Therefore rings and Z-algebras are equivalent concepts, in the same way that abelian groups and Z-modules are equivalent.

The Confucian idea of " Rid of the two ends, take the middle " is a Chinese equivalent of Hegel's idea of " thesis, antithesis, and synthesis ", which is a way of reconciling opposites, arriving at some middle ground combining the best of both.

Since ortho derivatives of benzene were never actually found in more than one isomeric form, Kekulé modified his proposal in 1872 and suggested that the benzene molecule oscillates between two equivalent structures, in such a way that the single and double bonds continually interchange positions .< ref >

A MIDI file is in no way a recording of actual music, it is a spreadsheet-like set of instructions, and can use a thousand times less disk space than the equivalent recorded audio.

Flipping front / back and left / right is equivalent to a rotation of 180 degrees about the vertical axis ( in the same way that text which is back-to-front and upside-down simply looks like it has been rotated 180 degrees on the page ).

Enrico Fermi, who developed the theory of beta decay, coined the term neutrino ( the Italian equivalent of " little neutral one ") in 1933 as a way to resolve the confusion.

It is not in any sense a judgement ... hence it is not in any way binding on any state ", while Charles de Visscher argued that in certain situations, an advisory opinion could be binding on the League of Nations Council and, under certain circumstances, some states ; M. Politis agreed, saying that the Court's advisory opinions were equivalent to a binding judgment.

An equivalent way of expressing this is that if most females are looking, for example, for long-tailed males, then each female individually does better to select a long-tailed male, since then her male children are more likely to succeed.

Carl Christian Rafn, in the first detailed study of the Norse exploration of the New World, " Antiquitates Americanae " ( 1837 ), interpreted these times as equivalent to 7. 30am and 4. 30pm, which would put the base a long way south of Newfoundland.

Thus there is no simple way to find an equivalent in the proleptic Julian calendar of a date quoted using the Roman pre-Julian calendar ( AUC or by reference to consuls ).

The idea behind this GA evolution proposed by Emanuel Falkenauer is that solving some complex problems, a. k. a. clustering or partitioning problems where a set of items must be split into disjoint group of items in an optimal way, would better be achieved by making characteristics of the groups of items equivalent to genes.

An 8-bit LRC such as this is equivalent to a cyclic redundancy check using the polynomial x < sup > 8 </ sup >+ 1, but the independence of the bit streams is less clear when looked at that way.

( This is equivalent to the way that an electronic time-domain reflectometer measures reflections caused by changes in the impedance of the cable under test.

In Northern Ireland, the equivalent to a Circuit Judge is a County Court Judge, and they are addressed and titled the same way as a Circuit Judge is in England and Wales.

An equivalent sentence would be " Newly formed bland ideas are inexpressible in an infuriating way.

An equivalent way to express the same process:

An equivalent way to express the same process:

In this way, the polling model is quickly inverted to become equivalent to the callback model, with the application performing its own event dispatching in the original manner.

Because of this correspondence, digital signatures are often described as based on public-key cryptosystems, where signing is equivalent to decryption and verification is equivalent to encryption, but this is not the only way digital signatures are computed.

Walt Disney had long wanted to make a film based on the Uncle Remus storybook, but it wasn't until the mid-1940s that he had found a way to give the stories an adequate film equivalent, in scope and fidelity.

( An equivalent way of stating this is: the smallest back rank interval containing the king, the castling rook, and their destination squares, contains no pieces other than the king and castling rook.

An equivalent way of looking at satisficing is epsilon-optimization ( that means you choose your actions so that the payoff is within epsilon of the optimum ).

After James Prescott Joule had determined the mechanical equivalent of heat, Lord Kelvin approached the question from an entirely different point of view, and in 1848 devised a scale of absolute temperature which was independent of the properties of any particular substance and was based solely on the fundamental laws of thermodynamics.

Hume, on this view, was a proto-positivist, who, in his philosophical writings, attempted to demonstrate how ordinary propositions about objects, causal relations, the self, and so on, are semantically equivalent to propositions about one's experiences.

With this view it turns out that the extractor property is equivalent to: for any source of randomness that gives bits with min-entropy, the distribution is-close to, where denotes the uniform distribution on.

The Roman Catholic Church holds that recognition by the Pope is an essential element in qualifying a council as ecumenical ; Eastern Orthodox view approval by the Pope of Rome as being roughly equivalent to that of other patriarchs.

God's decision, on such a view, is an inventive experience, almost precisely equivalent to the unfolding process of historical events ( thinking like this can be found in modern process theology and open theism ).

He criticized Whorf's examples from an objectivist view of language holding that languages are principally meant to represent events in the real world and that even though different languages express these ideas in different ways, the meanings of such expressions and therefore the thoughts of the speaker are equivalent.

However, some significant differences between neoplatonism and Gregory's thought exist, such as Gregory's statement that beauty and goodness are equivalent, which contrasts with Plotinus ' view that they are two different qualities.

In Georges Dumézil's view, Jovian theology ( and that of the equivalent gods in other Indo-European religions ) is an evolution from a naturalistic, supreme, celestial god identified with heaven to a sovereign god, a wielder of lightning bolts, master and protector of the community ( in other words, of a change from a naturalistic approach to the world of the divine to a socio-political approach ).

In support of this mission, SAMS ' leaders view AMSP as a three-phase program: ( 1 ) military intermediate level education at the United States Army Command and General Staff School or equivalent, ( 2 ) AMSP, and ( 3 ) a tour as an operational planner in the force.

* Suppose & B is equivalent to & D. If we acquire new information A and then acquire further new information B, and update all probabilities each time, the updated probabilities will be the same as if we had first acquired new information C and then acquired further new information D. In view of the fact that multiplication of probabilities can be taken to be ordinary multiplication of real numbers, this becomes a functional equation

This can be useful if extra telephoto reach is desired, as a certain lens on an APS sensor produces an image equivalent to a significantly longer lens on a 35mm film camera shot at the same distance from the subject, the equivalent length of which depends on the camera's field of view crop.

Due to the popularity of the 35 mm standard, camera – lens combinations are often described in terms of their 35 mm equivalent focal length, that is, the focal length of a lens that would have the same angle of view, or field of view, if used on a full-frame 35 mm camera.

On the other hand, Buckingham himself had motivation to kill the Princes, having a claim of his own to the throne equivalent to that of Henry Tudor, depending on one's view of the legitimacy of the Beaufort line.

In literary criticism, stream of consciousness is a narrative mode that seeks to portray an individual's point of view by giving the written equivalent of the character's thought processes, either in a loose interior monologue ( see below ), or in connection to his or her actions.

The two can be shown to be equivalent by Ludwig Boltzmann's statistical view of entropy ( 1870 ).

In this view, complex conjugation corresponds to reflection of a complex number at the x-axis, equivalent to a degree rotation of the complex plane about the Re axis.

So, to determine the focal length of a lens for a digital camera that will give the equivalent angle of view as one on a full-frame camera, the full-frame lens focal length must be divided by the crop factor.

For example, to get the equivalent angle of view of a 30 mm lens on a full-frame 35 mm camera, from a digital camera with a 1. 5 crop factor, one would use a 20 mm lens.

These libertarians view landowners as practically equivalent to the state.

This word had caused much trouble in recent times because of misconceptions that the Latin perfidis was equivalent to " perfidious ", giving birth to the view that the prayer accused the Jews of treachery ( perfidy ), though the word is more correctly translated as " faithless " or " unbelieving ".

Closely related to this, in constructive mathematics, fewer characterisations of compact spaces are constructively valid — or from another point of view, there are several different concepts which are classically equivalent but not constructively equivalent.