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Bibliographic record
Abstract
AbstractWe resolve and further study a sinc integral evaluation, first posed in this Monthly in [1967, p. 1015], which was solved in [1968, p. 914] and withdrawn in [1970, p. 657]. After a short introduction to the problem and its history, we give a general evaluation which we make entirely explicit in the case of the product of three sinc functions. Finally, we exhibit some more general structure of the integrals in question. Additional informationNotes on contributorsDavid BorweinDAVID BORWEIN obtained two B.Sc. degrees from the University of Witwatersrand, one in engineering in 1945 and the other in mathematics in 1948. From University College, London (UK) he received a Ph.D. in 1950 and a D.Sc. in 1960. He has been at the University of Western Ontario since 1963 with an emeritus title since 1989. His main area of research has been classical analysis, particularly summability theory.Jonathan M. BorweinJONATHAN M. BORWEIN is currently Laureate Professor in the School of Mathematical and Physical Sciences and Director of the Priority Research Centre in Computer Assisted Research Mathematics and its Applications at the University of Newcastle. He is also Distinguished Professor at King Abdulaziz University in Jeddah. An ISI highly cited scientist and former Chauvenet prize winner, he has published widely in various fields of mathematics. His most recent books are Convex Functions (with Jon Vanderwerff, vol 109, Encyclopaedia of Mathematics, Cambridge University Press, 2010) and Modern Mathematical Computation with Maple (with Matt Skerritt, Springer Undergraduate Mathematics and Technology, 2011).Armin StraubARMIN STRAUB graduated from Technische Universität Darmstadt, Germany, in 2008 under the guidance of Ralf Gramlich. Currently, he is a student of Victor Moll at Tulane University, New Orleans, planning to obtain his Ph.D. in Spring 2012. While he enjoys all sorts of mathematics, his research has a focus on the many aspects of special functions and their connections to computer algebra, number theory and combinatorics. He finds particular pleasure in making problems of diverse nature accessible to computation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it