Codex @codex  0

A preparation made by boiling medicinal material in a liquid, followed by the specified separation and volume adjustment. Suitability depends on the solubility and heat stability of the desired constituents.

A preparation obtained by allowing medicinal material to stand in a solvent for a specified time, at the prescribed temperature, then straining or filtering.

An extracted medicinal preparation supplied as a liquid of specified strength. The name alone does not impose a universal ratio of starting material to final liquid.

Extraction by allowing divided material to stand in contact with a solvent; distinguished from passing fresh solvent through a packed bed in percolation.

Historical concentrated aqueous ethanol used as a pharmaceutical solvent; its specified strength depends on the applicable standard.

Historical aqueous ethanol of specified proof strength; it is not synonymous with rectified spirit.

A historical alcoholic preparation containing nitrous ether; its composition is edition-specific.

Spiritus Myristicae is an alcoholic aromatic preparation associated with nutmeg. The spirit is a solvent-based preparation, distinct from intact seed material.^[ref]

A mucilage is a hydrated, viscous material rich in water-binding polysaccharides. In a pharmaceutical preparation it can influence suspension, coating and flow. Its physical function depends on composition and concentration rather than on a single universal molecule.

A pharmaceutical syrup is a concentrated aqueous sugar preparation that can serve as a vehicle for other ingredients. Sugar concentration influences viscosity and storage behavior. The named vehicle and any active drug dissolved in it play different roles.

Treacle is a concentrated sugar-rich syrup used historically as a pharmaceutical vehicle as well as a food. Its viscosity and sweetness affect formulation. It is a mixture rather than one chemically pure substance.

Ammonium acetate solution is an aqueous pharmaceutical preparation containing the ammonium salt of acetic acid. Its name specifies the principal solute but not, by itself, a concentration. Composition and strength must therefore be distinguished.

Cinnamon water is an aqueous aromatic preparation containing constituents from cinnamon. It differs from cinnamon oil in concentration and physical composition. Historical pharmaceutical specifications must be read in the edition in which they were defined.

Rose water is an aqueous aromatic preparation derived from rose material. It contains a small dispersed or dissolved fraction of volatile constituents rather than the full composition of the flower. A pharmacopoeial name also specifies how the preparation is defined.

For $F(x,y)=(y,a(x-x^3/3)-y)$, a genuine two-cycle obeys $F(x,y)=(y,x)$ with $x\ne y$. Subtracting its two component equations gives $x^2+xy+y^2=3$, then substitution gives the displayed factorization. Cancelling $x+y$ loses the antipodal cycle $(\sqrt{3},-\sqrt{3})\leftrightarrow (-\sqrt{3},\sqrt{3})$, present for every $a>0$. The nonzero-sum family instead has $xy=3/a$ and $x+y=\pm \sqrt{3+3/a}$, requiring $a>3$. Retaining all vanishing factors is essential in polynomial cycle classification.

Blood within the pericardium; a sufficiently rapid collection can cause cardiac tamponade. ^[ref]

Find a graph path whose least edge weight is as large as possible. In a connected undirected graph, use the unique route in a maximum spanning tree. Deleting a least-weight edge on that route gives a separating cut of a graph; a heavier crossing edge would improve the tree's total weight, so every competing route contains an edge no heavier than the deleted one. This proves the bottleneck optimum without assuming distinct weights.

An even-length graph path in an edge coloring is repetitively colored when its first half and second half have the same color sequence in the same order. For a path with distinct edges colored independently and uniformly from $k$ colors, the probability of a repetition on $2r$ edges is $k^{-r}$: after the first $r$ colors, the last $r$ colors are prescribed. Reversing the path preserves this property, so the corresponding bad events may be indexed by unoriented paths.

On $L^2(0,a)$, the midpoint parity operator is $(R_a\psi )(x)=\psi (a-x)$. Substitution $y=a-x$ gives $⟨f,R_{a}g⟩=⟨R_{a}f,g⟩$ and $\Vert R_{a}f\Vert =\Vert f\Vert$, so it is a bounded self-adjoint operator and a unitary operator, with $R_a^2=I$. It is the parity operator in the centered coordinate $x-a/2$.

For an infinite square well, ${\psi }_n=\sqrt{2/a}\sin (n\pi x/a)$ obeys $R_a{\psi }_n=(-1{)}^{n+1}{\psi }_n$. Reflection preserves the Dirichlet boundary conditions and commutes with the second derivative, so $R_a$ commutes with the Hamiltonian operator on its operator domain. By contrast, differentiating once gives $P{R}_a=-R_{a}P$ for the momentum operator. This distinction permits conserved midpoint parity with changing mean momentum.

Adjective referring to the parasympathetic nervous system.