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.

Elizabeth Woodville's arms as queen consort, the royal arms of England Impalement ( heraldry ) | impaling Wooville ( Quartlerly, first argent, a lion rampant double queued gules, crowned or ( Luxemburg, her mother ’ s family ), second quarterly, I and IV, gules a star if eight points argent ; II and III, azure, semée of fleurs de lys or ; third, barry argent and azure, overall a lion rampant gules ; fourth, gules, three bendlets argent, on a chief of the first, charged with a fillet in base or, a rose of the second ( here shown in inverse: the rose should be argent on a chief gules ); fifth, three pallets vairy, on a chief or a label of five points azure, and sixth, a fess and a canton conjoined gules ( Woodville ))

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.

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.

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 ).

* The ring of formal power series over a commutative ring R can be thought of as the inverse limit of the rings, indexed by the natural numbers as usually ordered, with the morphisms from to given by the natural projection.

Notably, Euler directly proved the power series expansions for and the inverse tangent function.

( Indirect proof via the inverse power series technique was given by Newton and Leibniz between 1670 and 1680.

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

In laser physics, gain may refer to the increment of power along the beam propagation direction in a gain medium, and its dimension is m < sup >− 1 </ sup > ( inverse meter ) or 1 / meter.

This consists of a refrigeration cycle, where heat is removed from a low-temperature space or source and rejected to a high-temperature sink with the help of external work, and its inverse, the thermodynamic power cycle.

The multiplicative inverse of a formal power series A is a formal power series C such that AC = 1, provided that such a formal power series exists.

Now we can define division of formal power series by defining B / A to be the product B A < sup > − 1 </ sup >, provided that the inverse of A exists.

With this formalism, we can give an explicit formula for the multiplicative inverse of a power series f whose constant coefficient a

Research at the Massachusetts Institute of Technology suggests that there is evidence the frequency of stock market crashes follows an inverse cubic power law.

Though the dioptre is based on the SI-metric system it has not been included in the standard so that there is no international name or abbreviation for this unit of measurement — within the international system of units this unit for optical power would need to be specified explicitly as the inverse metre ( m < sup >− 1 </ sup >).

The inverse of the power rule enables all powers of a variable except to be integrated.

Historically the power rule was derived as the inverse of Cavalieri's quadrature formula which gave the area under for any integer.

Nowadays the power rule is derived first and integration considered as its inverse.

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.

* Distance-weighted estimator – the measure uses weighting coefficients for x < sub > i </ sub > that are computed as the inverse mean distance between x < sub > i </ sub > and the other data points.

Gravity diminishes according to the inverse square of distance, but centrifugal force increases in direct proportion to the distance.

The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force.

The electric field acts between two charges in a similar manner to the way that the gravitational field acts between two masses, and like it, extends towards infinity and shows an inverse square relationship with distance.

since the magnitude decreases in inverse proportion to the distance travelled, and the phase changes as k times the distance travelled.

As the dimensions of these quantities are the inverse of each other ( one is distance per volume, the other volume per distance ) when taking the mean value of the fuel-economy of a range of cars one measure will produce the harmonic mean of the other – i. e. converting the mean value of fuel economy expressed in litres per 100 km to miles per gallon will produce the harmonic mean of the fuel economy expressed in miles-per-gallon.

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.

In the case of gravity, Newton's law of universal gravitation states that the force is proportional to the inverse square of the distance:

The force on a sail and the actual acceleration of the craft vary by the inverse square of distance from the sun ( unless close to the sun ), and by the square of the cosine of the angle between the sail force vector and the radial from the sun, so

Intermediate-field region: For an antenna, the transition region -- lying between the near-field region and the far-field region -- in which the field strength of an electromagnetic wave is dependent upon the inverse distance, inverse square of the distance, and the inverse cube of the distance from the antenna.

By 1679, Hooke thought gravitation had inverse square dependence and communicated this in a letter to Isaac Newton.

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.

A dependence diagram is equivalent to a success tree analysis ( STA ), the logical inverse of an FTA, and depicts the system using paths instead of gates.

Writing explicitly the dependence of on and the point at which the differentiation takes place and using Lagrange's notation, the formula for the derivative of the inverse becomes

It causes an ion-selective depletion of near surface layers of glasses and gives an inverse square root dependence of corrosion rate with exposure time.

* Technical contradiction-an inverse dependence between parameters / characteristics of a machine or technology ;

where the Euler angles are time-dependent and in fact determine the time dependence of by the inverse of this equation.

A multipole moment usually involves powers ( or inverse powers ) of the distance to the origin, as well as some angular dependence.

Except as noted in the Laplace resonance figure ( below ), a resonance ratio in this article should be interpreted as the ratio of number of orbits completed in the same time interval, rather than as the ratio of orbital periods ( which would be the inverse ratio ).

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 time-domain excitation waveform is formed from the inverse Fourier transform of the appropriate frequency-domain excitation spectrum, which is chosen to excite the resonance frequencies of selected ions.