Tinctura Ferri Perchloridi is a tincture containing ferric chloride. The historical word perchloride refers to the higher chloride of iron, not to a perchlorate.^[ref]

Vinum Ferri is an iron-containing medicinal wine. Historical wine-of-iron formulas differed, including solutions based on tartarated iron and preparations involving iron wire.^[ref]

The ferrous phosphate. The historical official powder was partly oxidized.

The potassium salt of iodate, formed together with potassium iodide in the reaction of iodine with hot potassium hydroxide.

An involution partitions its set into fixed points and pairs exchanged by the function. If there is exactly one fixed point, every finite model has odd size. Conversely any finite set of odd size admits such a function by pairing all but one element. The first-order sentence $\forall xf(f(x))=x\wedge \exists z(f(z)=z\wedge \forall x(f(x)=x\to x=z))$ consequently has exactly the positive odd finite model sizes. Its arbitrarily large finite models imply an infinite model by the compactness theorem.

An interval that includes exactly one endpoint, such as $[a,b)=\{x:a\le x<b\}$. Adjacent half-open intervals $[a,b)$ and $[b,c)$ are disjoint while covering $[a,c)$, which is useful for representing adjoining occupied cells without treating shared boundaries as overlaps.

The perineal artery is a branch within the internal pudendal distribution supplying superficial perineal structures and related tissues. Its branching pattern can vary. The name identifies a regional supply route rather than all arterial flow to the pelvis.

The artery of the bulb of the penis is a branch contributing to the vascular supply of the penile bulb and associated spongy tissue. It belongs to the internal pudendal distribution. Its territory is distinct from every other erectile or superficial penile arterial route.

The carotid sinus is a specialized dilated region near the origin of the internal carotid artery. Stretch-sensitive signaling contributes to blood-pressure reflex regulation. It should be distinguished from the nearby carotid body, which detects chemical conditions rather than the same mechanical input.

A primal-dual interior-point method solves perturbed KKT conditions while updating both the primal variables and Lagrange multipliers. For inequalities written as $c_i\ge 0$, a logarithmic-barrier path has positive $c_i,y_i$ and perturbed complementarity $c_i{y}_i=\mu$. A Newton system for these coupled equations gives primal and dual corrections together, with damping to preserve positivity. This can avoid explicitly forming the most ill-conditioned eliminated barrier Hessian, although scaling and regularity still matter.

An external intercostal muscle spans neighboring ribs in the superficial intercostal layer. It supports the intercostal spaces and can assist rib elevation during inspiration. Its fiber orientation differs from the deeper internal layer.

An internal intercostal muscle is part of the deeper intercostal layer. Its action depends on the portion considered: interosseous and interchondral regions can contribute differently to expiration and inspiration. Treating the entire layer as one uniform expiratory actuator loses that anatomical distinction.

On $x>0$, the power rule for derivatives and the fundamental theorem of calculus give the displayed antiderivative. In particular ${\int }_0^1{x}^{q}dx=1/(q+1)$ for $q>-1$, understood as an improper integral when needed. At $q=-1$, the antiderivative on $x>0$ is the natural logarithm $\log x+C$.

An inflection point of the graph of a differentiable real function at which its derivative is zero. It has a horizontal tangent and a change of concavity, but need not be a local maximum or minimum. For a three-times continuously differentiable function, $f^{\prime }(a)=f^{\prime \prime }(a)=0$ and $f^{\prime \prime \prime }(a)\ne 0$ suffice: the expansion $f^{\prime \prime }(a+h)=f^{\prime \prime \prime }(a)h+o(h)$ gives opposite signs on the two sides. The elementary example is $f(x)=x^3$ at zero. The word “saddle” is sometimes used for this one-dimensional situation in elementary examination papers, but the usual saddle point of a scalar function has a multivariable meaning; do not merge the two concepts.

Linear incompressible motion about rest in a frame rotating with $\mathbf{\Omega }=\Omega \mathbf{k}$ obeys ${\mathbf{u}}_t+2\mathbf{\Omega }\times \mathbf{u}=-\nabla P/\rho$. If $\zeta =v_x-u_y$ is its vertical vorticity, taking curl gives ${\zeta }_t=2\Omega w_z$, while eliminating pressure using continuity gives ${\partial }_t{\nabla }^{2}w+2\Omega {\zeta }_z=0$. Differentiating in time yields the displayed scalar equation. All three velocity components must be retained, even when the fields depend on only two spatial coordinates. The Coriolis acceleration generally generates a transverse velocity that is absent in a strictly two-component description.

For fixed vertical wavenumber $k_z$, the inertial-wave dispersion relation is ${\omega }^2=4{\Omega }^2{k}_z^2/(k_x^2+k_z^2)$. Its horizontal group velocity is the derivative displayed above, opposite in sign to $\omega k_x$. In a half-channel $x>0$, an outgoing propagating mode therefore requires $\omega k_x<0$. With time factor $e^{-i\omega t}$ and $q=|k_z|\sqrt{4{\Omega }^2/{\omega }^2-1}$, choose $e^{-i\mathrm{sgn}(\omega )qx}$. Above the inertial-frequency cutoff, the horizontal wavenumber is imaginary and the appropriate radiation condition instead selects the exponentially decaying solution. Energy transport, rather than the direction of phase travel alone, determines the outgoing sign.

An inertia tensor can be isotropic even when the body is not a sphere. An example is a uniform thin disc of radius $2a$ and mass $M$, with a thin rod of length $\sqrt{3}a$ and mass $2M$ attached normally at its center. The combined center of mass is one third of the rod length from the disc. Standard disc and rod moments and the parallel axis theorem give all three principal moments equal to $2M{a}^2$, so $J=2M{a}^{2}I$. The angular momentum is therefore a fixed scalar times the angular velocity. In torque-free motion, conservation of the inertial angular-momentum vector makes the angular-velocity vector constant for every initial spin. Rotational symmetry of the shape is not required; equality of its second moments is enough.

For linear interpolation at zero and $h>0$, an error $\delta$ in the second sampled value, with the first exact, changes the linear interpolant by $\Delta p(x)=\delta x/h$. On $[0,h]$, its uniform norm is exactly $|\delta |$, whereas the derivative change is the constant $\delta /h$. With independent absolute bounds $|{\delta }_0|,|{\delta }_1|\le \delta$ on both samples, the value change remains at most $\delta$ and the derivative change is at most $2\delta /h$, attained for opposite endpoint errors.

Thus bounded absolute sample noise can remain bounded under value interpolation while becoming unbounded under numerical differentiation as $h\to 0$. Fixed nonzero sample noise also prevents exact convergence of the value approximation; stability against perturbations and convergence to exact data are different assertions. For a second-sample error $aϵ(h)$ with fixed $a>0$, value convergence requires $ϵ(h)\to 0$, while derivative convergence requires $ϵ(h)=o(h)$ in little o notation, in addition to vanishing truncation error.

Equal volumes of ideal gases at the same temperature and pressure contain equal amounts of substance. Named after Amedeo Avogadro. From $pV=nRT$, $V/n=RT/p$ is common to them.

A hyperelastic material is homogeneous when its strain energy density $W(F)$ has no explicit dependence on the reference configuration position. Its first Piola-Kirchhoff stress tensor is $T=DW(F)$. Homogeneity of the material does not require the deformation gradient to be spatially constant.