By Otto Rössler. Physics Letters A 57(5), pages 397–398.

Author-uploaded record: www.researchgate.net/publication/223112399_An_Equation_for_Continuous_Chaos

By Steven H. Strogatz. Physica D 143, pages 1–20.

Author-hosted text: pagine.dm.unipi.it/alberti/ricerca/1992-96/sbv.pdf

Bollettino Unione Matematica Italiana, SezioneB(7),11(1997),375–382. Consulted Theorem1.4 onPDFpage4, uniform BV bound, equiintegrable gradients and jump control for SBV compactness; the wiki gives a bounded-domain sufficient special case. PDF running pages are1–8 rather than the final journal pagination.

Author-hosted text: webee.technion.ac.il/Sites/People/YoninaEldar/files/Fourier_phase_retrieval_arxiv.pdf

Exact authors verified from title page. Consulted section3.1, printed p6, trivial global-phase, translation and conjugate-reflection ambiguities; introduction and sections2–3 distinguish single-magnitude measurements from masked/STFT/FROG data. No unverified journal or edition date asserted.

Publisher full text: annals.math.princeton.edu/wp-content/uploads/annals-v182-n1-p09-p.pdf

Archive: arxiv.org/abs/1403.5335

Annals of Mathematics182(2015),351–389. Consulted Theorem1.1, printed p352, and cap definition on pp351–352. For the parabola, set n=2 and delta=1/R; the supercritical loss is R raised to1/4 minus3/(2p), with an arbitrarily small additional exponent.

Original paper scan: www.ms.uky.edu/~hislop/papers/ray-singer1.pdf

Advances in Mathematics 7(2), pages 145–210. Definition 1.6, page 149, gives analytic torsion by spectral zeta derivatives; Section 2 proves metric independence for acyclic closed-manifold coefficients; Section 3 handles nonzero homology and boundary data. DOI: doi.org/10.1016/0001-8708(71)90045-4

The original prints D. B. Ray and I. M. Singer. Their first names Daniel Ray and Isadore Singer are explicitly identified in the opening of the author-hosted historical article math.berkeley.edu/~lott/torsion.pdf .

Author-hosted notes: sites.pitt.edu/~hajlasz/Notatki/Functional%20Analysis2.pdf

Consulted passage: Proposition8.3 and proof, printed pp75–76 (PDF pages75–76, zero-based74–75), showing that a smooth real function with some vanishing derivative at each point is a polynomial. The proof uses the Baire category theorem twice and the perfect closed complement of the locally polynomial locus.

Author-hosted notes: pages.cs.wisc.edu/~deboor/887/notes.pdf

Consulted passages: Kolmogorov criterion (47), printed p.29; B-spline definition/recurrence (84)–(86), printed pp.53–54; Marsden identity (93)–(94), printed p.57; Schoenberg operator definition (124), printed p.65; Schoenberg–Whitney theorem (131), printed p.67. The slash in the title is a literal course name; normalize it to a hyphen when writing a magic link.

Author text: arxiv.org/abs/1211.3404

Consulted passages: Definition 2.1.1 and Examples 2.1.2 (printed pp.5–7), Definition 2.1.7 (p.8), Definition 2.1.12 (p.11), Corollary 2.3.10 (p.33), sections 2.5 and 3.2 (holomorphic and continuous functional calculus), and sections 5.5–5.6 (Borel calculus and polar decomposition).

Author course overview: terrytao.wordpress.com/2008/01/08/254a-lecture-1-overview/

Lecture9, Ergodicity, dated4February2008: terrytao.wordpress.com/2008/02/04/254a-lecture-9-ergodicity/

Lecture8, The mean ergodic theorem, dated30January2008: terrytao.wordpress.com/2008/01/30/254a-lecture-8-the-mean-ergodic-theorem/

Cited passages: Lecture9, Theorem2 and Remark3, pointwise ergodic theorem and norm convergence; Theorem3, characterizations of ergodicity. This is the author's expository lecture series; new mathematical examples in the concept articles are calculated explicitly. Exercises and exams are not being solved.

