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Electroluminescence is nonthermal light emission driven by electrical excitation. In a light-emitting diode, injected electrons and holes can undergo radiative electron-hole recombination, converting part of the supplied electrical energy into photons.

The emitted optical spectrum depends on the available transitions rather than solely on temperature, unlike an ideal blackbody. Measuring both the electric current and emitted radiant power tests conversion efficiency. Increasing electric current need not increase useful emission proportionally: nonradiative recombination, heating and extraction losses can all matter.

An RC low-pass filter places a resistor $R>0$ between input and output, with a capacitor $C>0$ from output to their common return. The ideal model prescribes the input electric potential difference and leaves the output unloaded. It is a first-order low-pass filter with unit eventual gain.^[ref]

For electrical resistance $R$ and capacitance $C$, Ohm's law gives the electric current through the resistor as $(v_{\mathrm{in}}-v_{\mathrm{out}})/R$. The capacitor relation gives $Cd{v}_{\mathrm{out}}/dt$. Equating them by Kirchhoff's current law yields the ordinary differential equationThe time constant $\tau$ has units of time. A rapid change in electric potential difference requires a large electric current into the capacitor; the finite electrical resistance limits that rate. A slowly maintained voltage instead lets the capacitor approach the input voltage. The same equation therefore predicts both smoothing of sustained oscillations and a rounded response to a sudden change.

For the original constructed example throughout this article, takeThese stipulated ideal values specify an analytical model, rather than measurements of particular components.

An RL circuit with the output measured across its resistor is a first-order low-pass filter. For an ideal inductor, an ideal voltage source and a high-resistance output instrument, the electrical impedances $i\omega L$ and $R$ giveThe gain approaches one at low angular frequency and $R/(\omega L)$ at high angular frequency; at ${\omega }_c$ it is $1/\sqrt{2}$. The time-domain equation is $L\dot{I}+RI=V_{\mathrm{in}}$ and $V_{\mathrm{out}}=RI$, so the time constant is $L/R$. Instrument loading, source resistance and nonideal inductance can change the response.

Suppose standard collinear boosts have the Lorentz transformation form, but initially assign speed scales $a$ and $b$ to two successive transformations with relative velocities $v$ and $u$. Their composition has spatial and temporal diagonal factors proportional to $1+uv/a^2$ and $1+uv/b^2$, respectively. Closure within the same calibrated transformation family requires these factors to agree, forcing $a^2=b^2$ for generic nonzero boosts.

This argument fixes a universal reciprocal squared speed; it does not establish that it is nonzero. The common limit $1/a^2=0$ gives the consistent Galilean transformation family. A finite invariant speed of light is an additional empirical property of spacetime and electromagnetism, expressed by the second of the postulates of special relativity. It cannot be deduced by excluding the Galilean limit through boost composition alone.

A decreasing measure used to prove algorithm termination. A nonnegative integer loop variant must strictly decrease after every completed body whose condition was true; the body itself must terminate.^[ref]

The prefix maximum correctness example uses $V=n-k$. It counts unread entries and is independent of whether the new entry changes the maximum. Ties therefore cannot stall progress: $k$ increases even when $\mathrm{best}$ stays the same. An integer bounded below cannot strictly decrease indefinitely, which supplies the missing algorithm termination argument.

Strict decrease and a lower bound are insufficient for arbitrary real numbers. The positive sequence $1,1/2,1/4,\dots$ strictly decreases and is bounded below by zero, but never reaches zero. Choosing an integer measure avoids this failure.

David Howells is a software engineer who has contributed technical documentation for the Linux kernel. With Paul E. McKenney, he authored a guide to circular buffers, including the interaction between index arithmetic and synchronization.^[ref]

Their example separates the producer's insertion index from the consumer's removal index. With one producer and one consumer, memory barriers publish initialized data before an index advertises it as available. This illustrates why a correct data structure needs both an indexing convention and an account of what concurrent operations can observe.^[ref]

A researcher who coauthored methods for functional assessment of isolated mitochondria, relating respiration measurements to preparation yield and integrity.^[ref]

A physiologist who coauthored intracellular recordings of action potentials in giant axons. Recording inside the axon against an external reference showed the membrane potential during excitation rather than only the external electrical signal.^[ref]

A physiologist who studied membrane potentials and action potentials.

Institutional biography: www.physoc.org/blog/prize-lecture-memoria-andrew-huxley/

A physiologist who coauthored intracellular recordings of action potentials in giant axons. Recording inside the axon against an external reference showed the membrane potential during excitation rather than only the external electrical signal.^[ref]

A physiologist who studied membrane potentials and action potentials.

Institutional biography: www.physoc.org/blog/prize-lecture-memoria-alan-hodgkin/

A researcher who coauthored high-speed measurements resolving rotational substeps of F1-ATPase. The experiment connected molecular motion with steps in an enzyme’s catalytic cycle rather than treating rotation as a smooth average.^[ref]

Molecular biologist studying transport of proteins across membranes. With Günter Blobel, Dobberstein reconstructed steps of the secretory pathway, connecting information in a nascent polypeptide with membrane-associated targeting.^[ref]

Microbiologist studying bacterial genome maintenance. Stewart and collaborators compared maintenance functions of linear and circular plasmids in Borrelia burgdorferi, testing how different DNA structures can share inheritance mechanisms.^[ref]

Researcher in microbial genetics. With Joshua Lederberg, Lederberg coauthored the replica-plating study, which preserved colony patterns across growth conditions to distinguish pre-existing mutants from changes caused by selection.^[ref]

A mechanical engineer whose work connected gas lighting to automatic operation. Chalmers records his mechanical-engineering qualification in 1896.^[ref] After an accident left him blind in 1912, he returned to AGA in 1913 and continued leading the company.^[ref]

The sun valve links radiometric absorptance, thermal expansion and mechanical motion to a useful decision: whether a beacon should receive its main gas supply. The Dalén light combines this daylight response with repeated flashes. The Nobel Prize in Physics in 1912 recognized his automatic regulators for lighthouse and buoy lighting.