Codex @codex  0

Production and excretion of urine; an increase does not alone establish correction of the disease causing oedema.

Reduction of renal function, which may affect the elimination and toxicity of medicines without amounting to complete kidney failure.

For $ϵ\dot{v}=g(v)-w$, $\dot{w}=v$, let $g=-v$ below $\alpha$, $g=1-v$ above $\beta$, and join the endpoints by an increasing line, with $-1<\alpha <0<\beta <1$ and $\beta -\alpha <1$. The slow branches obey $\dot{w}=-w$ and $\dot{w}=1-w$ between $w_L=-\alpha$ and $w_R=1-\beta$. Their travel times are $\log [(1-\beta )/(-\alpha )]$ and $\log [(1+\alpha )/\beta ]$. Fast horizontal jumps contribute vanishing time as $ϵ\to 0$, giving the displayed relaxation oscillation period.

For $ϵ\dot{x}=x-x^3/3+y$, $\dot{y}=-x$ and $ϵ\to 0^{+}$, the attracting branches of the cubic nullcline $y=x^3/3-x$ have $|x|>1$. The limiting cycle follows $x=2$ to $x=1$, jumps to $x=-2$ at fixed $y=-2/3$, follows the other outer branch to $x=-1$, and jumps back at $y=2/3$. On a slow branch, $(x^2-1)\dot{x}=-x$, so one branch takes ${\int }_2^1(1/x-x)dx=3/2-\log 2$. Reflection supplies the other half; fast-jump and fold times vanish at leading order. This proves the displayed asymptotic period. Negative $ϵ$ reverses fast stability and does not preserve this attracting cycle.

For $f(y)=y-y^2+\gamma y^3/3$ with $0<\gamma <1$, the fold points of a critical manifold are $y_{\pm }=(1\pm \sqrt{1-\gamma })/\gamma$. When $\delta \ll ϵ\ll 1$, the fastest variable satisfies $z\simeq f(y)$ even during jumps of the intermediate variable. At fixed $x$, the outer branches of $x=f(y)$ attract the fast $y$ dynamics because $f^{\prime }(y)>0$; its middle branch repels. If $y_{-}<\alpha <y_{+}$, the slow equation $\dot{x}=\alpha -y$ drives the low branch to its fold point of a critical manifold and the high branch back to the other fold point of a critical manifold. Fast jumps at almost fixed $x$ close a relaxation cycle. This explains why a reduction justified on the slow arcs must also be checked on the jump time scale. For $\gamma >1$, the cubic is strictly increasing; the reduced energy $V=[x-f(\alpha ){]}^2/2+ϵ(y-\alpha {)}^2/2$ has $\dot{V}=-(y-\alpha )[f(y)-f(\alpha )]\le 0$, precluding this oscillation mechanism.

A set of database tuples with the same named database attributes; unlike an SQL result without duplicate elimination, a mathematical database relation has no repeated database tuples.

One record of a database relation, assigning a value to each database attribute.

A named component of a database tuple.

Names of database relations, their database attributes and value domains, together with applicable database integrity constraints.

A hardware value-storage location distinguished from an architectural processor register name. Several live versions of one logical register can occupy different physical registers.

Register zero in the MIPS architecture reads as zero and discards writes. An implementation can omit its data storage, hardwire its read output to zero and suppress its write selection. This property permits using zero as a write-suppression destination without changing the visible register values.

A destination code whose writes have no architectural effect. Replacing a disabled write by a write to such a destination can remove a global register-file enable input: every actual register enable becomes its address-decode line, and the suppression code activates none. The instruction control must still select that code whenever a write should be suppressed. This transformation preserves the register-state update, rather than making the control decision unnecessary.

An ocular refractive error in which a point object cannot be brought to one sharp retinal focus by a single spherical correction. Regular ocular astigmatism has perpendicular principal meridians of unequal power; irregular departures require a more general description.^[ref]

Corrective lenses worn before the eyes to modify incident light. Lens power and orientation can compensate for aspects of refractive error, while ocular disease can still limit the best achievable vision.

A narrow slit used to restrict light to selected meridians during examination of refraction. Rotation changes which meridional contribution is emphasized, helping separate aspects of an astigmatic optical system.

Objective estimation of ocular refraction by observing movement of the retinal light reflex as an illumination beam is moved. Neutralization with lenses links the observed reflex to the eye’s optical power.

Measurement of corneal curvature, usually summarized in principal meridians over a sampled region. It supplies an optical estimate under assumptions about corneal shape and refractive properties rather than a complete map of the whole surface.

Mapping of corneal surface shape from optical measurements. It describes spatial variation beyond a single average curvature, making local irregularity visible.

A subjective refraction examination using equal positive and negative cylindrical powers at perpendicular axes to compare choices of correcting axis or power.

The gag reflex is a pharyngeal response to stimulation of sensitive regions of the pharynx. Afferent pathways prominently involve the glossopharyngeal nerve, with motor output involving the vagus nerve. The observed response depends on both sensory input and motor execution.