Endangered Hydrocarbons by Lesley Battler

A review of Lesley Battler\u27s Endangered Hydrocarbons

Descending Dungeons and Iterated Base-Changing

For real numbers a, b> 1, let as a_b denote the result of interpreting a in base b instead of base 10. We define ``dungeons'' (as opposed to ``towers'') to be numbers of the form a_b_c_d_..._e, parenthesized either from the bottom upwards (preferred) or from the top downwards. Among other things, we show that the sequences of dungeons with n-th terms 10_11_12_..._(n-1)_n or n_(n-1)_..._12_11_10 grow roughly like 10^{10^{n log log n}}, where the logarithms are to the base 10. We also investigate the behavior as n increases of the sequence a_a_a_..._a, with n a's, parenthesized from the bottom upwards. This converges either to a single number (e.g. to the golden ratio if a = 1.1), to a two-term limit cycle (e.g. if a = 1.05) or else diverges (e.g. if a = frac{100{99).Comment: 11 pages; new version takes into account comments from referees; version of Sep 25 2007 inculdes a new theorem and several small improvement

Trademark Vigilance in the Twenty-First Century: An Update

The trademark laws impose a duty upon brand owners to be vigilant in policing their marks, lest they be subject to the defense of laches, a reduced scope of protection, or even death by genericide. Before the millennium, it was relatively manageable for brand owners to police the retail marketplace for infringements and counterfeits. The Internet changed everything. In ways unforeseen, the Internet has unleashed a tremendously damaging cataclysm upon brands—online counterfeiting. It has created a virtual pipeline directly from factories in China to the American consumer shopping from home or work. The very online platforms that make Internet shopping so convenient, and that have enabled brands to expand their sales, have exposed buyers to unwittingly purchasing fake goods which can jeopardize their health and safety as well as brand reputation. This Article updates a 1999 panel discussion titled Trademark Vigilance in the Twenty-First Century, held at Fordham Law School, and explains all the ways in which vigilance has changed since the Internet has become an inescapable feature of everyday life. It provides trademark owners with a road map for monitoring brand abuse online and solutions for taking action against infringers, counterfeiters and others who threaten to undermine brand value

No TV for Woodpeckers by Gary Barwin, If Pressed by Andrew McEwan, and Ecology without Culture: Aesthetics for a Toxic World by Christine L. Marran

Review of Gary Barwin\u27s No TV for Woodpeckers, Andrew McEwan\u27s If Pressed, and Christine L. Marran\u27s Ecology without Culture: Aesthetics for a Toxic World

The Policies of State Succession: Harmonizing Self-Determination and Global Order in the Twenty-First Century Tai-Heng Cheng, State Succession and Commercial Obligations

I differ with Cheng\u27s appraisal of certain events and think that we need a more sophisticated analysis of the twin policy goals he identifies and embraces--self-determination and global order--before they can offer real policy guidance. But State Succession and Commercial Obligations stands out as a rigorously researched, original, and insightful effort to understand this quite confused and opaque body of international law. Cheng\u27s work will both enable and encourage a more candid, reasoned, and constructive debate about the global policies at stake each time “a state fundamentally changes its structures of power and authority, and an authoritative international response is needed to manage disruptions to international arrangements that may result from that change.” Briefly, I find Cheng\u27s analysis of the dynamics of State succession relative to commercial obligations sophisticated, pragmatic, descriptively comprehensive, and, for the most part, normatively compelling. But it may be too ambitious. Defining disruptions to global commerce as the principal indicia of State succession tends to inflect, and at times to bias, the general analysis of the diverse phenomena that fall within the rubric of State succession. This commercial focus can obscure or normatively predispose our understanding and appraisal of equally vital, but non-economic, dimensions of State succession, including the core policy goals--self-determination and global order--that Cheng identifies and recommends. And to a certain extent, this compromises the work\u27s descriptive accuracy and normative appeal

Rottenberg and the Economics of Sport after 50 years: An Evaluation

Simon Rottenberg’s seminal 1956 article in the Journal of Political Economy, 1956, is generally accepted as the starting point for the development of the economics of sport. While he recognised that certain features of professional sports leagues were unusual he saw little reason to treat this industry any differently from a conventional industry. He discusses the importance of uncertainty of outcome, the monopsonistic nature of the labour market, the nature of the product and demand (attendances). He considers alternatives to the reserve clause, such as equal revenue sharing, maximum salary limits, equal market franchise distribution and roster limits. Each of these is rejected in favour of a free market solution which, on the basis of the invariance principle, he suggests will perform just as well as the reserve clause in allocating talent to where it is most productive. The ensuing literature has focused on all these issues, many of which have created considerable debate amongst sports economists. In particular the assumption of profit maximisation has been challenged and a divergence of views, reflected in the so-called North American and European models of sports leagues has emerged. Over the last 50 years sports leagues have expanded, TV markets have opened up and legal challenges to existing practices have multiplied. This paper seeks to evaluate Rottenberg’s contribution to a rapidly expanding field and to judge its relevance today.Sport, Monopsony, Monopoly Power

Seven Staggering Sequences

When my "Handbook of Integer Sequences" came out in 1973, Philip Morrison gave it an enthusiastic review in the Scientific American and Martin Gardner was kind enough to say in his Mathematical Games column that "every recreational mathematician should buy a copy forthwith." That book contained 2372 sequences. Today the "On-Line Encyclopedia of Integer Sequences" contains 117000 sequences. This paper will describe seven that I find especially interesting. These are the EKG sequence, Gijswijt's sequence, a numerical analog of Aronson's sequence, approximate squaring, the integrality of n-th roots of generating functions, dissections, and the kissing number problem. (Paper for conference in honor of Martin Gardner's 91st birthday.)Comment: 12 pages. A somewhat different version appeared in "Homage to a Pied Puzzler", E. Pegg Jr., A. H. Schoen and T. Rodgers (editors), A. K. Peters, Wellesley, MA, 2009, pp. 93-11