When integrated along all possible paths, with a phase factor which is proportional to the path length, the interference of the wave-functions correctly predicts observable phenomena.

When integrated over the radius, this implies that for b = 1, the total number of stars is proportional to r < sup > 2 </ sup >.

When an area element is radiating as a result of being illuminated by an external source, the irradiance ( energy or photons / time / area ) landing on that area element will be proportional to the cosine of the angle between the illuminating source and the normal.

When most materials are polarized, the polarization induced, P, is almost exactly proportional to the applied external electric field E ; so the polarization is a linear function.

When light falls on a receptor it sends a proportional response synaptically to bipolar cells which in turn signal the retinal ganglion cells.

:: When the Hamiltonian operator acts on the wavefunction Ψ, the result might be proportional to the same wavefunction Ψ.

When one seat in a proportional representation constituency becomes vacant, the consequences vary.

When the wavelength of a gravity wave is less than twice the depth of the ocean or lake its behavior is governed by the nonlinear Schrodinger equation and its speed is proportional to.

When maximum cooling is not required, in any equipment fan speeds can be reduced below the maximum: fan noise has been found to be roughly proportional to the fifth power of fan speed ; halving speed reduces noise by about 15 dB.

When equilibrium is achieved, a granddaughter isotope is present in proportion to its half-life ; but since its activity is inversely proportional to its half-life, any nuclide in the decay chain finally contributes as much as the head of the chain.

When paramyxovirus genome was exposed to UV light, the level of inhibition of transcription was proportional to the distance from the leader sequence.

When a steady rotation speed has been reached, the speed is proportional to fluid velocity.

When in 1867 John Stuart Mill proposed a type of proportional representation, Cranborne argued that: " It was not of our atmosphere — it was not in accordance with our habits ; it did not belong to us.

* Few major parties, large number of minor parties — When there are only one or two major parties, but a relatively large number of minor parties that, combined, achieve a significant share of the total proportional vote, but fail to elect any constituency seats, the large parties often end up with overhang seats.

The diagram shows price points at the points labeled A, B, and C. When a vendor increases a price beyond a price point ( say to a price slightly above price point B ), sales volume decreases by an amount more than proportional to the price increase.

When the flux in the projectile lies in the linear portion of its material's B ( H ) curve, the force applied to the core is proportional to the square of coil current ( I )— the field ( H ) is linearly dependent on I, B is linearly dependent on H and force is linearly dependent on the product BI.

When the PV is within, say 10 ° of the SP the heat input begins to be reduced by the proportional controller.

When the PV is within, say 10 ° of the SP the heat input begins to be reduced by the proportional controller.

When a spring is compressed or stretched, the force it exerts is proportional to its change in length.

: When two reactants, A and B, react together at a given temperature in a " substitution reaction ," the affinity, or chemical force between them, is proportional to the active masses, and, each raised to a particular power

When an object is immersed in a liquid the liquid exerts an upward force which is known as buoyant force and it is proportional to the weight of displaced liquid.

When a charged particle — such as an electron — is placed in a magnetic field, it experiences a Lorentz force proportional to the strength of the field and the velocity at which it is traveling through it.

These crystals comprise stacks of Josephson junctions that exhibit a unique electrical property: When an external voltage is applied, an alternating current will flow back and forth across the junctions at a frequency proportional to the strength of the voltage ; this phenomenon is known as the Josephson effect.

When this happens, the voltage becomes proportional to the square root of current, and the resistance in the plasma becomes stable for the remainder of the flash.

When the information cell for Af has been determined, it is saved as a representation of Af.

When applied to the simplest two-electron molecule, H < sub > 2 </ sub >, valence bond theory, even at the simplest Heitler-London approach, gives a much closer approximation to the bond energy, and it provides a much more accurate representation of the behavior of the electrons as chemical bonds are formed and broken.

When progress and development is rapid, the faster method of political representation is adopted.

When the party is represented by members in the lower house of parliament, the party leader simultaneously serves as the leader of the parliamentary group of that full party representation ; depending on a minimum number of seats held, Westminster-based parties typically allow for leaders to form frontbench teams of senior fellow members of the parliamentary group to serve as critics of aspects of government policy.

When Polish notation is used as a syntax for mathematical expressions by interpreters of programming languages, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same.

When a string appears literally in source code, it is known as a string literal and has a representation that denotes it as such.

When geologist Henry De la Beche painted Duria Antiquior, the first widely circulated pictorial representation of a scene from prehistoric life derived from fossil reconstructions, he based it largely on fossils Anning had found, and sold prints of it for her benefit.

When many Hispanics protested that they were not offended, and fondly remembered Speedy Gonzales cartoons as a representation of their youth and nation's individuality, these shorts were made available for broadcast again in 2002.

When an OLE object is placed on the clipboard or embedded in a document, both a visual representation in native Windows formats ( such as a bitmap or metafile ) is stored, as well as the underlying data in its own format.

When Arkansas achieved statehood the same year Texas declared itself an independent republic in 1836 a dispute over the common border arose, with the area in Miller County having representation in both the Arkansas legislature and the Texas congress.

When an orthonormal basis that the vector a is represented in terms of is rotated, a's matrix in the new basis is obtained through multiplying a by a rotation matrix R. This matrix multiplication is just a compact representation of a sequence of dot products.

When the infant was only a few months old, Stone protested a tax assessed on her property, arguing since she was not able to vote, that this was " taxation without representation ".

When voters in the minority concentrate their votes in this way, it increase their chances for obtaining representation in a legislative body.

When Roth in 1962 appeared on a panel alongside the distinguished black novelist Ralph Ellison to discuss minority representation in literature, the questions directed at him soon turned into denunciations.

When France established the Third Republic in 1871, the colonies, Martinique among them, gained representation in the National Assembly.

:; Intermediate representations: When a language is compiled to an intermediate representation, that representation can be optimized or saved for later execution without the need to re-read the source file.

When the intermediate representation is saved, it is often represented as byte code.

When the Estates-General convened in Versailles on 5 May 1789, however, it became clear that the double representation was something of a sham: voting was to occur " by orders ", which meant that the collective vote of the 578 representatives of the Third Estate would be weighed the same as that of each of the other Estates.

When the input data to an algorithm is too large to be processed and it is suspected to be notoriously redundant ( e. g. the same measurement in both feet and meters ) then the input data will be transformed into a reduced representation set of features ( also named features vector ).

" When asked how this individual was " overcome ," he notes that " A creature who has spent his life creating one particular representation of his selfdom will die rather than become the antithesis of that representation.

When the communists took power in China, the agency represented the Chinese Communist Party in countries and territories with which it had no diplomatic representation, such as Hong Kong.