First-order unification solves a finite system of equations between first-order terms. A useful rule presentation deletes $t=t$, orients $t=x$ to $x=t$ when $x$ is a variable, decomposes equal outer function symbols into argument equations, and rejects unequal outer function symbols. For $x=t$, reject a nontrivial occurrence of $x$ in $t$ by the occurs check; otherwise propagate the substitution $x\mapsto t$ through the other equations. A solved system assigns distinct variables that do not occur in its right sides.^[ref]

For example,first becomes $x=g(y),y=a$. Propagating $y\mapsto a$ gives $x=g(a),y=a$, hence a most general unifier. Keeping $x=g(y)$ without composing the later substitution would leave an unsolved dependency.

The rules preserve the possible unifiers, apart from explicitly rejecting impossible equations. Decomposition works because identical first-order terms have identical constructors and arguments. At a solved system, any other unifier is obtained by instantiating its remaining free variables; this proves the most general unifier property. Efficient implementations share term graphs rather than repeatedly copying growing first-order terms.

A deubiquitinating enzyme cleaves ubiquitin from a substrate or edits ubiquitin chains. Removing a modification can rescue a substrate from recognition, recycle ubiquitin during degradation, or change a signalling outcome.

Ubiquitination covalently attaches ubiquitin to a substrate, usually through successive action of a ubiquitin-activating enzyme, ubiquitin-conjugating enzyme and ubiquitin ligase. The modification can change degradation, localization or signalling; attachment alone does not specify which outcome occurs.

In a fixed-production hydroxyl radical box, adding hydrogen by $\Delta [{\mathrm{H}}_2]$ changes $K$ to $K+k_{{\mathrm{H}}_2+OH}\Delta [{\mathrm{H}}_2]$. Methane lifetime scales as $K/P$ when its hydroxyl radical reaction coefficient is held fixed. The pre-existing hydrogen contribution is already in $K$ and must not be counted again.

A trophoblast-derived tissue adjacent to the early mouse epiblast. Its signalling interactions help organize gastrulation, while it is not itself an epiblast-derived germ layer.

A binary trie stores bit strings by following one edge for each bit, with child edges labeled zero and one. A chosen direction of traversal fixes whether low or high bits are read first.

An implicit treap represents a sequence by the inorder traversal of a treap, without storing explicit positional search keys. Each node stores its subtree size. If the left subtree has size $\ell$, the root has local index $\ell$; smaller indices descend left, while larger indices descend right after subtracting $\ell +1$.

An empty tree has size zero; splitting it at zero returns two empty trees. A split at $k$ returns the first $k$ entries and the remainder. If $k\le \ell$, split the left subtree and attach its returned suffix as the root's new left child. Otherwise split the right subtree at $k-\ell -1$ and attach its returned prefix as the root's new right child. Recompute sizes on the return path. A merge assumes that every entry of its first operand precedes every entry of its second; choose the higher-priority root and recursively merge the adjoining inner subtrees.

Both operations preserve inorder traversal order and heap order on priorities. They permit insertion, deletion or moving a contiguous segment through a few splits and merges. Independent identically distributed continuous random priorities give the underlying randomized search-tree balance and expected logarithmic operation cost; a particular tree can still be tall.^[ref]

Methyl-based NMR strategies exploiting favourable relaxation properties of selected methyl coherences, often with selective isotopic labelling in a largely deuterated protein.

A retroviral sequence inherited as part of the host genome. Some families retain mobilization capacity, whereas others are inactive remnants.

A mobile element whose replication involves an RNA intermediate.

A cross-dependent syndrome of germline defects caused in classic Drosophila systems by failure to control inherited transposable elements. Reciprocal crosses can differ because of maternal piRNA inheritance.

A small charge island coupled to source and drain through tunnel junctions and capacitively to a gate. Resolved island charging makes sequential tunnelling depend on discrete charge states.

A pendulum impact test on a specified notched specimen, commonly used to measure absorbed energy as a function of temperature. A transition curve characterizes a ductile-to-brittle transition, but its energy is not itself a fracture toughness value.^[ref]

Two sites are enantiotopic if separately replacing one or the other by the same distinguishing group gives enantiomers. Achiral conditions do not distinguish them by chirality alone.

The relationship and contact of opposing teeth during jaw closure and chewing. Precise correspondence of opposing surfaces permits specialized cutting and grinding.

A replacement pattern with two successive generations for the replaced tooth classes. It should not be taken to mean every tooth in the jaw is replaced exactly once.

A specialized shearing tooth. In Carnivora the principal opposing pair is the upper fourth premolar and lower first molar; other predatory lineages can specialize different teeth.

A dental construction in which cusps are connected into ridges. Ridge arrangement and wear influence the cutting and grinding performance of the surface.

A dental construction with crescentic ridges, characteristic of many ruminants.