By Haynes Miller, explicitly credited for the supplementary-note collection on the MIT OpenCourseWare readings page. The collection accompanies Differential Equations, MIT 18.03, Spring 2010. This course context does not establish a note publication date. MIT OpenCourseWare hosts the collection.

Collection attribution: ocw.mit.edu/courses/18-03-differential-equations-spring-2010/pages/readings/supp_notes/

By Dan Romik. The complete lecture-note collection is credited to him on its title page. The author note identifies Math 205A: Complex Analysis I at the University of California, Davis, in 2016 and 2018. These are course offerings. The front matter identifies the document version as 20 April 2018. Authors of the textbook followed by the course are not coauthors of these notes.

Online text: math.ucdavis.edu/~romik/data/uploads/teaching/math205a-2018/complex-analysis-2018.pdf

Cited passages: §9, items 81–82, printed p. 32, reciprocal-coordinate definitions at infinity; §9, item 84, printed p. 33, topological one-point compactification. The apparent inconsistent sphere equation in item 84 was not used.

Massachusetts Institute of Technology course, Spring 2018. Course instructor: Jeremy Orloff. MIT OpenCourseWare hosts the course notes; resource authorship is recorded separately from the instructor role.

By Bradley Efron, credited as B. Efron in the Stanford Department of Statistics catalogue. Technical report BIO 32, dated July 1977. This report record is distinct from the 1979 journal article. Stanford University issues and hosts the catalogue record.

Catalogue record: statistics.stanford.edu/technical-reports/bootstrap-methods-another-look-jackknife

Inspected locator: Report Number BIO 32; Author(s) B. Efron; Report Date Jul 1977. Only catalogue metadata was inspected; the linked technical report body was inaccessible.

By Bradley Efron, credited as B. Efron on the inspected bibliographic cover. Published in The Annals of Statistics 7(1), 1–26, January 1979. The University of Helsinki hosts the scanned copy. The access date and hosting path are distinct from publication.

Hosted copy: blogs.helsinki.fi/bk-club/files/2012/05/Efron_Bootstrap_AS1979.pdf

Inspected locator: bibliographic cover, author, title, journal volume and issue, January 1979 and page range. Only the cover metadata was inspected; neither the article body nor abstract was inspected.

University of Washington course identified by the inspected lecture heading as Autumn 2026. The course term is distinct from a lecture publication date; the URL directory 25A does not establish the term.

University of California, Berkeley course, Fall 2009. Course instructor: James Demmel, verified by his faculty homepage. This association does not establish authorship of every course resource.

Instructor and course listing: people.eecs.berkeley.edu/~demmel/

By Daniel Reem. The inspected source is arXiv:1002.3721v7, revised 8 February 2017. The first arXiv submission was 19 February 2010; this is distinct from the version 7 revision date. arXiv is the repository host.

Version metadata: arxiv.org/abs/1002.3721v7

Online text: arxiv.org/pdf/1002.3721v7

Cited passages: printed pp. 1–2, §1.1, equation (1), real domain and classical regularity criteria. Theorem 2.1 has a different measurability hypothesis.

By Václav Šimerka. Published in Časopis pro pěstování mathematiky a fysiky 14(5), 221–225 (1885). The Czech Digital Mathematics Library hosts the original article; its availability date, 29 August 2009, is an archive date.

Archive metadata: www.dml.cz/handle/10338.dmlcz/122245?show=full

Online text: dml.cz/bitstream/handle/10338.dmlcz/122245/CasPestMatFys_014-1885-5_3.pdf

Cited passage: printed p. 224, §9, numerical list and factorizations.

By Keith Conrad. Standalone expository notes hosted on the author's University of Connecticut website. The inspected title page is undated; no publication year is established.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/carmichaelkorselt.pdf

Cited passages: printed p. 1, Definition 1; printed p. 2, Theorem 2 and its proof; printed p. 3, Corollary 4 and its proof.

The citation panel credits Jay Abramson as author. The preface identifies him as lead author and senior contributing author, and lists a contributing team without assigning individual chapters. OpenStax publishes and hosts the book.

Whole-book publication: 21 December 2021, as given by the citation panel. The ©2026 footer is distinct from that publication date; no section revision dates are established.

Publisher: openstax.org/details/books/precalculus-2e

Author-role metadata: About the Authors, Senior Contributing Author and Contributing Authors; citation information

Online text: crypto.stanford.edu/pbc/notes/numbertheory/qr.html

By Ben Lynn. Stanford hosts the author's PBC Notes; it is not an institutional author. The inspected page is undated.

Cited passages: “Quadratic Residues”, opening definition and Euler criterion discussion; “The Legendre Symbol”, three values, odd-prime restriction, multiplication and square factors. The opening square-residue convention includes zero.

Online text: kconrad.math.uconn.edu/blurbs/ugradnumthy/QuadraticResiduePatterns.pdf

By Keith Conrad. These standalone notes are hosted on the author's University of Connecticut website. No document date is established.

Cited passages: printed p. 1, title/byline and §1 opening paragraph: nonzero convention and equal counts of squares and nonsquares; printed p. 2, §2 opening notation for the Legendre symbol.

Annealing uses controlled heating and cooling to change a solid's internal structure and properties. Its outcome depends on the temperature, duration and cooling history.

Sputtering ejects surface chemical atoms from a solid through bombardment by energetic incident particles, often ions.

Sintering joins particles into a coherent solid by heating, sometimes with applied pressure, without completely melting the material. It is used to consolidate powders of ceramics and metals.

A ceramic is an inorganic, nonmetallic solid, often formed by heating and cooling. Ceramics may contain several chemical compounds and need not have a single crystal structure.

Epitaxy is growth of a crystalline layer with an orientation relationship to a crystalline substrate. Homoepitaxy uses the same material; heteroepitaxy uses a different one. A substrate can guide atomic ordering, but a mismatch of lattice parameters introduces strain and can eventually produce misfit dislocations. Thus an apparently flat film need not be strain-free or defect-free. Molecular beam epitaxy controls incident material fluxes in vacuum, while other epitaxial methods use reactive vapors or liquids. The orientation relationship, layer thickness and strain state are distinct parts of the description.

Crystal growth adds atoms, ions or molecules to an ordered crystal structure from a melt, solution or vapor. Growth competes with nucleation: a seed can favor one growing crystal, whereas many independent nuclei can produce a polycrystalline solid. Temperature and concentration gradients control transport to the interface, while interfacial attachment determines how arriving species join the lattice. A flat interface is not guaranteed; instabilities can create cellular or dendritic shapes. Epitaxy is the special case where a substrate guides the orientation of the growing crystalline layer.

Atomic force microscopy maps surfaces and measures small interactions using a sharp tip attached to a compliant cantilever. In a common modern readout, a laser reflects from the cantilever onto a split photodetector, turning bending into an electrical signal. A scanner moves the tip relative to the sample; feedback can adjust height to maintain a chosen interaction signal. With calibrated stiffness $k$, a small static deflection $\delta$ gives force $F\approx k\delta$. The measured image combines surface geometry, tip geometry and interaction physics, so narrow features can appear broadened. Gerd Binnig, Calvin Quate and Christoph Gerber introduced the instrument in 1986.^[ref] Modern force measurements additionally require calibrated cantilever stiffness.^[ref]