A DNA ladder contains DNA fragments of known lengths in base pairs. Its gel bands supply size references. Match the sample's strandedness and shape, and use the specified lengths for that DNA ladder. A size reference need not provide a quantitative mass standard.^[ref]

In 1918, Irving Langmuir measured adsorption using freshly split mica strips, handled at their edges, separated by iron spacers and held with brass fasteners. A glass bulb contained the bundle; a similar blank contained matching iron and brass but no mica. Evacuated glass connections, Mercury seals, liquid air traps, and McLeod gauges provided controlled gas handling. Calibrated compartment volumes and pressure readings before and after expansion gave free-gas amounts; their deficit indicated uptake. Lowering pressure and measuring released gas tested desorption.^[ref]

Hydrogen blank runs calibrated cooling-related pressure differences. Irving Langmuir pre-cooled the bulbs to reduce thermal delay; he suggested slow diffusion between strips could control the remaining approach to equilibrium. Critically, blank uptake was not subtracted: he estimated the mica-bulb results were 10–30% too high. Liquid air temperature drift was unrecorded. These limits constrain inference of intrinsic binding from the uptake curve. The paper's pressure unit called “bar” was $1\mathrm{dyn}\mathrm{c}{\mathrm{m}}^{-2}=0.1\mathrm{Pa}$, unlike the modern bar used above.^[ref]

An adsorption isotherm relates equilibrium uptake to surrounding pressure or concentration at fixed temperature. For a gas, specify the partial pressure of the adsorbing chemical species. An uptake trace during incomplete equilibration need not be an adsorption isotherm.

Desorption releases material previously retained at a boundary. At chemical equilibrium, adsorption and desorption can both continue while their mean rates balance.

A monolayer is a single layer of chemical atoms or molecules. In the Langmuir adsorption model, a complete monolayer occupies every adsorption site; partial surface coverage leaves vacancies within that first layer. One layer need not mean one molecule per surface chemical atom.

An adsorption site is a position or local environment at which a chemical species can be retained at a boundary. Treating all adsorption sites as identical is an assumption about their binding properties, not a definition of adsorption.

The interfacial excess of a species relative to bulk reference phases extrapolated up to a chosen reference surface. An excess number density per area is denoted $\Gamma$; its molar counterpart is $\Gamma /N_A$. When an interface is dominated by a molecular layer, an effective area per adsorbed molecule is $\Sigma =1/\Gamma$. The reference-surface convention matters in multicomponent systems.

An acetyl group is the acyl unit $\mathrm{C}{\mathrm{H}}_3\mathrm{CO}-$. Its point of attachment lies at the carbonyl carbon, distinguishing it from an ethyl group or an acetate ion.

Transfer of an acetyl group changes a substrate's covalent structure. In biology, acetyl-CoA can supply such units, while acetylation of an amino group can alter charge and molecular recognition.

A loudspeaker converts an electrical signal into motion that drives acoustic waves. In a moving-coil design, electric current through a coil in a magnetic field produces a force on the attached diaphragm. The diaphragm displaces air, creating sound pressure variations.

A small coil, magnet and lightweight cup can demonstrate the conversion directly. ^[ref] In an idealized uniform-field geometry, the driving force scales as $B\ell I$. The emitted sound also depends on diaphragm inertia, suspension spring constant, damping and acoustic impedance, so the electrical waveform alone does not specify a flat acoustic frequency response.

In gallium nitride, incorporated hydrogen can neutralize magnesium acceptor impurities. Activation treatments restore electrical activity; adding magnesium alone does not establish a mobile electron hole population.

Chapter of Abstract Algebra by Romyar Sharifi, with the same Romyar Sharifi byline; no distinct contributed chapter author is established.

Online text: math.ucla.edu/~sharifi/notes/algebra-ch03.html

Cited passages: §3.9, Theorem 3.9.1 and proof, polynomial division when the leading coefficient is a unit; Proposition 3.9.7 and proof, the factor theorem. No publication date is inferred from the URL.

Unsigned lecture notes issued by Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. No individual author byline or PDF publication or revision date is established.

Lecture notes: ocw.mit.edu/courses/6-046j-design-and-analysis-of-algorithms-spring-2015/ff2a7015ff913fc01f0381d8f5126a9a_MIT6_046JS15_lec01.pdf

Cited passages: printed p. 2, Interval Scheduling and non-strict compatibility inequalities; printed pp. 3–4, Claim 2 and induction; printed pp. 4–5, Weighted Interval Scheduling and Dynamic Programming; PDF p. 6, institutional course footer.

Unsigned lecture notes in 6.006 Introduction to Algorithms, Fall 2011 by Massachusetts Institute of Technology, 6.006 course staff. Issued by the Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. No individual author byline is established. Fall 2011 identifies the course offering; no separate publication or revision date is established.

Lecture notes: ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/1b9e9f79b1c1012cfc1fa22c37b8e129_MIT6_006F11_lec11.pdf

Cited passages: Printed p. 4: High Precision Multiplication, high and low blocks, four products and branching factors; Printed p. 5: three-product identity, linear overhead and ideal recurrence; Printed p. 1: title and course term; final PDF page: MIT OpenCourseWare institutional course footer; PDF p. 5 visually inspected through browser screenshot tool.

Unsigned lecture notes in 6.006 Introduction to Algorithms, Fall 2011 by Massachusetts Institute of Technology, 6.006 course staff. Issued by the Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. No individual author byline is established. Fall 2011 identifies the course offering; no separate publication or revision date is established.

Lecture notes: ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/90a37c49b07b105ea7a027abc67eddc6_MIT6_006F11_lec03.pdf

Cited passages: Slide 18: Meet Merge Sort; slide 31: linear merging; Slides 32–44: balanced recurrence, levels, leaves and equal work per level; Slide 46: quadratic local-work recurrence; Final PDF page: MIT OpenCourseWare, 6.006 Introduction to Algorithms, Fall 2011.

Unsigned lecture notes in 6.006 Introduction to Algorithms, Fall 2011 by Massachusetts Institute of Technology, 6.006 course staff, issued by the Massachusetts Institute of Technology and hosted by MIT OpenCourseWare. No individual author byline is established. Fall 2011 identifies the course offering; no separate publication or revision date is established.

Lecture notes: ocw.mit.edu/courses/6-006-introduction-to-algorithms-fall-2011/3484e876d81aba07911a1109f5b5e81e_MIT6_006F11_lec21.pdf

Cited passages: Printed p. 1: lecture header and dynamic programming review; Printed p. 2: Parenthesization, outermost split, substring state, recurrence, one-matrix zero base case, increasing substring size, cubic time and parent pointers; PDF p. 6: MIT OpenCourseWare course and Fall 2011 footer.