An alveolar septum is the tissue partition between adjacent alveoli. It contains epithelial surfaces, supporting extracellular matrix and capillaries, bringing air and blood into close proximity. Its thinness aids gas transfer while its supporting structure maintains the exchange architecture.

An iron-based alloy with more carbon than ordinary steel, suitable for casting but with properties strongly dependent on composition and microstructure.

An alloy involving mercury.

One of the different structural forms of the same chemical element.

One of the related alkaloids obtained from cinchona bark. Different solubilities allow partial separation during crystallization and extraction.

A delta-complex is obtained by gluing standard simplexes along affine face maps, allowing different vertices or faces of one simplex to acquire the same image. Every simplex interior is mapped injectively, and the topology is determined simplexwise. Unlike an abstract simplicial complex, its simplexes need not be determined by their sets of global vertices. A circle built from one edge with its two endpoints identified is a basic example. Subdivisions remove these repeated-vertex and repeated-simplex obstructions.

The complex algebraic numbers form a field, the algebraic closure of $\mathbb{Q}$ inside $\mathbb{C}$. To see closure under the field operations, if $\alpha ,\beta$ are algebraic numbers, the tower law makes $\mathbb{Q}(\alpha ,\beta )$ a finite-dimensional field extension of $\mathbb{Q}$. Every element of this extension is an algebraic element, because its successive powers are linearly dependent. In particular it contains $\alpha \pm \beta$, $\alpha \beta$ and $\alpha /\beta$ when $\beta \ne 0$.

It is an infinite-degree algebraic extension. A primitive $p$th root of unity has minimal polynomial of an algebraic element $1+X+\cdots +X^{p-1}$ of degree $p-1$ for every prime $p$, so the degrees of its finite subextensions are unbounded. Finally a complex root of a polynomial whose coefficients are algebraic numbers is itself algebraic over their finite-degree coefficient field and hence over $\mathbb{Q}$, again by the tower law. Thus every such polynomial splits in this field, establishing the algebraic closure assertion.

A named way to construct one alternative of an algebraic data type. In data Tree a = One a | Two (Tree a) (Tree a), One has type signature a -> Tree a and Two has type signature Tree a -> Tree a -> Tree a. They construct values; the type constructor Tree instead constructs types from a type argument.

A data type whose values belong to one of several alternatives, with a logical tag distinguishing the chosen alternative. If Number n and Operator op are its constructors, pattern matching can distinguish the variants even if their payloads use similar representations. The tag need not occupy a separate physical memory field in every implementation.

Delirium tremens is a severe form of alcohol withdrawal involving delirium with marked physiological activation. Disturbances of attention and awareness distinguish it from isolated withdrawal tremor.

Its relationship to changing alcohol exposure differs from the nutrient-deficiency mechanism of Wernicke encephalopathy. The two can occur in related clinical settings without being synonyms.^[ref]

For an acoustic waveguide mode with transverse index $n\ge 1$, the dispersion relation ${\omega }^2=c^2[q^2+(n\pi /H{)}^2]$ permits a propagating axial wavenumber only above the displayed angular frequency. Below it the outgoing bounded response decays as $e^{-\alpha x}$, with $\alpha =\sqrt{(n\pi /H{)}^2-{\omega }^2/c^2}$. The $n=0$ mode has no positive cutoff. At cutoff, a nonzero imposed axial derivative requires $\Phi =A+Bx$, so no bounded periodic solution exists on a semi-infinite channel. Near cutoff, fixed wall-velocity forcing gives amplitudes proportional to $1/|q|$, which can invalidate linearization.

For a rigid cylinder of radius $a$ and height $h$, the velocity potential obeys the wave equation with Neumann boundary conditions. Separation in cylindrical coordinates gives radial factors $J_m(k_{m,n}r/a)$, angular sine and cosine factors of integer order $m$, and axial factors $\cos (\ell \pi z/h)$. The nonzero radial numbers satisfy $J_m^{\prime }(k_{m,n})=0$, yielding the displayed frequencies.

There is also a constant radial mode, with $m=0$ and radial number zero. A formal zero of $J_m^{\prime }$ at the origin for higher $m$ must not be counted by substituting $k=0$ into $J_m(kr)$, which would give the zero function. Solving the zero-radial-eigenvalue equation directly leaves only the constant mode under the side-wall condition. The fully constant potential has zero velocity and is a gauge mode; constant radial modes with nonzero axial index are physical longitudinal oscillations.

Granulation tissue is the vascular, cellular tissue formed during many wound-healing responses. New vessels, matrix-producing cells and immune cells contribute to it. It is a stage of repair rather than a synonym for a mature scar.

A scar is the tissue remaining after repair has replaced or reorganized injured tissue. Its extracellular structure can differ from the original architecture, changing strength, flexibility or function. Closure of a surface therefore does not necessarily demonstrate complete regeneration.

A separated acoustic wave in a straight rigid channel $0<y<H$ has transverse Neumann boundary conditions, giving factors $\cos (n\pi y/H)$ for integers $n\ge 0$. The velocity potential satisfies the wave equation, and its axial factor obeysHere $c$ is the sound speed. Real $q_n$ permits propagation; positive imaginary $q_n$ produces an evanescent wave. A prescribed wall velocity proportional to one transverse factor excites that mode alone in the linear straight-channel model. The physical field is the real part of the complex expression.

For a rightward acoustic waveguide mode with time convention $e^{-i\omega t}$, $\omega >0$ and real $q>0$, the displayed condition selects $e^{iqx}$ and excludes waves incident from positive infinity. If $q=i\alpha$ with $\alpha >0$, the corresponding selection is the decaying factor $e^{-\alpha x}$. Boundedness alone cannot distinguish outgoing and incoming propagating waves, while requiring decay for every frequency would incorrectly remove the propagating response. The condition must match the chosen temporal phase convention.

A changing pressure disturbance travels through a material with finite speed. This transient response is distinct from the eventual equilibrium balance of hydrostatic pressure. In an elastic liquid-filled tube the wall and liquid jointly determine the propagation speed.

A vitamin absorbed and distributed in association with lipids, conventionally including vitamins A, D, E and K. Storage and absorption differ from those of water-soluble vitamins, so solubility helps explain nutritional behavior without determining every physiological effect.

A vitamin also called vitamin B1. Its active coenzyme form supports reactions in carbohydrate and amino acid metabolism; deficiency therefore affects energy-demanding tissues rather than representing a simple shortage of dietary energy.

An essential dietary vitamin required for normal collagen synthesis. ^[ref]