A family of critically finite maps with symmetry

The symmetric group S_n acts as a reflection group on CP^{n-2} (for $n\geq 3$) . Associated with each of the $\binom{n}{2}$ transpositions in S_n is an involution on CP^{n-2} that pointwise fixes a hyperplane--the mirrors of the action. For each such action, there is a unique S_n-symmetric holomorphic map of degree n+1 whose critical set is precisely the collection of hyperplanes. Since the map preserves each reflecting hyperplane, the members of this family are critically-finite in a very strong sense. Considerations of symmetry and critical-finiteness produce global dynamical results: each map's fatou set consists of a special finite set of superattracting points whose basins are dense.Comment: 24 pages, 9 figure

Which firms use trademarks - and why? : representative firm-level evidence from Germany

Trademarking firms are more productive, generate higher profits, and have a better survival rate. Trademarking firms are in one word more successful, which might motivate non-trademarking firms to adopt a trademark strategy. But this seems not to be the case. The proportion of trademarking firms in the German business sector amounts to just 18%. This figure is quite low, given that nearly each firm has reputation to protect. But why has the vast majority of firms no registered trademarks? Using a representative sample of German firms, the present paper links certain firm characteristics to a firms' propensity to register trademarks. The empirical results point to circumstances under which trademarks are significantly more often used: this is the case where a large distance between a firm and its customers exists, a firm's product quality is difficult to assess, a firm's products are characterized by a limited (but not strong) substitutability, and where a firm is engaged in R&D and introduces innovative products. Trademarks are considerably less frequently used if none of this is the case

The impact of brand use on innovation performance : empirical results for Germany

The market launch of product innovations is the most visible output of a firm's investment in innovation activities. To achieve this objective most efficiently, firms strengthen their technological capabilities, acquire external knowledge in a number of different ways, and optimize their innovation process. The success of a firm's innovation strategy has two dimensions: First, the ability of a firm to master the research and development process, leading to the market introduction of a product innovation. Second, the ability to turn the market introduction of a product innovation into commercial success. While a firms technological abilities make a product innovation possible, this product might face a lack of interest among potential customers after its mar- ket introduction. The introduction of a product innovation under a brand name might generate interest, adds credibility and reputation and has the potential for the firm to better appropriate the returns from its innovations. This paper investigates the role of brand use for the commercial success of product innovations, using a representative sample of German firms. The results show that firms can improve the odds of commercial success by pursuing a branding strategy. The market introduction of a product innovation is shown to be associated with 35% larger sales if the firm uses an established brand to introduce the product innovation into the market

April 27–30, 2005 in Addis Ababa: Stemming the Tide: Efforts at Preserving Languages

 Conference Review