A calibration constraint allowing a small nonzero probability outside its principal range. It represents uncertainty but still needs biologically defensible tail probabilities.

Let $y^{\prime \prime }+{\omega }^{2}y=F(t)$ with $\omega >0$, zero initial displacement and velocity, and real-valued forcing with ${\int }_0^{\infty }|F(t)|dt<\infty$. The causal Green function gives $y(t)={\omega }^{-1}{\int }_0^{t}F(s)\sin [\omega (t-s)]ds$. Expanding the sine difference, the two coefficients tend to finite limits by absolute convergence. Thus $y(t)$ approaches a sinusoid whose amplitude is the displayed modulus of the one-sided Fourier transform, divided by $\omega$. The displacement error is at most ${\omega }^{-1}{\int }_t^{\infty }|F(s)|ds$, which tends to zero. This describes the surviving free oscillation after a transient force; an arbitrary nonzero initial oscillation must be added before taking the final amplitude.

For the convention $x=\mathrm{Im}(RF{e}^{i\omega t})$, viscous damping $b$ gives $R=[m({\omega }_0^2-{\omega }^2)+ib\omega {]}^{-1}$. Put $\delta =\omega -{\omega }_0$ and $\gamma =b/(2m)$. If both are small relative to ${\omega }_0$, the displayed approximation follows. Its squared modulus has half-width $\gamma$, and the displacement lags the force by $\pi /2$ at $\omega ={\omega }_0$.

The ratio of an evaporation cutoff to thermal energy. Keeping the cutoff fixed while lowering temperature increases this ratio and reduces population in the escaping tail.

For a classical three-dimensional harmonic trap of fixed frequencies, $E=3N{k}_{B}T$. If each lost atom removes mean energy ${ϵ}_{\mathrm{ev}}=(\eta +\kappa )k_{B}T$, differential energy balance gives $d\ln T/d\ln N=(\eta +\kappa -3)/3$. The result assumes rapid elastic equilibration and excludes separate work from changing trap frequencies.

A radiofrequency field induces transitions from trapped weak-field-seeking magnetic sublevels to untrapped states at a resonance surface. Atoms with sufficient energy reach that surface and leave. Sweeping the frequency changes the energy cutoff without equating every lost atom with the sample-average energy.

In the classical idealized parcel path, ascend dry adiabatically to condensation height $z_c$, continue at constant moist lapse rate ${\Gamma }_m$ to height $H>z_c$, lose condensate, then descend at dry lapse rate ${\Gamma }_d$ to the initial height. Adding the temperature changes gives the title. Complete condensate removal and an unsaturated descent are essential assumptions. A reversible dry ascent and descent with the same source air instead gives no net temperature increase at the same pressure.

Mountain blocking can prevent low-level upstream air from crossing the barrier while air from higher levels passes over and descends. In stable stratification that elevated source air has higher potential temperature; adiabatic descent can bring it into a lee valley warmer than the blocked low-level air. This source-air change permits a dry foehn without requiring condensation and rainout along the arriving parcel's path.

A product of number states with equal fixed populations in two modes. Its total particle number is $2N$. It differs from a pair of coherent states, whose number distributions fluctuate.

An orthonormal basis labelled by the occupations of specified single-particle modes. For one bosonic mode, $|n⟩=(a^{†}{)}^n|0⟩/\sqrt{n!}$ and the number operator has eigenvalue $n$. A coherent state's expansion in this basis gives its overlap and photon-number statistics.

The plane one focal length beyond a lens. In a paraxial imaging system, incident parallel rays of a given direction focus at one point in this plane; it is therefore an angular or diffraction plane distinct from a finite-distance object's image plane.

The thermal trace can be expanded in angular-momentum eigenstates or in lifted paths whose endpoints differ by $2\pi m$. A winding saddle is linear in imaginary time, and its flux weight is the Aharonov-Bohm phase $e^{2\pi ifm}$. The common fixed-endpoint fluctuation factor is $\sqrt{I/(2\pi {\hslash }^2\beta )}$; integrating the initial angle supplies $2\pi$. The Poisson summation formula converts the resulting winding Gaussian sum into the momentum sum with exactly cancelling prefactors. The Gaussian evaluation is exact for this free rotor.

fluorescence correlation spectroscopy analyzes fluctuations of detected fluorescence to infer quantities such as molecular number and movement through an observation volume. Photophysical fluctuations and background must be distinguished from transport.

fluorescence anisotropy measures the polarization dependence of emitted fluorescence after polarized excitation. It can constrain rotational freedom on the fluorescence-lifetime timescale, but probe orientation, lifetime and partitioning also affect the signal.

fluorescence recovery after photobleaching follows fluorescence return to a bleached region as unbleached labeled molecules redistribute. Recovery depends on geometry, transport, binding and immobile fractions; it is not a direct measurement of every aspect of membrane fluidity.

In fluorescence labeling, NBD denotes a nitrobenzoxadiazole fluorophore used in fluorescent derivatives, including labeled lipids. Its emission depends on local surroundings, so changing brightness can report an environmental change as well as a change in the number of labels.

For example, comparing a labeled lipid in aqueous solution and in a lipid bilayer requires accounting for different emission efficiencies. A fixed-illumination measurement of fluorescence alone is not an absolute concentration measurement unless that response is calibrated. ^[ref]

Fluorescence emitted by intrinsic sample components, which can contribute background in a labeled assay.

FITC is fluorescein isothiocyanate, a reactive derivative of fluorescein used to attach a fluorescent label to suitable targets. Its reactive group couples to accessible amino groups, so labeling a protein can make that protein observable by fluorescence microscopy or flow cytometry.

The label's presence is distinct from the specificity of the experiment. Unbound dye must be separated from the intended conjugate, and an unlabeled control estimates autofluorescence. Labeling can alter the target's behavior, while bleaching and environment-dependent emission affect measured intensity. ^[ref]

Spectroscopy measuring emitted light following excitation. Emission peak position and intensity can report changes of speciation, but concentration, excitation absorption and photochemical loss also influence the signal.

A molecule or material whose fluorescence changes when it binds a target ion.