Online text: scholarlycommons.pacific.edu/euler-works/53/

Cited passages: Euler Archive, E53: written date, publication date, original source citation.

By Leonhard Euler.

Published in Commentarii academiae scientiarum Petropolitanae.

Online text: www.cantab.net/users/michael.behrend/repubs/maze_maths/pages/euler.html

Cited passages: Solutio problematis ad geometriam situs pertinentis, §§6, 9, 20.

An edited online reference published by National Institute of Standards and Technology. The authorship tags on individual chapters refer to the credited chapter contributors, not to authorship of the entire reference.

Official website: dlmf.nist.gov/

Project description: dlmf.nist.gov/about/

By Jeremy Orloff, named on the first page of the notes for MIT 18.04, Complex Variables with Applications, Spring 2018. The credit here refers to this authored set of notes.

Official course resource: ocw.mit.edu/courses/18-04-complex-variables-with-applications-spring-2018/resources/mit18_04s18_topic11/

Online text: ocw.mit.edu/courses/18-04-complex-variables-with-applications-spring-2018/44f1db513a6a17d655abe0b6ff7748fc_MIT18_04S18_topic11.pdf

Cited passages: §11.2, Theorems 11.1 and 11.4, pp. 1–3, gives the argument principle and its residue theorem explanation; §11.2.3 covers Rouché's theorem; §11.3.6 explains the Nyquist stability criterion, including the sign from the clockwise contour used there. Our rational-function and sparse-sampling examples and images are independently calculated.

By Gavin C. Cawley, Nicola L. C. Talbot.

Published in Journal of Machine Learning Research, 11(70):2079–2107.

Online text: jmlr.org/papers/volume11/cawley10a/cawley10a.pdf

Cited passages: On Over-fitting in Model Selection and Subsequent Selection Bias in Performance Evaluation, introduction, pp. 2079–2080: selection as part of fitting and nested assessment.

Collection of sources; individual chapter authors and dates are recorded below.

Collection of sources; individual chapter authors and dates are recorded below.

Collection of sources; individual chapter authors and dates are recorded below.

By John A. Beachy, William D. Blair.

Publisher: Waveland Press, Inc..

By James S. Milne.

Online text: www.jmilne.org/math/CourseNotes/GT.pdf

Cited passages: Milne, Group Theory, corollary 4.8, printed page 61; Milne, Group Theory, example 4.6; Milne, corollary 4.8.

Additional cited passages: printed p. 57, Definition 4.1 and Example 4.2(c); p. 64, Action on the left cosets: stabilizer and kernel formulas preceding Remark 4.22, and Remark 4.22(a). James S. Milne is the verified sole author of the entire notes. The year 2025 identifies version 4.01; the cover and version-history dates differ by one day, so no exact publication day is assigned.

Collection of sources; individual chapter authors and dates are recorded below.

Publisher: Mathematics LibreTexts (verified host; original book publisher not established).

Collection of sources; individual chapter authors and dates are recorded below.

Publisher: Terence Tao, What's new (author website).

By A. F. Andersen. Published in Mathematisk-fysiske Meddelelser, volume I, number 4, Det Kgl. Danske Videnskabernes Selskab. The scanned title page names the author and gives Copenhagen and 1918.

Online text: gymarkiv.sdu.dk/MFM/kdvs/mfm%201-9/mfm-1-4.pdf

Cited passages: §1, printed p. 3, introduces orders of Cesàro summation and cites Ernesto Cesàro's 1890 publication in Bulletin des Sciences Mathématiques, series 2, volume 14, p. 114; §2, pp. 6–7, discusses the multiplication theorem and its role in developing summability theory. The original 1890 paper was not inspected here; the historical citation refers to Andersen's account.

By Vladimir Dobrushkin. An authored tutorial page for the second course, Part V, hosted at Brown University. No dated publication edition is specified here.

Online text: www.cfm.brown.edu/people/dobrush/am34/Mathematica/ch5/cesaro.html

Cited passages: the Cesàro-summation definition gives both zero-based and one-based partial-sum conventions; Example 1 discusses Grandi's series; Example 2 obtains the weighted geometric-series formula. Our finite examples and images are independently computed.

By Jiří Lebl.

By Jiří Lebl.

Publisher: MIT OpenCourseWare.

By Hubert W. Lilliefors.

Publisher: Taylor & Francis (current publisher platform).

Published in Journal of the American Statistical Association, volume 62, issue 318, pp. 399-402.

Online text: doi.org/10.1080/01621459.1967.10482916

Cited passages: Printed pp. 399-400: opening procedure and Table 1 of the original article; inspected mirrored text.

Publisher: R Project documentation, hosted by ETH Zurich.

Online text: stat.ethz.ch/R-manual/R-devel/library/stats/html/ks.test.html

Cited passages: Details, numeric second sample and two-sample ties; Source, exact and randomization distributions; Details: one-sample ties and rounding; numeric second sample; final paragraph on prespecified parameters.

Publisher: National Institute of Standards and Technology.

Section 1.3.6.6.11, Gamma Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda366b.htm gives density, shape/scale conventions and the gamma-function integral. Section 1.3.6.6.9, Lognormal Distribution: www.itl.nist.gov/div898/handbook/eda/section3/eda3669.htm defines the logarithmic-normal parameterization and gives mean, standard deviation and coefficient of variation. These conventions support the original inverse-moment derivations in the thickness-model article.

Section 7.2.4.1, Confidence intervals: www.itl.nist.gov/div898/handbook/prc/section2/prc241.htm . The subsections One-sided confidence intervals and Exact Intervals for Small Numbers of Failures explain one-sided limits and binomial-tail inversion. Inverting the extreme probabilities gives an upper event-probability bound one minus alpha raised to the power one over n for zero events, and a lower detection-probability bound beta raised to the power one over m for all-success calibration. The joint-coverage and rare-event examples are original derivations, not NIST experimental data.

Section 7.4.7.3, Bonferroni’s method, www.itl.nist.gov/div898/handbook/prc/section4/prc473.htm : simultaneously valid statements are obtained by dividing the allowed error probability among comparisons. This supplies the finite-candidate coverage principle used in the confidence-allocation article; the uniform-location counterexample there is an original construction.