Harmonic Shears of Slit and Polygonal Mappings

In this paper, we study harmonic mappings by using the shear construction, introduced by Clunie and Sheil-Small in 1984. We consider two classes of conformal mappings, each of which maps the unit disk D univalently onto a domain which is convex in the horizontal direction, and shear these mappings with suitable dilatations \omega. Mappings of the first class map the unit disk D onto four-slit domains and mappings of the second class take D onto regular n-gons. In addition, we discuss the minimal surfaces associated with such harmonic mappings. Furthermore, illustrations of mappings and associated minimal surfaces are given by using Mathematica.Comment: 17 pages, 6 figures, 2 table

Derivative relationships between volume and surface area of compact regions in R^d

We explore the idea that the derivative of the volume, V, of a region in R^d with respect to r equals its surface area, A, where r = d V/A. We show that the families of regions for which this formula for r is valid, which we call homogeneous families, include all the families of similar regions. We determine equivalent conditions for a family to be homogeneous, provide examples of homogeneous families made up of non-similar regions, and offer a geometric interpretation of r in a few cases.Comment: 15 page

HIGHER ORDER SCHWARZIAN DERIVATIVES FOR CONVEX UNIVALENT FUNCTIOS

We observe that in contrast to the class S, the extremal functions for the bound of higher order Schwarzian derivatives for the class S c of convex univalent functions are different. We prove the sharp bound for three first consecutive derivatives

Political Decision Making in Face-to-Face Groups: Theory, Methods, and an Empirical Application in Switzerland

This article presents a model of decision making and introduces a new theoretical variable to the literature, namely, the modes of decision making. The theoretical focus is on the face-to-face group, and the article also develops an innovative methodology for studying this type of decision-making behavior. Variation in the decision modes is explained as a function of the strategic considerations of individual decision makers. These considerations are affected by a set of four independent variables: structure of the decision group, substance of the conflict, context of the conflict, and the decision process. The data, drawn from observations of decision-making groups in Switzerland, are tested with discriminant analysis and a simulation. In both cases total correct classifications exceed 55 percent, indicating that there is a meaningful structure relating variation in the decision modes to the theoretical framewor

DONATIONS FROM ILL-GOTTEN GAIN: A JEWISH LEGAL PERSPECTIVE

© 2008 by Elliot N. Dorff Excerpts of more than 100 words from this publication may not be reproduced without permission. Editorial questions and permission inquiries may be addressed to: Publications Department The Center on Philanthropy at Indiana University 550 W. North St., Suite 301 Indianapolis, IN 46202-3272 Telephone: 317-274-4200 Web site: www.philanthropy.iupui.ed