The pattern of local and long-range base pairing within RNA. Pairing can hide a binding motif or an initiation region, making accessibility an experimentally testable regulatory variable.

A small regulatory RNA that guides an Argonaute-containing complex to target RNAs, influencing their stability or biological translation.

A small regulatory RNA can alter target-RNA translation or stability through base pairing or protein interactions. In bacteria, effects on initiation and RNA degradation should be separated experimentally with transcript and protein measurements.

An RNA pseudoknot forms when nucleotides in a loop pair with a region outside that loop, producing an interleaved pairing topology. Some pseudoknots resist ribosomal unwinding and contribute to programmed recoding.

The spatial distribution and directed or selective positioning of RNA within a cell or tissue.

A class of small noncoding RNA involved in nucleolar RNA processing and modification pathways. Some are generated from intronic sequences.

An RNA duplex formed by complementary strands or self-complementary segments. Purified duplex and single-strand controls distinguish a double-stranded trigger from a simple antisense effect in RNA interference.

Microrheology infers local mechanical response from microscopic probes embedded in a material. Active methods apply a calibrated force and measure displacement; passive microrheology uses thermal fluctuations. Probe size, boundary conditions at the probe, temporal resolution and material heterogeneity determine which continuum response can be inferred.

The yield stress is the stress threshold beyond which a material sustains irreversible flow under the specified loading conditions. Time-dependent materials require an operational measurement protocol; a single elastic modulus does not determine their yield stress.

Measurement of stress–deformation response using a calibrated rheometer. Geometry, temperature, sample history and possible wall slip must be controlled before interpreting a measured force or torque as a bulk constitutive response.

Assigning the origin and destination of atoms through a synthetic route. carbon counts and the positions of surviving carbonyls expose chain-length and ring-connectivity errors.

The cotangent kernel $\pi \cot (\pi z)$ has a simple pole of residue one at every integer. If a meromorphic $h$ is regular at the integers, these residues sample its integer values. Integrating around squares of half-side $N+1/2$ and applying the residue theorem converts a finite sum of samples into residues at the other poles. When the contour integral tends to zero and $h$ has only finitely many other poles, the limiting sum is the negative sum of those off-integer residues of $\pi \cot (\pi z)h(z)$. A uniform cotangent bound and sufficiently rapid decay of $h$ justify the vanishing contour term. At an integer where $h$ itself has a pole, use the full Laurent series to find the combined residue instead of substituting a divergent sample; the Basel problem calculation with $h(z)=z^{-2}$ illustrates this exception.

For $a,b>0$, integrate $(e^{iaz}-e^{ibz})/z^2$ over an upper semicircle with a small clockwise indentation excluding zero. The large arc vanishes; the small arc tends to $-i\pi$ times the residue $i(a-b)$, namely $\pi (a-b)$. The contour encloses no poles, so the remaining real-axis principal value is $\pi (b-a)$. Taking real parts gives the displayed ordinary integral, whose cancellation at zero removes its apparent singularity. Evenness of the cosine extends the formula to arbitrary real $a,b$, with zero frequencies obtained by a limit. The individual integrals of $\cos (ax)/x^2$ cannot be subtracted as separately convergent improper integrals.

A harmful interaction between alleles that evolved in separate lineages and are compatible with their own genetic backgrounds. For example, substitutions yielding $Ab$ and $aB$ can each be tolerated, while the combination $AB$ is harmful in a hybrid. This is a form of epistasis.

When one sex of first-generation hybrids is absent, rare or sterile, it tends to be the heterogametic sex. This predicts a sex bias within crosses, rather than a universal difference in isolation between birds and mammals.^[ref]

Greater divergence of mating signals or preferences in sympatry than outside contact. The pattern can follow reinforcement, but also ecological differences, sorting or interference without reduced hybrid fitness.

Reproductive incompatibility associated with an inherited cytoplasmic factor, including some bacterial symbionts. Reciprocal crosses, microbial manipulations and host-background controls identify its cause.

A source of fixed proper frequency and speed $v$ on a circle has instantaneous frequency extrema ${\nu }_0\sqrt{(1\pm \beta )/(1\mp \beta )}$ for a stationary coplanar receiver outside the circle. The extrema occur when the emission ray is tangent to the source circle, so line-of-sight speed reaches $\pm v$.

For a freely propagating photon between emitters and receivers rotating with the same angular velocity in flat spacetime, ${\nu }_r/{\nu }_e={\gamma }_r/{\gamma }_e$, provided the photon path is unobstructed. At equal radii the ratio is one. Positions and velocities at the actual emission and reception events must be used.