A description of the extent of a cancer, including local spread and involvement of other sites under a stated staging system. It differs from tumour grade, which describes microscopic characteristics.

A historical gross category for a pigmented tumour; it is not automatically synonymous with melanoma.

A primary cancer of lung tissue. It differs from metastasis to the lung, and its subtypes have different cellular and molecular properties.

A cancer involving ovarian tissue or classified within related tubo-ovarian disease categories. Distinct cellular origins and subtypes matter; the location of a mass alone does not determine its biology.

A cancer arising in breast tissue, commonly from epithelial lineages. Biological subtype and extent influence behavior, so an anatomical label does not describe one uniform disease.

Treatment that changes hormone production or hormone action to influence a hormone-responsive cancer. It targets a biological dependency and differs from assuming all cancers of an endocrine-related organ respond identically.

Linimentum Camphorae Compositum is a compound camphor liniment. Compound and simple camphor liniments have different accompanying ingredients.^[ref]

The result a called procedure supplies to its caller on returning. A calling convention specifies the processor register or memory location carrying it, separately from the return address, which identifies where execution resumes. In the elementary MIPS architecture convention, an integer result is placed in $v0, while $ra carries the return address.

The sequence of stack frames reached by following static links. A variable declared $d$ lexical levels outside the current procedure is accessed by following $d$ static links and applying its known frame offset.

The chain of active callers obtained by following dynamic links from the current stack frame. It records call history, whereas a static chain records lexical environments.

A table of pointers supporting direct access to active lexical environments without traversing a static chain. A conventional display is indexed by lexical level; a procedure-indexed alternative keeps the newest activation of each procedure and saves and restores the previous table entry on entry and return.

For direct calls under lexical scope, the executing activation's static chain contains the newest surviving activations of its enclosing procedures. This follows by mathematical induction on calls and returns: a direct call inherits a suffix of the caller's chain, and a return restores the previous chain after intervening activations finish. With procedural parameters, a passed programming closure can instead refer to an older still-active enclosing activation, so simply consulting the newest-activation table is insufficient.

A sufficiently regular admissible function at which the first variation of a functional vanishes for every permitted variation. An extremal is a stationary candidate; it need not be a local maximum or minimum. For a first-order integral functional with fixed endpoint values, it satisfies the Euler-Lagrange equation under the usual regularity assumptions.

For a sufficiently smooth functional $I[y]={\int }_a^{b}F(x,y,y^{\prime },y^{\prime \prime })dx$, the first variation in direction $\eta$ is $\int (F_y\eta +F_{y^{\prime }}{\eta }^{\prime }+F_{y^{\prime \prime }}{\eta }^{\prime \prime })dx$. Twice applying integration by parts gives the interior coefficient $F_y-(F_{y^{\prime }}{)}^{\prime }+(F_{y^{\prime \prime }}{)}^{\prime \prime }$ and boundary expression $[(F_{y^{\prime }}-(F_{y^{\prime \prime }}{)}^{\prime })\eta +F_{y^{\prime \prime }}{\eta }^{\prime }{]}_a^b$. Variations supported in the interior and the fundamental lemma of the calculus of variations force the displayed equation. The remaining boundary terms give the natural boundary conditions for second-derivative functionals.

For an autonomous smooth Lagrangian homogeneous of degree two in velocities, the Beltrami identity gives $\dot{q}\cdot L_{\dot{q}}-L=L$ constant on its Euler-Lagrange extremals. On a regular segment with this constant positive, the Euler-Lagrange expression for $\sqrt{L}$ equals that for $L$ divided by $2\sqrt{L}$, since the extra term is proportional to $\dot{L}$. Hence an energy extremal has the same path as a length extremal. Length is invariant under regular reparametrization: in two coordinates, on a graph $v=v(u)$, its density is $\sqrt{E+2F{v}_u+G{v}_u^2}|du|$. If a nonnegative semidefinite energy vanishes along a curve, the curve instead minimizes length at zero; division by $\sqrt{L}$ is not permitted there. For a positive definite metric, regular nonconstant curves have positive energy.

For a fixed-endpoint integral on $W^{1,\infty }(a,b)$, an admissible function $u$ is a weak local minimizer if $I(v)\ge I(u)$ whenever the Sobolev norm $\Vert v-u{\Vert }_{W^{1,\infty }}$ is sufficiently small. Both function and derivative must be close. “Weak” here labels the variational neighborhood convention, not the weak topology of a Banach space.

For a fixed-endpoint variational integral, an admissible function $u$ is a strong local minimizer if $I(v)\ge I(u)$ for all admissible $v$ whose uniform norm distance from $u$ is sufficiently small. Derivatives can be far apart. Hence strong local minimality implies weak local minimality, while a global minimizer implies both. Small narrow bumps and rapid low-amplitude oscillations explain why the reverse implication can fail.

This excess measures the height of the slope-dependent integrand above its tangent line at the reference slope $p$, evaluated at a trial slope $q$. A convex function of slope has nonnegative excess. At a smooth strong local minimizer, localized needle variations force nonnegative excess along the minimizing curve for every trial slope. It detects fast-gradient competitors that the second variation around a fixed derivative can miss.

The inequalities $0\le \log \cosh t\le t^2/2$ make this energy finite on $H^1$. Since the second derivative of its scalar potential is ${\mathrm{sech}}^{2}t\in (0,1]$, its Fréchet derivative is $DI(v)[h]=\int (\nabla v\cdot \nabla h+\tanh (v)h)$, with Taylor remainder between zero and half the squared $H^1$ norm of $h$. The derivative operator is strictly monotone because the hyperbolic tangent is strictly increasing.

The +2 oxidation state of cadmium. The actual aqueous species can depend on pH, hydrolysis and ligands; a bare ionic formula is an analytical shorthand.

Fetching a cache line before a demand access requires it, to overlap transfer latency with useful work. A software prefetch is one way to request this; unnecessary requests can cause cache pollution.