The original form of the theorem, contained in a third-century AD book The Mathematical Classic of Sun Zi ( 孫子算經 ) by Chinese mathematician Sun Tzu and later generalized with a complete solution called Da yan shu ( 大衍术 ) in a 1247 book by Qin Jiushao, the Shushu Jiuzhang ( 數書九章 Mathematical Treatise in Nine Sections ) is a statement about simultaneous congruences ( see modular arithmetic ).

:# With all the b < sub > i </ sub > known, we have enough simultaneous congruences to determine x using the Chinese remainder theorem.

The CRTC's simultaneous substitution rules require that when a Canadian network licences a television show from a US network and shows it in the same time slot, upon request by the Canadian broadcaster, Canadian broadcast distributors must replace the show on the US channel with the broadcast of the Canadian channel, along with any overlays and commercials.

The Oxford Dictionary of Music shows hemiola as a vertical 3: 2 ( three beats simultaneous with two beats ).

Following many budget cuts to local programming beginning in 1996, the vast majority of shows played on CJOH-DT simply consists of American programming simultaneous substitutions, or simsubs.

In the early 1960s, coaxial cable links, formed initially between Sydney and Melbourne, allowed the sharing of programmes and simultaneous broadcasts of live shows.

With the simultaneous ascendancy of alternative comedy, however, the popularity of light entertainment shows started to decline among audiences.

A CFA cat show actually consists of a number of simultaneous cat shows running at the same time within the same place.

In order to accommodate such a time zone difference and maximize simultaneous substitution opportunities with the American stations carried on cable, CIHF's schedule deviates from that of most other Global O & Os, with some shows airing on different nights compared to other Global stations.

" While the 208 wavelength schedule of Radio Luxembourg was aimed at serving the British Isles with a commercial radio station format of American shows that were not provided by the monopoly of the non-commercial BBC, its actual audience covered much of Europe and beyond via its simultaneous transmissions over 49. 26 meters in the Shortwave Band.

There were also 6 simultaneous fringe shows:

This first example shows how a genitive absolute with a present participle is used with simultaneous actions.

) This is the same system as was used in the field-sequential color-TV system which preceded the present simultaneous system.

It is distinctly possible, therefore, that simultaneous pressures in all three vessels would have rendered the shunts inoperable and hence, uninjectable.

James, he remarks in a letter to a friend, `` is attempting the impossible namely, to produce upon the reader, as a painting produces upon the gazer, a number of superimposed, simultaneous impressions.

In simultaneous microsporogenesis, there is no wall formation until all four cell nuclei are present.

Elaborate arborization is important for it allows for the simultaneous transmission of messages to a large number of target neurons within a single region of the brain.

As Th1 response is required for an effective immune response to tuberculous infection, concurrent infection with various parasites produces a simultaneous Th2 response, which blunts the effect of BCG.

Another type of MT is known as simultaneous multithreading, where instructions of multiple threads are executed in parallel within one CPU clock cycle.

The masking threshold is calculated using the absolute threshold of hearing and the principles of simultaneous masking — the phenomenon wherein a signal is masked by another signal separated by frequency, and, in some cases, temporal masking — where a signal is masked by another signal separated by time.

Comorbidity is the simultaneous presence of two or more medical conditions, such as schizophrenia and substance abuse.

The latency period is the time between infection and the ability of the disease to spread to another person, which may precede, follow, or be simultaneous with the appearance of symptoms.

The central idea of Diophantine geometry is that of a rational point, namely a solution to a polynomial equation or system of simultaneous equations, which is a vector in a prescribed field K, when K is not algebraically closed.

It is, in fact, possible to have multiple simultaneous de jure legalities that are not de facto.

In addition, a crucial element in polylogic epistolary novels like Clarissa, and Dangerous Liaisons is the dramatic device of ' discrepant awareness ': the simultaneous but separate correspondences of the heroines and the villains creating dramatic tension.

A DTM-capable mobile may use simultaneous voice and packet data, with the network coordinating to ensure that it is not required to transmit on two different frequencies at the same time.

Furthermore, available fingerstick glucose meters are only warranted to be accurate to within 15 % of a simultaneous laboratory value under optimal conditions, and home use in the investigation of hypoglycemia is fraught with misleading low numbers.

In more modern music, the fifth finger is used very rarely, for example in simultaneous cluster chords, such as in Daniel Kessner's Sonatina.

Although the resulting energy eigenfunctions ( the orbitals ) are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian ( that is, the energy eigenstates ) can be chosen as simultaneous eigenstates of the angular momentum operator.

