This is in contrast to dipole parts of the EM field close to the source ( the near-field ), which varies in power according to an inverse cube power law, and thus does not transport a conserved amount of energy over distances, but instead dies away rapidly with distance, with its energy ( as noted ) either rapidly returning to the transmitter, or else absorbed by a nearby receiver ( such as a transformer secondary coil ).

In these units, both distances and times are expressed in inverse energy units ( while energy and mass are expressed in the same units, see Mass – energy equivalence ).

The energy of a Keesom interaction depends on the inverse sixth power of the distance, unlike the interaction energy of two spatially fixed dipoles, which depends on the inverse third power of the distance.

The two components of the proton-motive force are thermodynamically equivalent: In mitochondria, the largest part of energy is provided by the potential ; in alkaliphile bacteria the electrical energy even has to compensate for a counteracting inverse pH difference.

Firstly, the spreading out of electromagnetic energy in free space is determined by the inverse square law, i. e.

If one allows arbitrary temperature dependence of the prefactor, the Arrhenius description becomes overcomplete, and the inverse problem ( i. e., determining the prefactor and activation energy from experimental data ) becomes singular.

So the inverse relation between momentum and wavelength is consistent with the energy the particle has, and so the energy of the particle has a connection to a wave, all in the same mathematical formulation.

The relative contributions of A, B and C terms to the MCD spectrum are proportional to the inverse line width, energy splitting, and temperature:

As the star collapses, the Fermi energy of the electrons increases to the point where it is energetically favorable for them to combine with protons to produce neutrons ( via inverse beta decay, also termed " neutralization " and electron capture ).

* The inverse square law of universal gravitation necessarily follows from the conservation of energy and of space having three dimensions.

In addition, fast electrons of energy over about 50 MeV may also induce giant dipole resonance in nuclides by a mechanism which is the inverse of internal conversion, and electron linacs can be used directly as sources of " virtual photons " that produce bombardment neutrons by a mechanism similar to that of photoneutrons.

The highest energy photons are believed to be created by inverse compton scattering by a high temperature corona near the black hole.

* The inverse of the solar updraft tower is the downdraft-driven energy tower.

In a nonrenormalizable effective field theory, terms in the Lagrangian do multiply to infinity, but have coefficients suppressed by ever-more-extreme inverse powers of the energy cutoff.

This is because there is no analogue of a bound particle in the unperturbed model and the energy of a soliton typically goes as the inverse of the expansion parameter.

Before the development of silicon power rectifier diodes, cuprous oxide and later selenium was used ; its low efficiency gave it a much higher forward voltage drop ( typically 1. 4 to 1. 7 V per " cell ", with multiple cells stacked to increase the peak inverse voltage rating in high voltage rectifiers ), and required a large heat sink ( often an extension of the diode ’ s metal substrate ), much larger than a silicon diode of the same current ratings would require.

The inverse of the proportionality constant, the " efficiency " of an otherwise-perfect thruster, is proportional to the area of the cross section of the propelled volume of fluid () and the density of the fluid ().

The zoom-lens of attention can be described in terms of an inverse trade-off between the size of focus and the efficiency of processing: because attentional resources are assumed to be fixed, then it follows that the larger the focus is, the slower processing will be of that region of the visual scene since this fixed resource will be distributed over a larger area.

Which is equal to the inverse of the ideal Carnot cycle efficiency because a heat pump is a heat engine operating in reverse.

The maximum theoretical efficiency of a fuel cell is the inverse of that of electrolysis.

If one assumes that the average flux did not change between measurements, a mass-distribution curve is obtained which relates the flux of particles larger than a given radius to the inverse 7/2 power of the radius.

Therefore, N is inversely proportional to the radius cubed and in fair agreement with the inverse 7/2 power derived from 1958 Alpha and 1959 Eta data.

We have shown that the graph of F contains at least one component whose inverse is the entire interval {0,T}, and whose multiplicity is odd.

The difficulty of analysis of any subsystem in the phonology is an inverse function of the size -- smaller systems are more troublesome -- for any given degree of morphophonemic complexity.

* Inverses: by definition every isomorphism has an inverse which is also an isomorphism, and since the inverse is also an endomorphism of the same object it is an automorphism.

The S-box used is derived from the multiplicative inverse over GF ( 2 < sup > 8 </ sup >), known to have good non-linearity properties.

To avoid attacks based on simple algebraic properties, the S-box is constructed by combining the inverse function with an invertible affine transformation.

This is the inverse of the particle-antiparticle annihilation process.

If and are invertible then is also invertible with inverse.

Either approach is adequate for most uses, provided that one attends to the necessary changes in language, notation, and the definitions of concepts like restrictions, composition, inverse relation, and so on.

A common misconception is to use inverse order of encryption as decryption algorithm ( i. e. first XORing P17 and P18 to the ciphertext block, then using the P-entries in reverse order ).

The decryption algorithm D is defined to be the inverse function of encryption, i. e., D = E < sup >− 1 </ sup >.

The inverse of this mapping ( and its first-order bilinear approximation ) is

Another method is to measure the brightness of an object and assume an intrinsic luminosity, from which the distance may be determined using the inverse square law.

A necessary and sufficient condition for this inverse function to exist is that the determinant of the Jacobian Matrix, often referred to simply as the Jacobian, should be different from zero.

It has an inverse which is denoted.

This formula is true whenever g is differentiable and its inverse f is also differentiable.

The dipole field has an intensity of about 30, 000-60, 000 nanoteslas ( nT ) at the Earth's surface, and its intensity diminishes as the inverse of the cube of the distance, i. e. at a distance of 2 Earth radii it only amounts to 1 / 8 of the surface field in the same direction.

Generally, for an irrotational vector field in n-dimensional Euclidean space, the intensity " I " of the vector field falls off with the distance " r " following the inverse ( n − 1 )< sup > th </ sup > power law

Sound intensity follows an inverse square law with distance from the source ; doubling the distance from a noise source reduces its intensity by a factor of four, or 6 dB.

Light from a point source travels in a spherical wave, decreasing in intensity ( or illuminance ) as the inverse square of the distance travelled.

* Some modern music is created using spectrograms as an intermediate medium ; changing the intensity of different frequencies over time, or even creating new ones, by drawing them and then inverse transforming.

Radiative far-field intensity decays more slowly with distance, following the inverse square law for total EM power that is typical of all electromagnetic radiation.

In a normal three dimensional setting, with a point source and point receptor, the intensity of sound waves will be attenuated according to the inverse square of the distance from the source.

The results showed that each of the behavioral variables ( temper frequency, temper intensity, irritability, crying, and demanding attention ) had a significant inverse relationship with attention span.

The ENZ-theory has also been applied to the characterization of optical instruments with respect to their aberration by measuring the through-focus intensity distribution and solving an appropriate inverse problem.

In photography reciprocity is the inverse relationship between the intensity and duration of light that determines the reaction of light-sensitive material.

The first zonal trip generation ( and its inverse, attraction ) analysis in the Chicago Area Transportation Study ( CATS ) followed the “ decay of activity intensity with distance from the central business district ( CBD )” thinking current at the time.

Its inverse is capital intensity.

( It can be easily and practically verified that a focused beam does not follow the simple inverse square law by measuring the light intensity of a household torch or theatre spotlight beam at various distances from the lamp.

This relationship is termed inverse proportional, often incorrectly described as the inverse square law ; the latter applies to sound intensity, not sound pressure.