The sparingly soluble sulfate $\mathrm{PbS}{\mathrm{O}}_4$. Its precipitation can retain lead in anode slime in sulfate-based copper electrorefining, but an adherent layer can also contribute to passivation.

The compound with formula $\mathrm{Fe}{\mathrm{S}}_2$. Its conversion with metallic lithium consumes four Li per formula unit and can form iron and two lithium sulfide units; that electron inventory sets an ideal battery capacity.

Lithium sulfide is $\mathrm{L}{\mathrm{i}}_2\mathrm{S}$, with lithium cations and sulfide anions. Sulfur has the formal oxidation state −2 in this composition.

Oxidation of sulfide toward elemental sulfur connects lithium sulfide with the chemistry of lithium-sulfur batteries. The transformation changes both oxidation state and solid-phase composition, so charge transport and material redistribution affect practical behaviour.

A chelate ring is a closed bonded path containing the central atom and a ligand with multiple attachments to it. A tethered Cp–pyridyl ligand can close such a path when the pyridyl N coordinates.

The chelate effect is the enhanced stability often associated with binding several donor sites from one ligand compared with comparable independent donors. Solvent release, effective local concentration and enthalpic contributions all matter; it is not simply a consequence of satisfying an electron-count rule.

The donor–metal–donor angle imposed by a chelating ligand. Tether length, ring conformation, donor distances and substituent crowding all influence it.

Enhanced complex stability associated with donor sites being held in a macrocycle, relative to comparable open-chain ligands. The comparison depends on donor geometry, solvation and strain.

A coordination ligand that coordinates one metal through three donor atoms. A facial tridentate donor set occupies the vertices of one face of an octahedron.

A lossless uniform transmission line has a forward travelling-wave voltage and current related by $V_0=Z_0{I}_0$ with $Z_0=\sqrt{L/C}$. Arbitrary independent DC voltage and current fields cannot simply acquire the same forward wave factor while retaining Maxwell consistency.

A radial force proportional to $r^{-3}$. For potential $V=B/r^2$, its outward radial component is $2B/r^3$: positive $B$ is repulsive and negative $B$ is attractive.

For $\mathbf{F}=-A\mathbf{r}$, the turning radii obey $L^2=mA{r}_{\min }^2{r}_{\max }^2$. A radial impulse preserves angular momentum. Its circular orbit therefore has $r_c^4=L^2/(mA)$, or $r_c=\sqrt{r_{\min }{r}_{\max }}$. Cancel the radial velocity where the original orbit crosses $r_c$.

For a taut elastic string with potential $k(r-L{)}^2/2$, a circular orbit has ${\omega }_0^2=k(r_0-L)/(m{r}_0)$. A radial impulse preserves angular momentum, so the curvature of the fixed-angular-momentum effective potential gives ${\Omega }^2=k/m+3{\omega }_0^2$. The ratio is three at $r_0=6L/5$ and approaches two at $r_0\gg L$. Rational linearized frequency ratios describe leading small-amplitude closed sketches without proving exact closure at finite amplitude.

Spherical averaging and self-consistent optimization impose different conditions on an atomic model. Spherical averaging replaces an angularly varying effective potential energy by one depending only on radius. It simplifies atomic orbitals into radial functions multiplied by angular functions, but does not determine those radial functions by itself.

Self-consistency instead requires the orbitals used to construct an effective potential energy to agree with the orbitals obtained by solving its Schrödinger equation. One can solve a prescribed spherical potential energy without self-consistency, or iterate a spherically averaged Hartree method model until it is self-consistent. Neither operation alone supplies all electron correlation.

Respiratory carbon loss by primary producers. Subtracting it from gross primary production gives net primary production.

Respiratory carbon loss by organisms using organic matter produced by others. It includes important decomposer fluxes and must be distinguished from autotrophic respiration.

Labelling of existing accessible wall followed by growth without the same free label. Comparing old label with new surface distinguishes inheritance of old wall from local deposition of new material.

Reduced proliferation or movement in response to cellular contacts under a specified context. Tissue growth control involves additional signals beyond contact alone.

Expansion of a lymphocyte lineage sharing clonal ancestry. Detection of a clone is not by itself proof of aggressive malignant disease.

Organization of epithelial cells into distinct apical and basolateral domains. Individual apical identity and coordination of apical surfaces into a shared tissue lumen are related but distinct properties.