For a randomized experiment, the assumption of unit-treatment additivity implies that the variance is constant for all treatments.

For constant bin width these two expressions can be simplified using:

For an ideal gas, the temperature remains constant because the internal energy only depends on temperature in that case.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For the analysis to correspond usefully to the actual execution time, the time required to perform a step must be guaranteed to be bounded above by a constant.

For example, if the numbers involved in a computation may be arbitrarily large, the time required by a single addition can no longer be assumed to be constant.

For N to be constant for all values of w, a ' tan w '/ a tan w must also be constant.

For incompressible flows, density remains constant.

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For example, the first assumption has been tested by observations showing that largest possible deviation of the fine structure constant over much of the age of the universe is of order 10 < sup >− 5 </ sup >.

For example, adding more S from the outside will cause an excess of products, and the system will try to counteract this by increasing the reverse reaction and pushing the equilibrium point backward ( though the equilibrium constant will stay the same ).

For each specific consistent effectively represented axiomatic system for the natural numbers, such as Peano arithmetic, there exists a constant N such that no bit of Ω after the Nth can be proven to be one or zero within that system.

For measurement at constant experimentally controlled volume, the isochoric coefficient of pressure rise with temperature, is defined by

For a curve of constant width such as the Reuleaux triangle, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.

For the mathematical constant, see e ( mathematical constant ).

For example, a thermocouple might be used to help ensure a furnace's temperature remains constant.

For any circle, its circumference, divided by its diameter, is equal to the constant pi, ( approximately 3. 14 ).

For quasistatic processes under constant pressure, ΔH is equal to the change in the internal energy of the system, plus the work that the system has done on its surroundings.

For systems at constant pressure, the change in enthalpy is the heat received by the system.

For an exothermic reaction at constant pressure, the system's change in enthalpy equals the energy released in the reaction, including the energy retained in the system and lost through expansion against its surroundings.

For positive integer m the derivative of gamma function can be calculated as follows ( here γ is the Euler – Mascheroni constant ):

For instance, endothermic animals ( mammals and birds ) maintain a constant body temperature, while ectothermic animals ( almost all other organisms ) exhibit wide body temperature variation.

For hydrogen-1, hydrogen-2 ( deuterium ), and hydrogen-3 ( tritium ) the constant must be slightly modified to use the reduced mass of the system, rather than simply the mass of the electron.

For those affiliated with it, the A.L.A.M. pool was a haven from the infringement actions involving detail patents that beset the industry with mounting intensity after 1900.

For a serious young man who plays golf with a serious intensity, Palmer has such an inherent sense of humor that it relieves the strain and keeps his nerves from jangling like banjo strings.

For example, changes in signal strength may be used to specify the sounds to be reproduced by a loudspeaker, or the light intensity of television pixels.

For fluorophores in solution this means that the intensity and polarization of the emitted light is dependent on rotational diffusion.

For platformist anarcho-communist Wayne Price " Today ’ s proposals for Parecon, in which workers are rewarded for the intensity and duration of their labor in a cooperative economy, would fit into Bakunin ’ s or Marx ’ s concept of a transitory, beginning, phase, of a free society ... Kropotkin rejected the two-phase approach of the Marxists and the anarchist-collectivists.

For example, on 19 May 2011 an earthquake of magnitude 0. 7 in Southern California, USA 4 km deep was classified as of intensity III by the United States Geological Survey ( USGS ), while a 4. 5 magnitude quake in Salta, Argentina 164 km deep was of intensity I.

For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.

For an incident intensity, this implies the following equality

For a transmitted ray we could do something similar but in that case the distance traveled through the object would cause even faster intensity decrease.

For a known albedo, it is possible to estimate the surface temperature, and correspondingly the intensity of heat radiation.

For every reflection corresponding to a point q in the reciprocal space, there is another reflection of the same intensity at the opposite point-q.

For example, the sampling process in any standard image sensor ( CCD or CMOS camera ) is relatively far from the ideal sampling which would measure the image intensity at a single point.

For example, the intensity of radiation from the Sun is 9126 watts per square meter at the distance of Mercury ( 0. 387 AU ); but only 1367 watts per square meter at the distance of Earth ( 1 AU )— an approximate threefold increase in distance results in an approximate ninefold decrease in intensity of radiation.

For a Gaussian intensity ( i. e. power density, W / m < sup > 2 </ sup >) distribution in a single-mode optical fiber, the mode field diameter is that at which the electric and magnetic field strengths are reduced to 1 / e of their maximum values, i. e., the diameter at which power density is reduced to 1 / e < sup > 2 </ sup > of the maximum power density, because the power density is proportional to the square of the field strength.

For a lightly damped linear oscillator with a resonance frequency Ω, the intensity of oscillations I when the system is driven with a driving frequency ω is typically approximated by a formula that is symmetric about the resonance frequency:

For example, " the intensity of pressure " is meaningless, since the parameters of those variables do not match.

For an ideal point source the intensity of the Arago spot equals that of the undisturbed wave front.

" For the climactic battle, Eidelman starts the music quietly, building the intensity as the battle progresses.

For many services there is labor intensity as services usually involve considerable human activity, rather than a precisely determined process ; exceptions include utilities.

For example, measurements for the intensity of usage, such as incidence and frequency, vary by study.

For confined housing where light control is possible, lowering light intensity so that birds cannot see each other as easily reduces antagonistic encounters and aggressive behaviour.

For example, the Solar storm of 1859 struck the Earth with such intensity that the northern lights could be seen as far south as Rome, approximately 42 ° north of the equator.

For a detailed discussion of the intensity and spectrum ( color ) of incandescence, see the article: thermal radiation.