A silver wire composed of five twinned fcc domains around its axis, commonly with a pentagonal cross section. Sidewall passivation and atom addition at ends can favour one-dimensional growth from a multiply twinned seed. Cross-sectional microscopy and diffraction are stronger evidence for this structure than the outer wire outline alone.^[ref]

A dense structural polymorph of silicon dioxide. Comparing its unit-cell volume per formula unit with that of a coexisting phase supplies the specific-volume difference needed in a Clapeyron equation calculation.

A structural polymorph of silicon dioxide. In a coesite–stishovite transition calculation, the entropy-change sign must use the same conversion direction as the specific-volume change.

Polycrystalline silicon, containing many crystalline grains. Deposited polysilicon can form structural layers in surface micromachining; grain structure, doping and residual stress influence its properties.

A seiche is a standing oscillation of water in an enclosed or partly enclosed basin. A disturbance can displace water toward one end; restoring gravity and reflection at boundaries then support repeated oscillation. Wind and atmospheric-pressure changes can excite such motion in natural basins.^[ref]

For an ideal straight basin of length $L$, uniform shallow depth $h$ and two closed ends, no normal flow at the walls gives surface-displacement modes proportional to $\cos (m\pi x/L)$. The shallow-water dispersion relation then gives ${\omega }_m=m\pi \sqrt{gh}/L$ for $m=1,2,\dots$. The fundamental period is $T_1=2L/\sqrt{gh}$.

An illustrative model with $L=2\mathrm{m}$, $h=0.10\mathrm{m}$ and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$ gives $T_1\simeq 4.04\mathrm{s}$. A gently disturbed tank can test the period. Variable depth, open connections, friction and finite wave amplitude modify this ideal prediction.

Water depth is the local vertical distance from the bed to the free surface. If the bed has elevation $b(x,y)$ and the surface has elevation $\eta (x,y,t)$ in the same vertical coordinate, then $h=\eta -b$. The datum used to define the two elevations cancels from their difference.

Keeping the distinction matters in the shallow water equations: the horizontal hydrostatic pressure gradient depends on surface elevation, while the transported volume depends on depth. A sloping bed with a horizontal free surface can have a varying water depth without a horizontal gravitational driving term. Conversely, the same bed can support a flow driven by a sloping surface.

Differential responsiveness to potential mates or mating cues. Preference must be distinguished from the realized mating pattern produced by encounter, competition and acceptance.

Behaviour influencing which potential partner contributes to reproduction. The opportunity to choose and the costs of searching constrain its expression.

Given a set $U$ and a family of its subsets, an exact cover selects members of that family so that each element of $U$ belongs to exactly one selected member. Thus the selected members are disjoint sets whose set union is $U$. Anchoring a recursive choice at the smallest uncovered element avoids counting a cover in different orders.

A partition of cyclically ordered points into blocks whose connections can be drawn inside the circle without crossings between blocks. Equivalently, no two distinct blocks contain alternating points $a,b,c,d$ with $a,c$ in one block and $b,d$ in the other. The number on $n$ points is the $n$th Catalan number.

An ordered set partition of a finite set $S$ is a tuple $(B_1,\dots ,B_k)$ of nonempty, pairwise disjoint subsets whose union is $S$. Elements inside each block of a set partition are unordered, but exchanging two blocks changes the ordered set partition. Thus $(\{1,2\},\{3\})$ and $(\{3\},\{1,2\})$ differ. For $|S|=n$, there are $k!S(n,k)$ such objects with $k$ blocks: first choose a set partition using the Stirling number of the second kind, then order its blocks in $k!$ ways. The unique ordered set partition of the empty set has zero blocks.

A protease whose chymotrypsin-family examples favour small substrate side chains through an obstructed specificity pocket. Related fold and catalytic architecture do not imply identical specificity.