M 311 Spring 2004 HOMEWORK SUMMARY REPORT Chapter number: 6 Section number: 1 Exercise number: 6 Number of papers received: 5 Reviewing committee: Iota List all participating committee members: Clark, DenBleyker Author(s) of paper(s) chosen for publication: Madsen and Zhang Comments: Three of the five solutions we received were excellent. The three conditions for an inner product to exist (RI1-RI3) were either mentioned or applied in these responses, and were very helpful in the explanations of the answers. Also, the boundedness of the functions was mentioned as requested in the problem. One of the papers seemed a bit rushed and incomplete. There were no major errors in any paper, but we did find Jason Madsen's and Xujia Zhang's to be the best of the five, and we recommended them for publication. There is a small notation problem with Madsen's, but once he corrects it, it will be ready for publication. Zhang's does not absolutely need any revision, but we did suggest a few possible areas of improvement. Also, Zach Olson's response was very good, but it was handwritten, which is the reason we did not recommend it for publication. GRADER'S COMMENT: Nobody said anything to indicate WHY the required conditions RI1-3 are met. INSTRUCTOR'S COMMENTS: (1) Part (c) is a trap, which everyone fell into (including me, until the last minute). The problem says to consider functions defined on (0,\infty), not (0,2). The bilinear function (c) is NOT POSITIVE DEFINITE because = 0 for any nonzero function that vanishes for 0 < t < 2. (2) The two recommended papers were rather similar. I think that Jason's will be sufficient, once it is revised.