A computer bus whose communication resources serve multiple attached components. A common physical path reduces wiring, but competing bus transactions must share its capacity. Address bus, data bus and control bus name logical roles; they need not be three permanently separate bundles of wires. Some designs reuse lines for addresses and data in different phases.^[ref]

For pairwise comaximal ideals in a commutative ring, reduction has the displayed ring isomorphism. The kernel is their intersection, equal to their product. Choose $e_i\in {\prod }_{j\ne i}{I}_j$ with $e_i\equiv 1(\mathrm{mod}{I}_i)$; then ${\sum }_i{a}_i{e}_i$ lifts any prescribed residue tuple. The equality between intersection and product follows from $1=u+v$, $u\in I$, $v\in J$, which writes each $x\in I\cap J$ as $xu+xv\in IJ$.

For positive integer moduli $m,n$, the simultaneous integer congruences $x\equiv a(\mathrm{mod}m)$ and $x\equiv b(\mathrm{mod}n)$ are solvable exactly when $a\equiv b(\mathrm{mod}\gcd (m,n))$. When solvable, they determine a unique congruence class modulo $\mathrm{lcm}(m,n)$. To see the condition, put $x=a+mk$: the remaining equation is the linear congruence $mk\equiv b-a(\mathrm{mod}n)$, which is solvable exactly when the greatest common divisor divides $b-a$.

For example, $x\equiv 1(\mathrm{mod}6)$ and $x\equiv 3(\mathrm{mod}8)$ give $6k\equiv 2(\mathrm{mod}8)$, hence $3k\equiv 1(\mathrm{mod}4)$ and $k\equiv 3(\mathrm{mod}4)$. Thus $x\equiv 19(\mathrm{mod}24)$. Changing the second remainder to two makes the conditions incompatible: the first requires an odd integer, while the second requires an even integer. Article 32 of Carl Friedrich Gauss's Disquisitiones arithmeticae gives a successive construction for simultaneous remainders, including the greatest common divisor and least common multiple that enter this general case. ^[ref]

Online text: homepage.physics.uiowa.edu/~fskiff/Physics_132/New%20Lab%20Manual/int_lab_man/pdfs/A4_ESR_v6.pdf

The document says Last Revised July 2007. No personal or institutional byline verified; the University of Iowa is the host.

Cited passages: Electron Spin Resonance, revised July 2007: printed pp. 4–7, sweep behavior, field mapping, local fitting and anomalous spikes.

By Shree Sowndarya S. V., Peter C. St. John, Robert S. Paton.

Publisher: Royal Society of Chemistry.

Published in Chemical Science, 12, 13158–13166.

Online text: pubs.rsc.org/en/content/articlehtml/2021/sc/d1sc02770k

Cited passages: A quantitative metric for organic radical stability and persistence using thermodynamic and kinetic features, Shree Sowndarya S. V., Peter C. St. John and Robert S. Paton, 2021: Abstract and Introduction, thermodynamic stabilization versus kinetic persistence.

By International Union of Pure and Applied Chemistry.

Publisher: International Union of Pure and Applied Chemistry.

This source is credited to an organization.

Published in Pure and Applied Chemistry, 66, 1077–1184.

Online text: iupac.qmul.ac.uk/gtpoc/R.html

Cited passages: Glossary of Terms Used in Physical Organic Chemistry, IUPAC Recommendations 1994: radical (or free radical), opening definition and metal-ion qualification; Glossary of Terms Used in Physical Organic Chemistry, IUPAC Recommendations 1994: radical ion, benzene examples and dot/charge placement.

By Nasima Arshad.

Publisher: Allama Iqbal Open University.

Online text: online.aiou.edu.pk/LIVE_SITE/SoftBooks/2569.pdf

Cited passages: Unit 7, Experiment 1, printed pp. 62–63: reaction, ionic conductances, inverse resistance, platinum electrodes and alternating-voltage bridge; Experiment 2, p. 66: hydroxide replaced by acetate; Unit 7, Experiment 2, printed pp. 66–67: Procedure and Calculations; title page credits Nasima Arshad as manual author.

Additional cited passages: Unit 7, Experiment 1, printed p. 63 (PDF p. 67), platinum electrodes and alternating-voltage Wheatstone bridge; Experiment 2, printed pp. 66–67 (PDF pp. 70–71), temperature equilibration, rinsing, mixing and timed resistance readings, NaOH–water initial-signal comparison and KCl cell calibration. The title page identifies Nasima Arshad as whole-manual author; the introduction states the separate Course Development Coordinator role. Allama Iqbal Open University is issuer and host. No publication year is established.

By International Union of Pure and Applied Chemistry.

Publisher: International Union of Pure and Applied Chemistry.

This source is credited to an organization.

Online text: iupac.qmul.ac.uk/gtpoc/NO.html

Cited passages: Glossary of Terms Used in Physical Organic Chemistry, IUPAC Recommendations 1994, entry “order of reaction”, final paragraphs: elementary versus stepwise reactions; Glossary of Terms Used in Physical Organic Chemistry, IUPAC Recommendations 1994, entry “order of reaction”: constant B, observed coefficient and pseudo-first-order coefficient.

By International Union of Pure and Applied Chemistry.

Publisher: International Union of Pure and Applied Chemistry.

This source is credited to an organization.

Online text: iupac.qmul.ac.uk/gtpoc/M.html

Cited passages: Glossary of Terms Used in Physical Organic Chemistry, IUPAC Recommendations 1994, entry “molecularity”: elementary event and exclusion of solvation medium.

