The relational model represents data as database relations, which are sets of database tuples over specified value domains. A relational schema names the database attributes and states database integrity constraints; an instance supplies their current values. Relational algebra describes operations on this logical data, while storage order, indexes and access paths belong to its implementation.

For example, the database relation Reading(sample, value) can contain $(A,3),(B,8)$. A relational selection for values above five followed by relational projection onto sample identifiers returns $\{B\}$. Changing the underlying file layout or adding an index need not change that query's meaning. Mathematical database relations have set semantics; SQL often uses bag semantics and has additional SQL NULL behavior.

In his 1970 paper, E. F. Codd argued for data independence: application logic should not rely on particular stored orderings, indexes or navigational paths. His relational formulation made that separation central to database design.^[ref]

An oxidation-reduction reaction in which one starting species supplies products with both higher and lower oxidation states.

Two or more functions are mutually recursive when their definitions call one another in a cycle. Two algebraic data types can likewise be mutually recursive when constructors of each refer to the other. For alternating sequences Zig a b and Zag b a, descending one constructor exchanges the type parameters; a pair of mapping functions must exchange its arguments correspondingly. A mutually recursive fold may have two independent result types $r,s$: its handlers have types a -> s -> r and b -> r -> s, with empty results of types r and s. Equality of the two result types is not required by type inference.

A recursive definition in which returning around a recursive dependency requires progress of the kind relevant to its semantics. In communicating sequential processes, the visible guard must survive CSP hiding; a loop whose apparent guard becomes a CSP internal action is not visibly guarded.

A receptor activated by a neurotransmitter.

An ionotropic receptor directly changes channel opening, whereas a metabotropic receptor signals through intracellular partners. These routes can differ in timing and amplification, allowing the same transmitter class to influence both rapid electrical responses and slower cellular regulation. ^[ref]

A visibility ray or finite segment from a surface toward a light source. An opaque blocker before the source removes that source's direct illumination at the surface. Intersections beyond a finite light source must not count.

A Monte Carlo method for estimating light transport through random paths of successive surface interactions. A sampled continuation contributes its scattering response and cosine divided by its sampling probability density function. Next-event estimation makes direct source connections explicit, including connections to ideal point lights.

Jack Bresenham's raster graphics algorithm selects a thin sequence of pixels to represent a line segment by exact incremental integer arithmetic. For a first-octant segment with $0\le \Delta y\le \Delta x$, a scaled midpoint line decision chooses between the next same-row and next higher-row pixels.

A balanced binary sequence of length $2n$ has $n$ entries of each kind. Uniformly sample an $n$-element subset of the positions and place the first kind there. If $2n$ is a power of two, repeatedly draw uniform positions using ${\log }_2(2n)$ fair random bits, reject previously selected positions, and stop after $n$ distinct positions. Each new position is uniform among those remaining, making every $n$-element subset equally likely. The expected number of draws is ${\sum }_{s=0}^{n-1}2n/(2n-s)<2n$, giving $O(n\log n)$ expected random bits.

A quantum mechanics physicist studies quantum mechanics through mathematical theory, observation or experiment. The field determines the relevant physical systems and measurements, while the individual biographies below connect particular contributions with their scientific ideas.

Respiratory mechanics relates the movements of the thorax and respiratory diaphragm to pressure changes and airflow.

A tube placed in the trachea to provide an airway or a connection to respiratory recording apparatus.

Entry of material into the airways from the mouth, pharynx or stomach.

An airway is a passage conducting respiratory gas. The larynx, trachea, bronchi and bronchioles are examples in human anatomy. Resistance and patency depend on geometry and wall properties, while gas exchange chiefly occurs in more distal specialized surfaces.

A lung-inflation reflex carried through vagus nerve sensory pathways that inhibits inspiration. It was described in 1868 by Ewald Hering and Josef Breuer, after the 1867 examination.

Artificial respiration supports gas movement when spontaneous ventilation is absent or inadequate. The term concerns a physiological function, while particular devices and clinical methods differ. Moving gas is distinct from restoring blood circulation, so ventilation alone cannot substitute for every component of oxygen transport.

Hyperventilation is ventilation in excess of the level required to remove the carbon dioxide being produced, tending to reduce arterial carbon-dioxide partial pressure. It is not defined merely by a high respiratory rate: breath depth, dead space and metabolic production also matter.

Alveolar ventilation is the effective rate of fresh gas reaching exchanging alveolar regions. In a simple uniform-breath model, ${\dot{V}}_A=f(V_T-V_D)$, where $f$ is breathing frequency, $V_T$ tidal volume and $V_D$ dead-space volume per breath.

For an invented example, $15(500-150)=5250$ millilitres per minute differs from $30(250-150)=3000$, even though both patterns move $7500$ millilitres per minute in total. Equal total pulmonary ventilation therefore need not imply equal alveolar gas renewal.

Suspension of breathing. In nineteenth-century accounts it can include the developing asphyxial condition; its meaning must be established from context rather than automatically identified with a modern sleep-disorder diagnosis.

A one-compartment carbon-dioxide balance couples metabolic production with pressure-dependent ventilatory removal. A positive-part response models a nonnegative threshold-linear respiratory drive, and a transport/response delay can destabilize negative feedback. With $T=t/\tau$, $P=P_0+[M/(G{P}_0)]p$, the scaled law is $p^{\prime }=\alpha [1-(1+\mu p)[p(T-1){]}_{+}]$, where $\alpha =\tau G{P}_0/K$ and $\mu =M/(G{P}_0^2)$. Its positive equilibrium is $2/[1+\sqrt{1+4\mu }]$; $1/(1+\mu )$ is only its first-order small-$\mu$ approximation.