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

He formulated the second law of electrolysis stating " the amounts of bodies which are equivalent to each other in their ordinary chemical action have equal quantities of electricity naturally associated with them.

This is equivalent to stating that the average distance separating the gas particles is large compared to their size.

Following is a list of rivers stating the Latin and equivalent English name.

While the laogai has attracted widespread criticism for the poor conditions in the prisons, Seymour and Anderson claim that reports are exaggerated, stating that " even at its worst, the laogai is not, as some have claimed, ' the Chinese equivalent of the Soviet gulag.

There are several different ways of stating Langlands conjectures, which are closely related but not obviously equivalent.

An equivalent way of stating the law is that the solubility of a gas in a liquid is directly proportional to the partial pressure the gas above the liquid.

Propositions 30 and 32 together are essentially equivalent to the fundamental theorem of arithmetic stating that every positive integer can be written as a product of primes in an essentially unique way, though Euclid would have had trouble stating it in this modern form as he did not use the product of more than 3 numbers.

In view of property 3, the integrality condition is equivalent to stating that β and its reflection σ < sub > α </ sub >( β ) differ by an integer multiple of α.

If S is a set of graphs, and M is a subset of S containing one representative graph for each equivalence class of minimal elements ( graphs that belong to S but for which no proper minor belongs to S ), then M forms an antichain ; therefore, an equivalent way of stating the theorem is that, in any infinite set S of graphs, there must be only a finite number of non-isomorphic minimal elements.

Another equivalent way of stating this is that any set of graphs can have only a finite number of minimal elements under the minor ordering.

Brennan concluded by stating that electrocution is " nothing less than the contemporary technological equivalent of burning people at the stake.

The concept of relative rest is closely linked to that of inertial observers and the statement that nothing is at absolute rest is loosely equivalent to stating that there are no frames of reference which are truly inertial.

The Austrian School of economics is critical of fractional-reserve banking, stating that the increase of money in the banking system is equivalent to an artificial injection of credit, which is the source of the business cycle.

The theory of perfect graphs developed from a 1958 result of Tibor Gallai that in modern language can be interpreted as stating that the complement of a bipartite graph is perfect ; this result can also be viewed as a simple equivalent of König's theorem, a much earlier result relating matchings and vertex covers in bipartite graphs.

An equivalent way of stating Dilworth's theorem is that, in any finite partially ordered set, the maximum number of elements in any antichain equals the minimum number of chains in any partition of the set into chains.

Coakley opposed with a brief stating that, under military law, a persistent refusal to work by two or more men — something that might be called a " strike " among civilians — was sufficient proof of a conspiracy to override superior military authority and was equivalent to mutiny.

Birkett ( 2003 ) defined bioequivalence by stating that, " two pharmaceutical products are bioequivalent if they are pharmaceutically equivalent and their bioavailabilities ( rate and extent of availability ) after administration in the same molar dose are similar to such a degree that their effects, with respect to both efficacy and safety, can be expected to be essentially the same.

Haines was later to claim that this was the album that started Britpop, though he later showed disdain towards the movement, stating in a 2003 interview that Britpop consisted of " a bunch of bands who weren't good enough to exist in their own right, like music's equivalent of the Bloomsbury Group.

This behaviour is commonly described by stating the effective dielectric constant ( or effective relative permittivity ) of the microstrip ; this being the dielectric constant of an equivalent homogeneous medium ( i. e., one resulting in the same propagation velocity ).

Proponents typically quote the Journal of the American Medical Association stating: " A moderately conditioned person can easily sweat off 500 grams in a sauna, consuming nearly 300 kcal, which is equivalent to running 2 – 3 miles.

In the Baopuzi, Ge places a high value on literature and regards writing as an act of social and political significance, equivalent to virtuous action, and at one point stating, " The relationship between writings and virtuous actions is that of two different names for one thing ".

This is equivalent to stating that for a complete market, all cash flows for a trading strategy can be replicated using a similar synthetic trading strategy.