Conversion of a material such as starch into smaller sugars by appropriate chemical or enzymatic hydrolysis.

Hydrolysis of sucrose into glucose and fructose. The products share an elemental formula while having different molecular structures.

For a nonnegative integer $\ell$, this Coulomb potential energy eigenstate has principal quantum number $\ell +1$ and maximal magnetic quantum number. Put $b=(\ell +1)a$. Including the spherical volume element, its radial probability density is a gamma distribution proportional to $r^{2\ell +2}{e}^{-2r/b}$; its polar density is proportional to ${\sin }^{2\ell +1}\theta$, while its azimuth is uniform. Radial and polar variables are independent. Their moments satisfyThe radial identities follow by successive integration by parts; the angular identity follows from ${\int }_0^{\pi }{\sin }^{j+2}\theta d\theta =(j+1){\int }_0^{\pi }{\sin }^j\theta d\theta /(j+2)$.

Set $h=(2\ell +3{)}^{-1/3}$. Chebyshev's inequality and Markov's inequality give $\mathbb{P}(|r/\mu -1|>h)\le h$ and $\mathbb{P}(|\cos \theta |>h)\le h$. By the union bound, outside an event of probability at most $2h$, the point lies at distance $O(\mu h)$ from the equatorial circle of radius $\mu$. The quantum state therefore concentrates near a classical circular orbit in relative units as $\ell$ grows. The absolute orbit radius and absolute transverse width both grow; this statement does not assert localization in a fixed narrow tube.

For a negative Coulomb energy, remove the exponential decay and regular radial power to obtain a confluent-hypergeometric series. Its recurrence terminates only when $n=q+\ell +1$, with $q$ a nonnegative integer. Regularity at the origin and normalizability at infinity then give the hydrogenic energy levels. Without those physical boundary conditions the radial differential equation has other solutions.

Human chorionic gonadotropin is a glycoprotein hormone produced by placental trophoblast tissue. In early pregnancy, it supports the corpus luteum and hence continued progesterone secretion before placental production is sufficient. Its production provides a detectable endocrine signal, while detection alone does not identify the anatomical location or continuing viability of a pregnancy. ^[ref]

Deliberate removal of blood for a therapeutic purpose. Historical practices include venesection, wet cupping and medicinal leeches; their historical rationale must be separated from present-day indications for venesection.

A historical explanatory system in which health and disease depend on the mixture and balance of bodily fluids. The four-fluid scheme includes blood, humoral phlegm, yellow bile and black bile. These categories are not a modern analysis of blood composition. ^[ref]

Historical explanatory power thought to transform food into bodily nourishment by digestion. In Aretaeus of Cappadocia, weakness of this power explains the coeliac affection of Aretaeus; this is not the modern mechanism of coeliac disease. ^[ref]

The historical chronic disease described by Aretaeus of Cappadocia through wasting, diarrhoea and incomplete digestion. This symptomatic category is not automatically coextensive with modern coeliac disease. ^[ref]

A nineteenth-century explanation of changing therapeutic practice: inflammatory diseases were said to have become less vigorous or more debilitating, requiring less depletion. It competed with explanations based on improved pathology and better evaluation of treatment. This is a historical theory, not a general modern law. ^[ref]

The pale upper layer seen in some clotted blood collected during historical bloodletting. Its appearance was used in inflammatory theories, but it is not an infallible diagnostic sign and should not be confused without qualification with the leukocyte layer of centrifuged blood.

Application of suction cups to intact skin, without the incisions used in wet cupping. It therefore does not itself constitute removal of blood. ^[ref]

Use of systematically recorded groups of cases and numerical comparisons to evaluate treatment, associated especially with Pierre Charles Alexandre Louis. Such comparisons need not be randomized controlled trials and remain vulnerable to confounding. ^[ref]

Collection of ancient medical writings traditionally associated with Hippocrates. Association does not establish his personal authorship of every work.

Historical study of medicinal substances, their origins, preparation and effects; a predecessor and continuing descriptive component of pharmacology and pharmacognosy.

Application of an irritant to one part in the expectation of relieving symptoms elsewhere. Historical claims of remote cure require evidence beyond the demonstrated irritation.

Historical therapeutic removal of serous fluid from an artificially raised blister or maintained superficial wound; loss of fluid alone does not establish clinical benefit.