This can be seen from the inverse properties above: operating twice gives the original data in reverse order, so operating four times gives back the original data and is thus the identity matrix.

However, this distribution of meanings between the two terms used to be precisely inverse at the time they were coined: The Oxford English Dictionary defined “ racialism ” as “ belief in the superiority of a particular race ” and gives a 1907 quote as the first recorded use.

f. Thus, every pair of ( mutually ) inverse elements gives rise to two idempotents, and ex

It shows how astronomical observations prove the inverse square law of gravitation ( to an accuracy that was high by the standards of Newton's time ); offers estimates of relative masses for the known giant planets and for the Earth and the Sun ; defines the very slow motion of the Sun relative to the solar-system barycenter ; shows how the theory of gravity can account for irregularities in the motion of the Moon ; identifies the oblateness of the figure of the Earth ; accounts approximately for marine tides including phenomena of spring and neap tides by the perturbing ( and varying ) gravitational attractions of the Sun and Moon on the Earth's waters ; explains the precession of the equinoxes as an effect of the gravitational attraction of the Moon on the Earth's equatorial bulge ; and gives theoretical basis for numerous phenomena about comets and their elongated, near-parabolic orbits.

* Multiplicative inverse, in mathematics, the number 1 / x, which multiplied by x gives the product 1, also known as a reciprocal

Homogenizing the vector, or multiplying it by the inverse of the homogeneous variable such that the homogeneous variable becomes unitary, gives us our resulting 2-D location in the x and y coordinates.

In mathematical analysis, the Lagrange inversion theorem, also known as the Lagrange – Bürmann formula, gives the Taylor series expansion of the inverse function of an analytic function.

For spherical and hyperbolic spatial geometries, the curvature gives a scale ( either by using the radius of curvature or its inverse ), a fact noted by Carl Friedrich Gauss in an 1824 letter to Franz Taurinus.

The inverse power method, which finds some smallest root first, is what drives the Jenkins – Traub method and gives it its numerical stability and fast convergence even in the presence of multiple or clustered roots.

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.

Furthermore, for any nonzero complex number z, conjugation gives a multiplicative inverse,

* Multiplying by-1 gives the additive inverse: (- 1 ) v =-v.

Stated another way, the inverse function gives the solution for y of the equation

In mathematics, specifically differential calculus, the inverse function theorem gives sufficient conditions for a function to be invertible in a neighborhood of a point in its domain.

The theorem also gives a formula for the derivative of the inverse function.

In this case, the theorem gives a formula for the Jacobian matrix of the inverse.

gives a formula for the inverse.

He gives the formulae in the inverse order ; i. e. first the formula to be used by a soul which has passed through the highest heaven and desires to enter the Ogdoad ; next the formula to be used in order to gain admission to the highest heaven, and so on.

There are norm maps whenever, and this gives us the data of an inverse system.

( There is a notorious trap here: cohomology does not commute with taking inverse limits, and the ℓ-adic cohomology group, defined as an inverse limit, is not the cohomology with coefficients in the étale sheaf Z < sub > l </ sub >; the latter cohomology group exists but gives the " wrong " cohomology groups.

For a correspondence of curves, there is a more general formula, Zeuthen's theorem, which gives the ramification correction to the first approximation that the Euler characteristics are in the inverse ratio to the degrees of the correspondence.

Applying the inverse system to gives the following.

Temporal filtering amounts to removing the periodic waves not of interest to us from the power spectrum, and then summing the waves back again, using the inverse Fourier transform to create a new timecourse for the voxel.

correlate and store a huge amount of information-and have the advantage that the inverse transform returns the results of correlation into the spatial and temporal patterns that guide us in navigating our universe.

The more general concept of sousveillance goes beyond just inverse surveillance and the associated twentieth century political " us versus them " framework for citizens to photograph police, shoppers to photograph shopkeepers, or passengers to photograph taxicab drivers.

So we see that the inverse system allows us to determine uniquely the input from the output.

The action principle then tells us that the variation of this action with respect to the inverse metric is zero, yielding

" " It typifies Davis's method that her ' historical ' chapters reflect an inverse relationship between what available sources, documents, statistics, and the like allow us to know about women in a given period and the space she devotes to that period.

Since tangents and inverse tangents are both continuous, our identification function is a homeomorphism between the real line and the unit circle without ∞.