Under Galilean transformations, the time t < sub > 2 </ sub > − t < sub > 1 </ sub > between two events is the same for all inertial reference frames and the distance between two simultaneous events ( or, equivalently, the length of any object, | r < sub > 2 </ sub > − r < sub > 1 </ sub >|) is also the same.

Integrated Services Digital Network ( ISDN ) is a set of communications standards for simultaneous digital transmission of voice, video, data, and other network services over the traditional circuits of the public switched telephone network.

" The Court allowed the guilty plea only with a simultaneous protestation of innocence as there was enough evidence to show that the prosecution had a strong case for a conviction, and the defendant was entering such a plea to avoid this possible sentencing.

However, the difference from the electromagnetic aether of Maxwell and Lorentz lies in the fact, that " because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four dimensional, since there was no objective way of ordering its states by time alone .".

This allows for output rates that exceed 57 kHz per channel and increases the number of possible voices ( simultaneous sounds ) through software mixing.

Somewhat earlier, exploration of mathematical practice and quasi-empiricism in mathematics from the 1950s to 1980s had sought alternatives to metamathematics in social behaviours around mathematics itself: for instance, Paul Erdős's simultaneous belief in Platonism and a single " big book " in which all proofs existed, combined with his personal obsessive need or decision to collaborate with the widest possible number of other mathematicians.

They show explicitly that the necessary condition to realize a negative ( pulling ) optical force is the simultaneous excitation of multipoles in the particle and if the projection of the total photon momentum along the propagation direction is small, attractive optical force is possible.

Hans Daalder, Professor of political science at the Rijksuniversiteit Leiden wrote: " Did such simultaneous developments not result in a possible failure to lay down the limits of the royal prerogratives with some precision-which implied that the view of the King as the Keeper of the Nation, with rights and duties of its own, retained legitimacy?

Composition Zones pushes collaboration a step further than just simultaneous text / picture ( as possible with Quark CopyDesk since 1991 ), as it allows layout and graphic elements to be edited outside the layout application.

After the advent of the telegraph, simultaneous surface weather observations became possible for the first time, and beginning in the late 1840s, the Smithsonian Institution became the first organization to draw real-time surface analyses.

Everything possible was done in order to decrease access times and increase data rates ( bandwidth ), including the simultaneous use of multiple grids of core, each storing one bit of a data word.

In the 1980s further software ( mainly from third-party vendors ) made it possible for a terminal to have simultaneous sessions with different applications or application environments.

The simultaneous increase in car ownership in the 1940s and 1950s made the development of Endwell possible.

It should be noted that " internationalized " does not necessarily mean that a system can be used absolutely anywhere, since simultaneous support for all possible locales is both practically almost impossible and commercially very hard to justify.

Rainbow tables are tested against a captured WPA / WPA2 Hash Code via a computer's processor with relatively low numbers of simultaneous processes possible.

This would explain the rumour of victory and near simultaneous attack, but is only one possible theory.

Multitracking became possible with the idea of simultaneously recording different audio channels to separate discrete " tracks " on the same tape — a " track " was simply a different channel recorded to its own discrete area on tape whereby their relative sequence of recorded events would be preserved, and playback would be simultaneous or synchronized.

Given a set S of matrices, each of which is diagonalizable, and any two of which commute, it is always possible to simultaneously diagonalize all of the elements of S. Equivalently, for any set S of mutually commuting semisimple linear transformations of a finite-dimensional vector space V there exists a basis of V consisting of simultaneous eigenvectors of all elements of S. Each of these common eigenvectors v ∈ V, defines a linear functional on the subalgebra U of End ( V ) generated by the set of endomorphisms S ; this functional is defined as the map which associates to each element of U its eigenvalue on the eigenvector v. This " generalized eigenvalue " is a prototype for the notion of a weight.

In 1976, Taito released Crashing Race, a simultaneous two-player competitive car racing game where each player must try to crash as many computer-controlled cars as possible to score points, and the player with the most points wins.

This way 64 simultaneous colors are possible ( 32 arbitrary colors plus 32 half-bright components ) while only using 32 color registers.

In particular, commensurability involves the extent to which paradigmatic concerns " can be retrofitted to each other in ways that make the simultaneous practice of both possible ".

Books and other written materials have described a number of possible ways to use the sword including " fast draw techniques centered around drawing the sword and cutting as a simultaneous defensive or attacking action ", with " a thrust fencing technique ", and with a " reverse grip ".

It is possible that this background afterimage induces simultaneous contrast on the " empty shape ".

After the advent of the telegraph, simultaneous surface weather observations became possible for the first time, and beginning in the late 1840s, the Smithsonian Institution became the first organization to draw real-time surface analyses.