* Multiplicative ( self-synchronizing ) scramblers

Multiplicative scramblers ( also known as feed-through ) are called so because they perform a multiplication of the input signal by the scrambler's transfer function in Z-space.

Multiplicative notation is typically used when numerical multiplication or a noncommutative operation interprets the group operation.

The residue classes ( mod n ) that are coprime to n form a group under multiplication ( see the article Multiplicative group of integers modulo n for details.

Multiplicative characters are linearly independent, i. e. if are different characters on a group G then from it follows that.

In November 1944, David Hawkins and Ulam addressed this point in a report entitled " Theory of Multiplicative Processes I ", whose last page gives some suggestions pertinent to bomb design.

Multiplicative scrambler / descrambler is defined similarly by a polynomial ( for the scrambler on the picture it is ), which is also a transfer function of the descrambler.

Multiplicative inverses can be defined over many mathematical domains as well as numbers.

Multiplicative number theory deals with the distribution of the prime numbers, such as estimating the number of primes in an interval, and includes the prime number theorem and Dirichlet's theorem on primes in arithmetic progressions.

* Eliminative and Multiplicative Materialism by Albert P. Carpenter

These include Bayesian Networks, clustering models, latent semantic models such as singular value decomposition, probabilistic latent semantic analysis, Multiple Multiplicative Factor, Latent Dirichlet allocation and markov decision process based models.

Multiplicative constants in the amount of time used do not change the power of DTIME classes ; a constant multiplicative speedup can always be obtained by increasing the number of states in the finite state control.

* Multiplicative composition denies the structural rules of weakening and contraction.

A Fast Algorithm for Computing Multiplicative Inverses in GF ( 2 < sup > m </ sup >) Using Normal Bases.

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

* Multiplicative partition, a way to write a number as a product of other numbers

* Multiplicative number theory ( 1967 )

* Additive scramblers must be reset by the frame sync ; if this fails massive error propagation will result as a complete frame cannot be descrambled.

Mode scramblers are used to provide a modal distribution that is independent of the optical source for purposes of laboratory, manufacturing, or field measurements or tests.

Mode scramblers are primarily used to improve reproducibility of multimode fiber bandwidth measurements.

Unconventional fiber size was not an issue, as they were developed by fiber manufacturers, but some test equipment has difficulty complying with revised qualification standards, and now use " Step Index with Bends " mode scramblers, which can be adjusted to purpose.

Step Index with Bend mode scramblers are created simply by routing a specially designed step-index multimode fiber through a series of small radius bends, or by compressing fiber against surfaces with specific roughness.

Some modern scramblers are actually encryption devices, the name remaining due to the similarities in use, as opposed to internal operation.

Unlike additive scramblers, multiplicative scramblers do not need the frame synchronization, that is why they are also called self-synchronizing.

The first voice scramblers were invented at Bell Labs in the period just before World War II.

It was the need to synchronize the scramblers that suggested to James H. Ellis the idea for non-secret encryption which ultimately led to the invention of both the RSA encryption algorithm and Diffie-Hellman key exchange well before either was reinvented publicly by Rivest, Shamir, and Adleman, or by Diffie and Hellman.

The latest scramblers are not scramblers in the truest sense of the word, but rather digitizers combined with encryption machines.

Using modern public-key systems, these " scramblers " are much more secure than their earlier analog counterparts.

The " scramblers " used in cable television are designed to prevent casual signal theft-not to provide any real security.

Various episodes of Deep Space Nine and Voyager have introduced two anti-transporter devices: transport inhibitors and transporter scramblers.

As shrubs, members of this family may be twine climbers, or scramblers.

Those that lighted on her head or shoulders were most prized by the scramblers.

Above all, scramblers are advised to know their limits and to turn back before they get into difficulties.

A good starting point for budding scramblers is the guides by W A Poucher, which describe the many walking and scrambling routes in the British hills.

Black ice or verglas is a particular problem in cold weather, and mist or fog can disorient scramblers very quickly.

