Let (M, g) be a complete two dimensional simply connected Rie-mannian manifold with Gaussian curvature K ≤ −1. If f is a compactly supported function of bounded variation on M , then f satisfies the Sobolev inequality 4π Z M f 2 dA + Z M |f | dA 2 ≤ Z M f dA 2. Conversely, letting f be the characteristic function of a domain D ⊂ M recovers the sharp form 4πA(D) + A(D) 2 ≤ L(∂D) 2 of the isoperimetric inequality for simply connected surfaces with K ≤ −1. Therefore this is the Sobolev inequality "equivalent" to the isoperimetric inequality for this class of surfaces. This is a special case of a result that gives the equivalence of more general isoperimetric inequalities and Sobolev inequalities on surfaces. Under the same assumptions on (M, g), if c : [a, b] → M is a closed curve and wc(x) is the winding number of c about x, then the Sobolev inequality implies 4π Z M w 2 c dA + Z M |wc| dA 2 ≤ L(c) 2 , which is an extension of the Banchoff-Pohl inequality to simply connected surfaces with curvature ≤ −1.

In this study, we developed a three-dimensional framework to characterize post-secondary Calculus I final exams. Our Exam Characterization Framework (ECF) classifies individual exam items according to the cognitive demand required to answer the item, the representation of both the task statement and the solution, and the item's format. Our results from using the ECF to code 150 post-secondary Calculus I final exams from across the United States revealed that the exams generally require low levels of cognitive demand, seldom contain problems stated in a real-world context, rarely elicit explanation, and do not require students to demonstrate or apply their understanding of the course's central ideas. We compared the results from analyzing individual instructor's exams with survey data of their beliefs about the conceptual orientation of their exams. Our analysis revealed inconsistencies between our characterization of Calculus I final exams and instructors' perceptions of their final exams relative to their conceptual focus and the extent to which the exam items ask students to explain their thinking. We also compared the characteristics of our sample of final

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Recently, the subject of research relevancy has received a great deal of attention in the IS academic press. Several leading academic journals, such as MIS Quarterly, Information Systems Research, and Information Resources Management Journal have devoted special issues and/or articles to this topic. Typically, these articles have been opinion pieces from leading IS academics (i.e., Benbasat, Zmud, Robey, Lee, etc.) and have not included significant input from practitioners within the IS area. This chapter tries to capture the IS practitioners' perspective on research relevance through a survey sent to 400 IS practitioners. The results indicate that IS practitioners (1) do not know where academic research is published; (2) find academic research dated; (3) find academic research difficult to read; and/or (4) find the recommendations included in academic research to be of little value.

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