Berlin's argument was partly grounded in Wittgenstein's later theory of language, which argued that inter-translatability was supervenient on a similarity in forms of life, with the inverse implication that our epistemic access to other cultures entails an ontologically contiguous value-structure.

Thus, our sampling of the DTFT causes the inverse transform to become periodic.

However in mono-vision, such as that of photographs, the elimination of our depth perception causes multistable perception to take over, and this can cause the craters to inverse their depth values and instead look like plateaus rather than pits.

# Inverse cosine: Using an inverse cosine table, find two angles whose cosines are our two values.

Forward kinematic animation can be distinguished from inverse kinematic animation by this means of calculation-in inverse kinematics the orientation of articulated parts is calculated from the desired position of certain points on the model.

In the Fourier domain or FFT domain you correct the frequency response according to your desired specs and compute the inverse FFT.

Proximity effects ( due to electron scattering ) can be addressed by solving the inverse problem and calculating the exposure function E ( x, y ) that leads to a dose distribution as close as possible to the desired dose D ( x, y ) when convolved by the scattering distribution point spread function PSF ( x, y ).

In " inverse scanning ", the switch is held down to advance the scan, and released to choose the desired iem.

* However, if we think of as the field of real numbers, then the direct product does not exist-naively defining in a similar manner to the above examples would not result in a field since the element does not have a multiplicative inverse.

As a result, we can speak of the inverse of an element, rather than an inverse.

Roos has since shown ( in " Derived functors of inverse limits revisited ") that his result is correct if C has a set of generators ( in addition to satisfying ( AB3 ) and ( AB4 *)).

In 1953, B. Smith showed that a nonlinear DAC could result in the inverse nonlinearity in a successive-approximation ADC configuration, simplifying the design of digital companding systems.

This fundamental result enables the inverse square law of gravitation to be applied to the real solar system to a very close degree of approximation.

Newton's tract ' De motu ...', which he sent to Halley in late 1684, derived what are now known as the three laws of Kepler, assuming an inverse square law of force, and generalized the result to conic sections.

* Logarithm, ( often abbreviated as log ) the mathematical operation that is the inverse of exponentiation, or the result of this operation

Conversely, by the inverse function theorem, there can be at most one value for σ that, when applied as an input to, will result in a particular value for C.

As an important result, the inverse function theorem has been given numerous proofs.

It is also observed that the result can be described as an inverse limit in the category of graded rings.

are often used for arcsin, arccos, etc., but this convention logically conflicts with the common semantics for expressions like sin < sup > 2 </ sup >( x ), which refer to numeric power rather than function composition, and therefore may result in confusion between multiplicative inverse and compositional inverse.

With the inverse of A available, it is only necessary to find the inverse of C < sup >− 1 </ sup > + VA < sup >− 1 </ sup > U in order to obtain the result using the right-hand side of the identity.

The Sunyaev – Zel ' dovich effect ( often abbreviated as the SZ effect ) is the result of high energy electrons distorting the cosmic microwave background radiation ( CMB ) through inverse Compton scattering, in which the low energy CMB photons receive an average energy boost during collision with the high energy cluster electrons.

Sometimes the result is expressed as percent transmission and sometimes it is expressed as the inverse logarithm of the transmission.

hence for the inverse iteration method similar result sounds as:

Mirtazapine is a very strong H < sub > 1 </ sub > receptor inverse agonist and as a result, it can cause powerful sedative and hypnotic effects.

An inverse Laplace transform of this result will yield the output in the time domain.

As a result, the transpose of Q is equal to the inverse of Q: Q is an orthogonal matrix.

Each type in the tower conceptually " sits on " a more fundamental type, so an integer is a rational number and a number, but the inverse is not necessarily true, i. e. not every number is an integer ; this asymmetry implies that a language can allow implicit coercions of numerical types — without creating semantic problems — in only one direction: coercing an integer to a rational loses no information and does not affect the results of a function, but to coerce most reals to an integer could well result in a problem ( for example, the real 1 / 3 does not equal any integer ).

Semilattices can also be defined algebraically: join and meet are associative, commutative, idempotent binary operations, and any such operation induces a partial order ( and the respective inverse order ) such that the result of the operation for any two elements is the least upper bound ( or greatest lower bound ) of the elements with respect to this partial order.

This is a simple form of inverse modeling, since the result ( s ) is measured in the well, r, t, and Q are observed, and values of T and S which best reproduce the measured data are put into the equation until a best fit between the observed data and the analytic solution is found.