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For a current dipole in a homogeneous insulating sphere of radius $a$, let $\lambda =r^2/a^2$ and let $\Psi$ be its primary electric potential. The displayed representation solves the interior Neumann boundary condition up to an additive constant. It rewrites the spherical Kelvin transform correction and a distributed dipole correction using the dipole line-integral identity. The image parameters depend on the observation radius; this is an exact parametrized representation rather than a fixed collection of image source positions.

Cellular respiration transfers energy from chemical fuels into usable forms including ATP. Plants carry out cellular respiration as well as photosynthesis; in its aerobic form, cellular respiration consumes molecular oxygen and releases carbon dioxide. See OpenStax Biology 2e, 8.3: energy flow.

Carbon fixation incorporates carbon from carbon dioxide into organic chemical compounds. It identifies a material transformation, rather than a particular source of energy: carbon fixation can be supported by photosynthesis or by other metabolism. The Calvin cycle is one pathway, not the definition of all carbon fixation.

Gluconeogenesis synthesizes glucose from non-carbohydrate precursors. It is distinct from glycogenolysis, which mobilizes an existing glycogen store.

Glycogenesis builds glycogen; glycogenolysis breaks it down. Their opposing directions matter in the insulin and glucagon circuit.

Glycogen is a highly branched polysaccharide of glucose units, serving as a storage form of glucose in animals. Liver and muscle provide familiar examples. The classical second messenger experiments measured regulation of an enzyme involved in glycogen breakdown, glycogen phosphorylase. ^[ref]

In its biochemical sense, fermentation is metabolism that obtains ATP from breakdown of organic substrates without a respiratory electron transport chain. The alcoholic route is one example; not every fermentation produces ethanol. See Clark, Douglas and Choi, Biology 2e, 7.5: fermentation versus anaerobic respiration.

Ethanol is the chemical compound produced by the alcoholic fermentation described under Saccharomyces cerevisiae. Its two carbon chemical atoms explain the product bookkeeping there. See NIST Chemistry WebBook: ethanol formula and identity; the Biology 2e section cited under Saccharomyces cerevisiae identifies ethanol as the alcohol product.

A psychoactive drug is a substance that changes mental activity, mood or perception. In population causal inference, its per-user adverse-event risk and its total population harm are distinct: the latter also depends on how many people use it, for how long, and on substitution between substances.

Isolation separates recognized infected or ill individuals from susceptible contacts to limit transmission. Quarantine instead concerns exposed individuals who may or may not be infected.

In infection modelling, immunity is protection against infection or disease, with its strength and duration represented by the chosen host states. A SIR model has a permanently protected recovered state, whereas a SIS model has no lasting post-recovery protection.

An infection involves invasion and multiplication of an infectious agent in a host. Bacteria are one possible cause; an agent capable of causing disease is a pathogen. The National Cancer Institute defines infection through invasion and growth in the body. ^[ref].

In a SIR model, acquiring infection moves a member of the susceptible compartment into the infectious compartment. That immediate transition is a model assumption: the SEIR model instead includes an exposed stage before infectiousness. Specify these states when translating a biological process into compartmental models.

Online text: loss.math.gatech.edu/16FALLTEA/NOTES/weierstrassbernstein.pdf

Cited passages: The Weierstrass approximation theorem, Lemmas 0.1–0.2 and Theorem 0.3, printed pp. 1–2: weights, binomial moments and polynomial construction; The Weierstrass approximation theorem, Theorem 0.3, printed p. 2: uniform polynomial approximation on the unit interval.

Online text: www.arponr.com/files/f24-18.901/notes.pdf

Course offering: Fall 2024. Arpon Raksit is the verified instructor and personal-site host; the PDF has no named byline. The course page records a December 6 update, rather than a publication date.

Cited passages: Lecture 12, Exercise 12.1.2(1)-(2), printed page 43: box basis, comparison with the product topology, and finite-factor equality; Lecture 5, Proposition 5.3.2, printed page 21: continuity into a product is equivalent to continuity of all component functions.

Publisher: Trinity College Dublin (archive host).

Online text: www.maths.tcd.ie/pub/HistMath/People/Hamilton/Icosian/

Cited passages: The Icosian Calculus, Hamilton papers archive: opening historical introduction and quoted report of the 1857 British Association presentation: dodecahedron projection and ivory pins.

By George B. Dantzig, Delbert Ray Fulkerson, Selmer M. Johnson.

Publisher: Operations Research Society of America (original); INFORMS (current archive).

Published in Journal of the Operations Research Society of America 2(4), pp. 393–410.

Online text: pubsonline.informs.org/doi/abs/10.1287/opre.2.4.393?journalCode=jors

Cited passages: Solution of a Large-Scale Traveling-Salesman Problem by G. Dantzig, R. Fulkerson and S. Johnson, abstract; Journal of the Operations Research Society of America 2(4), pp. 393–410 (1954).

By Peter J. Huber.

Publisher: Institute of Mathematical Statistics.

Published in The Annals of Mathematical Statistics, volume 35, number 1, pp. 73-101.

Online text: doi.org/10.1214/aoms/1177703732

Cited passages: Peter J. Huber, Robust Estimation of a Location Parameter, §11, pp. 95-96: estimating location when normal-component scale and contamination fraction are unknown; Peter J. Huber, Robust Estimation of a Location Parameter, §3, p. 78: derivative normalization; §4(iii), p. 79: clipped location criterion and central-mass denominator.

By Frank R. Hampel.

Publisher: Taylor & Francis on behalf of the American Statistical Association (mirror wrapper metadata).

Published in Journal of the American Statistical Association, volume 69, number 346, pp. 383-393.

Online text: doi.org/10.1080/01621459.1974.10482962

Cited passages: Frank R. Hampel, The Influence Curve and Its Role in Robust Estimation, p. 383, §2: pointwise right-limit definition along mixtures with a point mass; Frank R. Hampel, The Influence Curve and Its Role in Robust Estimation, §4, p. 386: exact asymptotic curve supplemented by behavior at other distributions, especially empirical ones.