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Historical formulation name; composition is identified by pharmacopoeial edition.

Historical formulation name; composition is identified by pharmacopoeial edition.

Historical formulation name; composition is identified by pharmacopoeial edition.

Historical formulation name; composition is identified by pharmacopoeial edition.

Historical formulation name; composition is identified by pharmacopoeial edition.

Historical formulation name; composition is identified by pharmacopoeial edition.

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.

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.

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.