Morck et al (2000) and Campbell et al (2001) show that the US in the post war period experienced an increase in firm specific stock return variations and thus a reduction in synchronicity. We show that a similar international trend, albeit weaker, is visible for many countries. Using both regre...