Since good weather is the exception rather than the rule in the British mountains, scramblers normally go equipped with a waterproof jacket and other protective clothing as well as emergency supplies of food and drink.

Additive scramblers ( they are also referred to as synchronous ) transform the input data stream by applying a pseudo-random binary sequence ( PRBS ) ( by modulo-two addition ).

Above all, scramblers are advised to know their limits and to turn back before they get into difficulties.

One problem with sports arbitrage is that bookmakers sometimes make mistakes and this can lead to an invocation of the ' palpable error ' rule, which most bookmakers invoke when they have made a mistake by offering or posting incorrect odds.

Carelessness about this can lead to error.

There was no scoring until the 14th inning when the Mets would take the lead on a Wally Backman single and an error by left fielder Billy Hatcher.

Executable data is particularly error intolerant and read errors would lead to arbitrary results.

It is believed that every word, or marking, has divine meaning, and that not one part may be inadvertently changed lest it lead to error.

While this reasoning error often can produce a relatively good approximation of the correct hypothesis probability value, it can lead to a completely wrong result and wrong conclusion in case the base rate is very low and the reliability of the test is not perfect.

These factors cause an attenuated receiver signal and lead to higher bit error ratio ( BER ).

Michael compounded his error by rebuffing Bryennios after he had already ordered the restored general to lead a division of 3, 000 men to reinforce the army in Cappadocia.

A card played to a lead may be taken up again to save a revoke or to correct the error of not winning a trick when able, and then only prior to another card being led.

What was extraordinary about Cavendish ’ s experiment was its elimination of every source of error and every factor that could disturb the experiment and its precision in measuring an astonishingly small attraction, a mere 1 / 50, 000, 000 of the weight of the lead balls.

In numerical linear algebra the singular values can be used to determine the effective rank of a matrix, as rounding error may lead to small but non-zero singular values in a rank deficient matrix.

A significant error on the Kingsmen's version occurs just after the lead guitar break ; as the group were going by the Wailers ' version, which has a brief restatement of the riff, two times over, before the lead vocalist comes back in, it would be expected that Ely would do the same.

The over-convergence associated with the extra accommodation required to overcome a hyperopic refractive error can precipitate a loss of binocular control and lead to the development of esotropia.

As a result, sampling error can lead to load averages inaccurately representing actual system behavior.

However, Dutch driver Arie Luyendyk disputed Boat's win, claiming that he was in the lead when a scoring error by USAC ( who had scored all IRL races up until that time ) gave Boat the checkered flag.

However, it is incorrect for the browser to place the error message in the page cache, as this would lead it to display the error again when the user tries to load the same page-even after the network is back up.

Austin warns us to take care when removing words from their ordinary usage, giving numerous examples of how this can lead to error.

" For the invincibly ignorant, he saw their path to salvation as being through the mediation of the Church's missionary activity: " the sons of the Catholic Church … should always be zealous to seek them out and aid them, whether poor, or sick, or afflicted with any other burdens, with all the offices of Christian charity ; and they should especially endeavor to snatch them from the darkness of error in which they unhappily lie, and lead them back to Catholic truth and to the most loving Mother the Church, who never ceases to stretch out her maternal hands lovingly to them, and to call them back to her bosom so that, established and firm in faith, hope, and charity, and ' being fruitful in every good work ' ( Colossians 1: 10 ), they may attain eternal salvation.

Although the NORC study was not primarily intended as a determination of which candidate " really won ", analysis of the results, given the hand counting of machine-uncountable ballots due to various types of voter error, indicated that they would lead to differing results, reported in the newspapers which funded the recount, such as The Miami Herald ( The Miami Herald Report: Democracy Held Hostage ) or the Washington Post.

A one-time, single-bit error in either player's interpretation of events can lead to an unending " death spiral ".

The idea was to create a forced error and turn-over, followed by swift movement to Lockett who had ample space to lead into.