Formation of an ester from an acyl component and an alcohol. Intramolecular esterification of a hydroxy acid makes a lactone. Fischer esterification is the acid-catalysed carboxylic-acid/alcohol case.

Interaction of waste glass with water through ion exchange, network dissolution and alteration-product formation. Dissolved-element release need not equal the total extent of glass alteration.

An isotropic pure $L=0$ spatial state has zero electric quadrupole moment. The nonzero deuteron quadrupole moment consequently requires anisotropic structure. With ground-state $J^P=1^{+}$, a nuclear tensor force can mix ${}^3{S}_1$ and ${}^3{D}_1$ waves while preserving total angular momentum and parity. A purely central spin-independent potential cannot produce this mixing. The inference of an orientation-dependent force was already explicit in 1939.^[ref]

A nuclear receptor responding to glucocorticoid ligands, with regulated localization and recruitment of transcriptional partners.

Ligand-dependent regulation changes nuclear activity and interaction with DNA-associated factors. Because the receptor directly connects a small-molecule hormone to gene regulation, its response can include delayed changes requiring transcription and protein synthesis. ^[ref]

Gaseous fission-product constituents, notably xenon and krypton. Retention, bubble formation and release can change fuel void swelling and internal pressure.

Mechanical contact and load transfer between expanding or cracking fuel pellets and their enclosing nuclear fuel cladding. Local stress depends on clearance, fuel deformation and the cladding's evolving material properties.

Alloys based on zirconium, widely used for water-reactor nuclear fuel cladding because of their useful combination of low neutron absorption and material properties. Corrosion, hydrogen uptake, creep and irradiation-induced dimensional changes limit performance.

The burnup accumulated by a fuel batch when it is removed from its specified irradiation service. Its residence can span more than one operating cycle, so it is not generally the increment of burnup accumulated in a single cycle.

The germline nuclear compartment of a ciliate. It contributes meiotic and zygotic inheritance, rather than supplying most vegetative transcription.

The somatic nuclear compartment of a ciliate, often highly polyploid. Development can involve DNA elimination and amplification, and vegetative inheritance can involve amitotic division.

A tube in which releasing an initial pressure difference produces a shock, often accompanied by an expansion wave and a contact surface. Spatially separated pressure probes can measure shock arrival speed and jump size. The shock and the contact surface must be identified separately when interpreting the downstream state.

A member of the UPF surveillance-factor system. Artificial recruitment downstream of a termination codon can trigger nonsense-mediated decay when the required downstream machinery is present.

The order-$n$ response has one output vector index and $n$ input vector indices. Material point-group invariance, permutation of input index-frequency pairs, and reality of the electric polarization impose different constraints. They must not be conflated with the stronger dispersion-neglecting Kleinman symmetry.

The ratio $|⟨k|V|i⟩/(E_i-E_k)|$ measures a leading admixture between unperturbed eigenstates. Small matrix elements compared with relevant gaps justify a nondegenerate expansion locally. A small overall perturbation does not suffice near a coupled degeneracy, where the nearly degenerate block needs diagonalization.

Sufficient single-mode witnesses include a Fano factor $\mathrm{Var}n/⟨n⟩<1$, an optical quadrature variance below $1/4$ for $[X,P]=i/2$, or photon antibunching with $g^{(2)}(0)<1$. Classical mixtures obey $\mathrm{Var}n\ge ⟨n⟩$, and $g^{(2)}(0)=\mathbb{E}(|\alpha {|}^4)/\mathbb{E}(|\alpha {|}^2{)}^2\ge 1$ by nonnegative variance. The tests are sufficient rather than necessary and exclude the vacuum case when dividing by zero mean occupation.

Invariance under a shift of the time coordinate, with other required background structures held fixed. A continuous time-translation symmetry gives an energy conservation law through Noether theorem. A generic expanding cosmological background is not stationary and need not supply a corresponding globally conserved total energy.

For a complex scalar field multiplet with canonical kinetic term and scalar potential invariant under $\Phi \mapsto e^{i\epsilon T}\Phi$, a constant Hermitian matrix $T$ gives the displayed Noether current. Vary the field and its conjugate independently in the Noether current for a first-derivative scalar field. A common alternative convention reverses both the parameter and current sign. Its divergence vanishes on shell.

For $\mathcal{L}=\rho ({\dot{\psi }}_y^2+{\dot{\psi }}_z^2)/2-F(({\psi }_y^{\prime }{)}^2+({\psi }_z^{\prime }{)}^2)/2$, constant displacement symmetry in $y$ gives $j^0=\rho {\dot{\psi }}_y$ and $j^x=-F{\psi }_y^{\prime }$. The wave equation implies ${\partial }_t{j}^0+{\partial }_x{j}^x=0$. Its integrated charge is physical transverse momentum; endpoint forces can change that charge on a finite segment.

Rotating the two transverse displacement components around the string axis gives density ${\ell }_x=\rho ({\psi }_y{\dot{\psi }}_z-{\psi }_z{\dot{\psi }}_y)$ and flux ${\mathcal{J}}_x=-F({\psi }_y{\psi }_z^{\prime }-{\psi }_z{\psi }_y^{\prime })$. The pair of wave equations yields ${\partial }_t{\ell }_x+{\partial }_x{\mathcal{J}}_x=0$. The total charge is physical angular momentum about the axis; it is conserved only when the net endpoint torque flux vanishes.