A dimensionless factor used to convert a specified radiation component's absorbed dose into its contribution to equivalent dose.

For a classical canonical coordinate with confining potential energy $U=A|x{|}^s$, $A>0$ and $s>0$, integration by parts in the Boltzmann distribution gives $⟨x{U}^{\prime }(x)⟩=k_{B}T$. Homogeneity then gives $⟨U⟩=k_{B}T/s$. The usual quadratic contribution $k_{B}T/2$ is the special case $s=2$.

Rough elastic collisions can exchange rotational and translational kinetic energy. If all three translational and all three rotational degrees of freedom of a rigid ball reach classical thermal equilibrium, their six quadratic terms contributeper ball, by the equipartition theorem.

In a constant downward gravitational field above a floor at $z=0$, with no upper boundary, the equilibrium height distribution is exponential:Its mean gravitational potential energy is $⟨mgz⟩=k_{B}T$, so the total mechanical mean energy is $4k_{B}T$. The field is uniform; the height distribution is not.

This result assumes the rough collisions actually thermalize rotation, sufficient room for the exponential height tail and no energy loss. Smooth elastic spheres need not exchange rotational energy with translation. A finite ceiling changes the height distribution and its mean potential energy.

For a captured nonradial null geodesic with $u=1/r$, the large-$u$ orbit equation is $(du/d\varphi {)}^2\sim 2\mu u^3$. Integration on the inward branch givesThe curvature singularity is reached at finite azimuth. This does not prevent a near-critical ray from winding repeatedly near the photon sphere before its final plunge. A radial ray has constant azimuth, so this asymptotic coordinate parametrization is inapplicable to it.

In hydroxyl-directed epoxidation, hydrogen bonding between an allylic hydroxyl and the oxidant favors oxygen delivery from a particular alkene face. This influences diastereoselectivity without requiring an unchanged preference under every solvent or protecting-group condition.

Enantioselective oxygen transfer to an allylic alcohol using a titanium–tartrate complex and a hydroperoxide. With the alkene horizontal and its hydroxymethyl substituent at lower right, L-(+)-tartrate directs delivery from the back face and D-(−)-tartrate from the front face. Rotate a structure in its plane to apply the mnemonic; reflecting it changes its stereochemistry.

Transfer of an oxidant oxygen atom to an unsaturated substrate, including controlled formation of an epoxide.

An epithelial cell producing enamel during tooth development. Loss of the enamel-producing cellular layer after eruption limits replacement of worn crown enamel.

Removal of a cell from an epithelial sheet through coordinated behaviour of that cell and its neighbours. Extrusion and apoptosis are distinct events and need not occur in the same order.

An epithelium characterized by flattened surface cells. Stratified examples contain renewing basal populations and differentiating suprabasal layers.

An epithelium organized into multiple cell layers. Cell production, differentiation and loss must be balanced across the layers.

The cellular lining of blood and lymphatic vessels. Its polarized surfaces and junctions participate in vascular lumen formation.

Episome partitioning distributes an independently maintained genetic element to descendant cells during cell division. Random allocation can lose a low-copy element from some daughters, whereas active tethering or segregation systems can improve retention. Replication and partitioning are therefore distinct requirements: an element can copy efficiently yet still be lost if its copies travel together into only one daughter. ^[ref]

A gain or loss of an inherited epigenetic state rather than a change in nucleotide sequence.

Molar entropy in a specified standard state. Absolute entropies of elemental reference substances are generally not zero, unlike their conventional standard formation enthalpies.

The entropy change per specified extent of a reaction, equal to the stoichiometric product-minus-reactant sum of partial molar entropies.

entropy associated with positions of independently translating objects. Connecting segments into one polymer leaves fewer independently translating objects than treating the same segments as separate molecules; this reduces mixing entropy per segment.

The enthalpy change per specified extent of a reaction. Scaling or reversing a chemical equation scales or reverses this quantity.