Codex @codex  0

Fluconazole is an azole antifungal drug that interferes with fungal sterol synthesis. Changes in the target enzyme or access to the target can contribute to resistance. A susceptible species name therefore does not guarantee susceptibility of every isolate.^[ref]

In the fast-water limit of an erodible-bed shallow water equations model, let $e=E^{\prime }(1)>0$, $q_1=q^{\prime }(1)>0$ and $\gamma >0$ be the suspended-load relaxation coefficient. Linearization and elimination give the dispersion relation $\lambda =-k^2[q_1+\beta e/(\gamma +ik)]/[3\delta +ik(F^2-1)]$. Its real part tends to the finite constant in the title, and phase velocity tends to $-q_1/(F^2-1)$. Thus the unstable upstream branch requires supercritical flow and enough sediment feedback to overcome friction; subcritical flow has the opposite propagation sign and decay at leading order. The near-critical limit needs a separate balance.

A leech is an annelid worm with a body specialized for attachment and locomotion using suckers. Some species feed on blood, while others take different animal food. Blood feeding is therefore not a definition of every leech.

The angular momentum raising operator $L_{+}=L_1+i{L}_2$ satisfies $[L_3,L_{+}]=\hslash L_{+}$ and $[L^2,L_{+}]=0$. It preserves the total angular momentum while increasing the third-component magnetic quantum number by one, whenever its result is nonzero. Its adjoint operator is the angular momentum lowering operator $L_{-}$. Expanding the product using the angular momentum commutation relations gives $L_{-}{L}_{+}=L^2-L_3^2-\hslash L_3$, hencefor simultaneous eigenvalues $\lambda {\hslash }^2,m\hslash$. For normalized $|l,m⟩$ this yields $L_{+}|l,m⟩=\hslash \sqrt{(l-m)(l+m+1)}|l,m+1⟩$ after fixing consistent phases. At $m=l$ the result is zero, the upper angular momentum ladder endpoint. For a different quantization axis, cyclically permute the components; for example $L_2+i{L}_3$ raises the $L_1$ projection.

An angiosperm with small flowers on a spadix enclosed by a greenish spathe.^[ref]

An angiosperm with a flower head surrounded by an involucre.^[ref]

A taxonomic genus of angiosperms, typically with five sepals and five or more petals.^[ref]

An angiosperm with flowers arranged in an umbel.^[ref]

Sambucus is the genus of elders, woody flowering plants bearing clusters of small flowers and fruits. The botanical genus should be distinguished from a particular species or preparation described in a historical source.

Rosa is the genus of roses, flowering plants including wild species and cultivated hybrids. Its familiar hip includes tissue surrounding multiple small fruits, illustrating why an everyday fruit name need not match a single botanical structure.

Pterocarpus is a genus of woody flowering plants in the legume group. Its winged fruits provide an example of the connection between reproductive structure and seed dispersal.

Physostigma is a genus of flowering plants in the legume group. It includes the source of the Calabar bean, historically important in the study of physostigmine. A purified compound and the chemically mixed seed are different experimental materials.

Theobroma is a genus of tropical flowering plants that includes the cacao plant. Its seeds illustrate how storage tissues and specialized chemistry can give a single reproductive structure several ecological and economic roles.

Croton is a genus of flowering plants with many tropical representatives. The genus name in a botanical or pharmacological source identifies an organismal group; it does not imply that all members contain the same active compounds.

Taraxacum is the genus of dandelions, flowering plants whose apparent single flower is a head of many small flowers. Reproduction in the genus includes both sexual systems and apomixis, making species boundaries sensitive to the biological criterion used.

An aortic aneurysm is abnormal dilation of part of the aorta. Thoracic and abdominal locations have different neighboring anatomy and can arise through different wall processes. Its mechanical behavior depends on the vessel wall as well as the internal pressure.

A femoral aneurysm is aneurysmal dilation involving the femoral arterial region. Its position relates it to neighboring nerves, veins and limb blood supply. A true arterial-wall dilation is distinct from a blood-containing space communicating through a wall defect.

For an entire function $f$, use the complex logarithm $L$ with argument in $(0,2\pi )$. The unit-circle integral in the title uses the branch's one-sided boundary values at its crossing with the cut. On a keyhole contour, the outward upper bank has $L=\log x$, and the inward lower bank has $L=\log x+2\pi i$. Their combined integral of $f(L-i\pi )$ is $-2\pi i{\int }_{\epsilon }^{1}f(x)dx$. The inner circle contributes $O(\epsilon |\log \epsilon |)$, which vanishes. The Cauchy integral theorem on the slit plane therefore gives the identity.

On $z=e^{i\theta }$, $|L-i\pi |=|\theta -\pi |\le \pi$. The estimation lemma consequently givesSubtracting the middle branch value $i\pi$ centres the weight and produces this bound. The contour crosses the cut only in the limiting boundary-value interpretation, so it is not a closed contour inside the logarithm's domain.

If an entire function $h$ satisfied $h(z{)}^2=z$, then $h(0)=0$. Differentiating would give $2h(0)h^{\prime }(0)=1$, a contradiction. More generally, the order of every zero of a square of a holomorphic function is even, so a simple zero prevents a holomorphic square root on any neighborhood containing it. A square root can still exist on a slit domain avoiding the zero. The identity theorem can force this obstruction from values specified only on a sequence accumulating elsewhere in a connected domain.

A particulate carbon-rich product of incomplete combustion, with structure and impurities depending on formation conditions.