This paper introduces new mathematical expressions which describe surface patches with three, five or six sides. Each side of a patch is given as a space curve expressed in Bézier type of second or third degree. Patch shape is modified predictably by moving its control points in the same way as with a four-sided patch. Distribution of cross tangent vectors along a patch boundary is also expressed in the same form with a few control vectors belonging to the boundary concerned. Therefore it can be connected with its surrounding four-sided patches smoothly. A general method of derivation of these equations is explained for further applications.
In about one-third of US IPOs between 1996 and 2000, executives received stock options with an exercise price equal to the IPO offer price rather than a market-determined price. Among firms with such “IPO options”, 58% of top executives realize a net benefit from underpricing: the gain from the options exceeds the loss Basket Blazer Femme Grise from the dilution of their pre-IPO shareholdings. If executives can influence either the IPO offer price or the timing and terms of their stock option grants, there should be a positive relation between IPO option grants and underpricing. We find no evidence of such a relation. Our results contrast sharply with the emerging literature on managerial self-dealing at shareholder expense.
This research examined the role of three Big Five-related personality traits (Prudence, Sociability, Blazer Noir and Ambition) as unique predictors of academic performance. Two successive undergraduate classes (entering in 1998 and 1999) Chaussure Nike Blazer Basse completed personality inventories upon entering college. The authors obtained grade point averages (GPA’s) for all students in the Spring of 2003. Two of the traits, Prudence and Sociability, contributed unique variance to GPA when the effects of high school percentile rank and achievement test scores were controlled for both classes. There was a decline in incremental validity for these two personality traits as predictors of GPA later in student tenure. Ambition was unrelated to academic performance for both classes.
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