Publisher: Amrita Vishwa Vidyapeetham Virtual Lab.

By IUPAC-IUB Joint Commission on Biochemical Nomenclature.

Publisher: IUPAC and IUB; web version hosted by Queen Mary University of London.

This source is credited to an organization.

Online text: iupac.qmul.ac.uk/AminoAcid/AA1n2.html

Online text: iupac.qmul.ac.uk/AminoAcid/AA3t5.html

Cited passages: 3AA-1, Table 1 and its note on hypothetical uncharged formulas; 3AA-2.2.1, acyclic-amino-acid numbering; 3AA-1, Table 1: alpha-amino acids incorporated into protein under mRNA direction; 3AA-1, Table 1: glycine, alanine and proline structures; 3AA-2.2.5, backbone and side chain.

Cited passages: 3AA-3.2, note: glycine itself is achiral; 3AA-3.3 and 3AA-3.5, protein-source L configuration.

Publisher: Royal Society of Chemistry.

Online text: edu.rsc.org/download?ac=500795

Cited passages: Iron Tablet Determination Analytical Competition, “Setting the Scene”: both half-reactions and the overall equation; “Setting the Scene”, final two paragraphs: burette, conical flask, decolourisation, endpoint and excess sulfuric acid.

By Pavel Karen, Patrick McArdle, Josef Takats.

Publisher: De Gruyter.

Published in Pure and Applied Chemistry.

Online text: www.cup.lmu.de/ac/kluefers/homepage/L/kc2/literature/iupac_oxidation_state_2016.pdf

Cited passages: Karen, McArdle and Takats, Comprehensive definition of oxidation state (IUPAC Recommendations 2016), §2, pp. 832–833: definition and equal splitting of same-element bonds; §3 and §4.1, pp. 833–834: Allen electronegativity, electron allegiance and the reversible Lewis-acid-ligand caveat; §5.5, pp. 836–837: ambiguous assignments.

By Anna M. Michałowska-Kaczmarczyk, Tadeusz Michałowski.

Publisher: Springer.

Published in Journal of Solution Chemistry.

Online text: link.springer.com/article/10.1007/s10953-015-0342-0

Cited passages: §2, Definition of Dynamic Buffer Capacity, equations (1)–(3): reagent concentration in the combined volume and its derivative.

By Jaime Maldonado-Estudillo, Rodrigo Navarro Crespo, Ángel Marcos-Fernández, María Dolores de Dios Caputto, Gustavo Cruz-Jiménez, José E. Báez.

Publisher: MDPI.

Published in Polymers 17(5), article 668.

Online text: www.researchgate.net/publication/389435408_Experimental_Design_2_to_Improve_the_Reaction_Conditions_of_Non-Segmented_Polyester-urethanes_PEUs_Derived_from_ao-Hydroxy_Telechelic_Polye-caprolactone_HOPCLOH

Cited passages: sections 2.1 and 2.3: flask, heating apparatus and varied conditions; sections 3.2–3.3; Figure 3 discussion of the water comparison; section 5.1 and Figure 8: independent conversion and GPC readouts and low-signal limitation.

By Emilio Meaurio.

Publisher: Springer Nature.

Published in Scientific Reports 14, article 27281.

Online text: www.nature.com/articles/s41598-024-78476-2

Cited passages: Introduction, equations (1)–(6): Carothers equation, end-group count and limiting-$A$ conversion; Introduction, equations (2)–(6), especially the paragraph before equation (3): A is the limiting reactant used to define p.

By Liya Lu, Pan Jiang, Hong Gao.

Publisher: Elsevier B.V. on behalf of KeAi Communications Co. Ltd..

Published online 13 August 2022; print issue: Fundamental Research 5(1), pp. 151–157 (2025).

Online text: www.researchgate.net/publication/362682561_Accurate_measurements_of_the_bond_dissociation_energies_of_14N2_14N15N_and_15N2

Cited passages: Lu, Jiang and Gao, §2, printed manuscript pp. 2–3: nozzle, tube, pump/probe and imaging readout; §1: image-radius equation; §2: wavemeter and probe scan; §3 and Figure 4: fits; §4: atomic excitation correction; §2: shielding plate and timing; §3: state-selected channels; §4 and Table 2: isotope consistency and limitations.

By F. J. Lovas, D. R. Lide, Jr., R. D. Suenram, D. R. Johnson.

Publisher: National Institute of Standards and Technology.

Published in Journal of Research of the National Institute of Standards and Technology 117, 268–296.

Online text: tsapps.nist.gov/publication/get_pdf.cfm?pub_id=911001

PDF text accessible; screenshot request returned cache miss. Does not establish detailed pulse/readout electronics for the 2024 commercial instrument. No measured frequencies copied.

By Ann Adele Byars, Khushi R. Kompally, Emily Mechnick, Reilly E. Sonstrom, Alexander Mikhonin, Justin L. Neill, Ruth Boetzel, James MacGregor, Courtney Talicska, Jian Li, Yizhou Liu.

Publisher: American Chemical Society and University of Science and Technology of China.

Published in Precision Chemistry 2(2), 57–62.

Online text: pmc.ncbi.nlm.nih.gov/articles/PMC11504610/

By National Institute of Standards and Technology.

Publisher: National Institute of Standards and Technology.

This source is credited to an organization.