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.

An equivalent way to view an extractor is as a bivariate function

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.

A choice of isomorphism is equivalent to a choice of basis for V ( by looking at the image of the standard basis for R < sup > n </ sup > in V ).

It was an integral part of the Confucian philosophy and was seen by the Chinese as equivalent to the familial relation of younger sons looking after older parents by devoting part of their wealth, assets, or goods to that purpose.

As with Lagrangian mechanics, Hamilton's equations provide a new and equivalent way of looking at Newtonian physics.

* Banana equivalent dose-a whimsical way of looking at radiation exposure

But behind the self-publicizing avant-garde antics, Ramón developed not only an extravagant public persona ( megalomaniac some would say ), but also his own equivalent of what Shattuck defines as a ‘ reversal of consciousness ’, deliberately divesting himself of conventional ways of thinking and being in order to adopt a peculiarly innovative, almost phenomenological, way of looking at the world, one which influenced the younger 1927 Generation of poets ( as Luis Cernuda has explained ) and in Ramón ’ s case produced some of the most original and brilliantly creative prose writing of the period.

It is the Thévenin equivalent impedance looking back into the output terminals.

Tescos is also looking to develop a site just off the bypass to build a supermarket equivalent in size to Morrisons in Chippenham.

Graduating with an education equivalent to that of high school, Lat started looking for a job and had his sights set on becoming an illustrator.

Roger Hodgson has said that the song was written to be an equivalent to " Gone Hollywood ", looking at how Americans live, though he confessed that he had only a limited familiarity with USA culture at the time of writing.

Suggesting a connection of hearwa with Gothic hauri " coal ", Old Norse hyr-r " fire ", Old English heorþ " to roast ", heorð " hearth ", Tolkien tentatively concludes that in the Sigelhearwan we may be looking at " rather the sons of Muspell than of Ham ", an ancient class of demons " with red-hot eyes that emitted sparks and faces black as soot ", English equivalent of the Norse fire giants ruled by Surtr,

Measuring ' the ' price level involves looking at goods other than burgers, but most goods in a consumer price index ( CPI ) show the same pattern ; equivalent things tend to cost more in high income countries.

( An equivalent form is the Landau-Lifshitz-Gilbert equation, which replaces the final term by a more " simply looking " equivalent one.

But, in spite of this, I, at present a man 31 years of age and a College Professor, have been recalled `` by direction of the President '' to report on November 25th to Fort Devens, Massachusetts, for another twelve months of Active Duty as an Sp 4 ( the equivalent of a PFC ).

Conventional energy for processing foods is available in the range of at most a few cents per kwhr for electric power and the equivalent of a few mills per kwhr for process steam.

This reduces to the relationship: Af, where Af is the intercept at zero thickness of the extrapolation of the slope indicated in eqn. ( 1 ), Af is the thickness of the coating equivalent to the rounding off of the knife tip, Af is a straight line first approximation of this roundness, and the other symbols are equivalent to those of eqn. ( 1 ).

Most European domestic power supplies run at 230 V, so the current drawn by a particular European appliance ( in Europe ) will be less than for an equivalent American one ( in the United States ).< ref group =" Note "> The formula for power is given by

In that case it is equivalent to saying that if we have several ( a finite number of ) boxes, each containing at least one item, then we can choose exactly one item from each box.

Economic analysts say that the project would cost at least $ 1 billion ( equivalent to about 40 percent of Armenia's 2008 state budget ).

On the scale he used, the boiling-point of water was marked at + 73 and the melting-point of ice at 51, so that the zero of his scale was equivalent to about − 240 on the Celsius scale.

His steel enterprises were bought out at a figure equivalent to 12 times their annual earnings —$ 480 million ( presently, $) which at the time was the largest ever personal commercial transaction.

The absolute magnitude is then equivalent to the apparent magnitude an object would have if it were at a standard luminosity distance ( 10 parsecs ) away from the observer, in the absence of astronomical extinction.

The total value of the prizes captured at the Nile and subsequently bought into the Royal Navy was estimated at just over £ 130, 000 ( the equivalent of £ as of )

Occasionally a code word achieves an independent existence ( and meaning ) while the original equivalent phrase is forgotten or at least no longer has the precise meaning attributed to the code word.

Prior to the creation of the group management board in 2006, HSBC's chairman essentially held the duties of a chief executive at an equivalent institution, while HSBC's chief executive served as the deputy.

It relies on the following equivalent definition of differentiability at a point: A function g is differentiable at a if there exists a real number g ′( a ) and a function ε ( h ) that tends to zero as h tends to zero, and furthermore

* It is Turing equivalent to the halting problem and thus at level of the arithmetical hierarchy.

Scanning velocity is 1. 2 – 1. 4 m / s ( constant linear velocity ) – equivalent to approximately 500 rpm at the inside of the disc, and approximately 200 rpm at the outside edge.

Such a definition can be formulated in terms of equivalence classes of smooth functions on M. Informally, we will say that two smooth functions f and g are equivalent at a point x if they have the same first-order behavior near x.

Tadpoles have been found to tolerate salt concentrations equivalent to at most 15 % that of seawater.

Similarly, the men of the Mountain Land from north of Kabol-River equivalent to medieval Kohistan ( Pakistan ), figure in the army of Darius III against Alexander at Arbela with a cavalry and fifteen elephants.