The commutator of two operators acting on a Hilbert space is a central concept in quantum mechanics, since it quantifies how well the two observables described by these operators can be measured simultaneously.

The tensile strength of a material quantifies how much stress the material will endure before suffering permanent deformation.

WordNet quantifies this by the frequency score: in which several sample texts have all words semantically tagged with the corresponding synset, and then a count provided indicating how often a word appears in a specific sense.

It is generally believed that it is due to the inertia of the fluid as a whole: the culmination of time dependent and convective acceleration ; hence flows where inertial effects are small tend to be laminar ( the Reynolds number quantifies how much the flow is affected by inertia ).

Electrical resistivity ( also known as resistivity, specific electrical resistance, or volume resistivity ) is a property of a material ; it quantifies how strongly the material opposes the flow of electric current.

It quantifies how often the fading crosses some threshold, usually in the positive-going direction.

The average fade duration quantifies how long the signal spends below the threshold.

In terms of that notion, the fractal dimension of a coastline quantifies how the number of scaled measuring sticks required to measure the coastline changes with the scale applied to the stick.

In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they can be.

The emittance of an object quantifies how much light is emitted by it.

The inertial mass, on the other hand, quantifies how much an object accelerates if a given force is applied to it.

Hydrodynamic dispersivity ( α < sub > L </ sub >, α < sub > T </ sub >) is an empirical factor which quantifies how much contaminants stray away from the path of the groundwater which is carrying it.

Oscillation can be used to define continuity of a function, and is easily equivalent to the usual ε-δ definition ( in the case of functions defined everywhere on the real line ): a function ƒ is continuous at a point x < sub > 0 </ sub > if and only if the oscillation is zero ; in symbols, A benefit of this definition is that it quantifies discontinuity: the oscillation gives how much the function is discontinuous at a point.

Species richness is a simple count of species, whereas species evenness quantifies how equal the abundances of the species are.

Return on invested capital ( ROIC ) is a financial measure that quantifies how well a company generates cash flow relative to the capital it has invested in its business.

* it uses a cost function that quantifies how well the map is trained.

Basically, resolution quantifies how close lines can be to each other and still be visibly resolved.

The volume of distribution quantifies just that by specifying how big a volume you would need in order to observe the blood concentration actually measured.

The absorbance of an object quantifies how much of the incident light is absorbed by it ( instead of being reflected or refracted ).

* Prognostic Horizon ( PH ) quantifies how much in advance an algorithm can predict with a desired accuracy before a failure occurs.

* Convergence quantifies how fast the performance converges for an algorithm as EoL approaches.

The local clustering coefficient of a vertex ( node ) in a graph quantifies how close its neighbors are to being a clique ( complete graph ).

As an extension of the Player Efficiency Rating, Hollinger also developed a simpler formula that quantifies how impressive a player's individual performance is in a given game.

This approach quantifies the number of poor individuals and households but does not take into account how the impoverished population lacks basic needs such as housing, food, health and education.

The scale quantifies the effects of an earthquake on the Earth's surface, humans, objects of nature, and man-made structures on a scale from I ( not felt ) to XII ( total destruction ).

A hydropathy analysis uses an algorithm that quantifies the hydrophobic character at each position along the polypeptide chain.

To measure transpiration rate directly, rather than the rate of water uptake, utilize a scientific instrument which quantifies water transfer at the leaves.

The Berry – Esseen theorem, or Berry – Esseen inequality, quantifies the rate at which this convergence takes place by giving a bound on the maximal error of approximation between the normal distribution and the true distribution of the sample mean.

The Shannon index equals log (< sup > q </ sup > D ), and in practice quantifies the uncertainty in the species identity of an individual that is taken at random from the dataset.

The Simpson index equals 1 /< sup > q </ sup > D and quantifies the probability that two individuals taken at random from the dataset ( with replacement of the first individual before taking the second ) represent the same species.

The fluctuation-dissipation theorem is a general result of statistical thermodynamics that quantifies the relation between the fluctuations in a system at thermal equilibrium and the response of the system to applied perturbations.

Surface tension quantifies the cohesive force present at the surface of a droplet.

The solidus quantifies the temperature at which melting of a substance begins, but not necessarily the substance is melted completely, i. e., the solidus is not necessarily a melting point.

The oscillation of a function at a point quantifies these discontinuities as follows:

If the mean biotemperature is between, Holdridge quantifies the climate as subpolar ( or alpine, if the low temperature is caused by altitude ).

Through this work, Febvre became very involved in the field of ethnology, a field of study that quantifies human behavior.

The abstraction is completed when a labour market is established which very exactly quantifies the money-price applying to all kinds of different occupational functions, permitting equations such as:

* Test of color blindness with the indication of the weaknesses in various colors, quantifies green red blue deficiency ( ISHIHARA test alternative )

The image is analysed by densitometry, which evaluates the relative amount of protein staining and quantifies the results in terms of optical density.

In computer science, the time complexity of an algorithm quantifies the amount of time taken by an algorithm to run as a function of the length of the string representing the input.

In mathematics, oscillation quantifies the amount which a sequence or function tends to move between extremes.

In information theory, the conditional entropy ( or equivocation ) quantifies the amount of information needed to describe the outcome of a random variable given that the value of another random variable is known.