Author-hosted text: www.mat.univie.ac.at/~gerald/ftp/book-schroe/schroe.pdf

Full subtitle: With Applications to Schrödinger Operators. Graduate Studies in Mathematics99. Consulted PDF title/copyright pages identify Gerald Teschl, first-edition2009, version12February2009; this is not the second-edition GSM157 linked in a later cover notice.

Cited passages: §1.3, Theorem1.8, printed p44, Riesz functional representation (source uses second-argument-linear convention); §4.1, Theorem4.3, printed p114, Stone formula and half endpoint weights.

Primary source: doi.org/10.1017/S0022112065000745

Publisher text: www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/general-approach-to-linear-and-nonlinear-dispersive-waves-using-a-lagrangian/0B2CF85E51FBB983969B30C94EF3C83C

Cited passage: abstract, general averaged variational formulation for slowly varying wave trains. The simple linear-wave example in the concept articles is derived explicitly there rather than attributed to an uninspected page of the paper.

Publisher author G. B. Whitham is verified as Gerald Beresford Whitham by the Caltech Library author authority: feeds.library.caltech.edu/people/Whitham-G-B/article.html . Original publication: Journal of Fluid Mechanics22(2), June1965, pp273–283. Cambridge online-posting date 28 March2006 is distinct from original journal publication.

Primary source: arxiv.org/abs/physics/0503066

Full text: arxiv.org/html/physics/0503066v3

Cited passages: §1, Theorems I–II and §2, divergence relationships and dependencies.

Consulted edition/version: original1918; English translation1971; consulted arXivv3,30May2018.

Emmy Noether original author, M.A.Tavel translator. Original Göttinger Nachrichten235–257; translation journal pages differ between abstract186–207 and fulltext183–207, so omit uncertain translation pagination.

Primary source: www.dpmms.cam.ac.uk/~adblg2/EllipticPDELent2026.pdf

Cited passages: §4.4, Corollary 4.19; §4.5, Proposition 4.20 and equations (4.25)–(4.27).

Consulted edition/version: 27 March 2026.

Primary source: www.math.ucdavis.edu/~hunter/pdes/ch4.pdf

Cited passages: Chapter 4, §§4.1, 4.5–4.7; Definition 4.16.

Additional author-hosted chapters used here:

Primary lectures: arxiv.org/abs/1903.08304

Full text: arxiv.org/pdf/1903.08304

Cited passages: Lecture 1, pp. 5–6, oriented-contour plus/minus sides, jump matrix and matrix boundary equation; Lecture 2, Cauchy operators and boundary values. The consulted version is arXiv version 1, 20 March 2019.

Author-hosted notes: www.math.lmu.de/~philip/publications/lectureNotes/philipPeter_FunctionalAnalysis.pdf

Originally prepared for the summer-semester 2017 LMU course; the consulted title page is dated 22 March 2024. Cited passages: sections 1.4–1.5, boundedness and seminorm/local convexity; section 3.1, Hahn-Banach separation. The existing topological-vector-space root already cites this primary text externally.

Primary preprint: arxiv.org/abs/cond-mat/0112414

Full text: arxiv.org/pdf/cond-mat/0112414

Cited passages: equations (1.4)–(1.5), lens transforms between free and harmonically trapped mass-critical NLS; Proposition 2.1, local solution and continuation statements. Coefficients are rescaled to the wiki convention with Laplacian coefficient one.

Author-hosted text: www.math.ucla.edu/~tao/preprints/chapter.pdf

Cited passages: Theorem 2.3, homogeneous and dual Schrödinger Strichartz estimates, including the excluded two-dimensional endpoint; sections 3.3–3.5, local theory, conservation laws and global existence; the source is an author-hosted book draft, so no edition/year is inferred from its URL.

Publisher record: annals.math.princeton.edu/1983/119-2/p05

Primary paper: www1.cmc.edu/pages/faculty/MONeill/Math%20138/papers138/Lieb.pdf

Annals of Mathematics 118, 349–374. The PDF byline spells Elliott with two t's. Cited passages: introduction and Theorem 1.1, exponent relation and bilinear Hardy-Littlewood-Sobolev inequality. The publisher URL contains 119, but the article record and PDF identify volume 118.