This paper introduced what is now called the ring of Gaussian integers, the set of all complex numbers a + bi where a and b are integers.

The ring of Gaussian integers was introduced by Carl Friedrich Gauss in his second monograph on quartic reciprocity ( 1832 ) ( see ).

This paper not only introduced the Gaussian integers and proved they are a unique factorization domain, it also introduced the terms norm, unit, primary, and associate, which are now standard in algebraic number theory.

where is the optical phase error introduced by atmospheric turbulence, R ( k ) is a 2 dimensional square array of independent random complex numbers which have a Gaussian

Erwin Schrödinger was searching for the most classical-like states when he first introduced minimum uncertainty Gaussian wave-packets.

McMurchie and Davidson ( 1978 ) introduced Hermite Gaussian functions to take advantage of differential relations.

This is also the instant at which TAI introduced corrections for gravitational time dilation.

Finally, it should be noted that some early generalizations of Einstein's gravitational theory, known as classical unified field theories, either introduced a cosmological constant on theoretical grounds or found that it arose naturally from the mathematics.

) Newton's gravitational attraction, an invisible force able to act over vast distances, had led to criticism that he had introduced " occult agencies " into science.

The reformulation of general relativity introduced by Ashtekar, which goes under the name of Ashtekar variables represents the gravitational field using fields similar to the electric and magnetic fields.

This fan shape can also be explained with a thermodynamic justification: the system of sediment introduced at the apex of the fan will tend to a state which minimizes the sum of the transport energy involved in moving the sediment and the gravitational potential of material in the fan.

Samuel Tolver Preston illustrated that many of the postulates introduced by Le Sage concerning the gravitational particles, such as rectilinear motion, rare interactions, etc .., could be collected under the single notion that they behaved ( on the cosmological scale ) as the particles of a gas with an extremely long mean free path.

This is also the instant at which TAI introduced corrections for gravitational time dilation.

This is also the instant at which TAI introduced corrections for gravitational time dilation.

Freundlich was a working associate of Albert Einstein and introduced experiments for which the general theory of relativity could be tested by astronomical observations based on the gravitational redshift.

Wheeler introduced the notion of geons, gravitational wave packets confined to a compact region of spacetime and held together by the gravitational attraction of the ( gravitational ) field energy of the wave itself.

In theoretical physics, when Einstein originally tried to produce a general theory of relativity, he found that the theory seemed to predict the gravitational collapse of the universe: it seemed that the universe should either be expanding or collapsing, and to produce a model in which the universe was static and stable ( which seemed to Einstein at the time to be the " proper " result ), he introduced an expansionist variable ( called the Cosmological Constant ), whose sole purpose was to cancel out the cumulative effects of gravitation.

Terms were introduced, including black holes and ' gravitational singularity '.

During this period, many of the concepts and terms which continue to inspire the imagination of gravitation researchers ( and members of the general public ) were introduced, including black holes and ' gravitational singularity '.

when Josiah Willard Gibbs introduced " a heat function for constant pressure ".

He introduced a string of austerity measures ( the " Bokros Package ") on 12 March 1995 which had the following key points: one-time 9 % devaluation of the forint, introducing a constant sliding devaluation, 8 % additional customs duty on all goods except for energy sources, limitation of growth of wages in the public sector, simplified and accelerated privatization.

He also introduced the concept of the chemical potential of a given chemical species, defined to be the rate of the increase in U associated with the increase in the number N of molecules of that species ( at constant entropy and volume ).

Two drugs named zanamivir ( Relenza ) and oseltamivir ( Tamiflu ) that have been recently introduced to treat influenza prevent the release of viral particles by blocking a molecule named neuraminidase that is found on the surface of flu viruses, and also seems to be constant across a wide range of flu strains.

However, note that depending on the language and the function, NaNs can silently be removed in expressions that would give a constant result for all other floating-point values e. g. NaN ^ 0, which may be defined as 1, so in general a later test for a set INVALID flag is needed to detect all cases where NaNs are introduced ( see section Function definition below for further details ).

Arnold Sommerfeld introduced the fine-structure constant in 1916.

Arnold Sommerfeld introduced the fine-structure constant in 1916, as part of his theory of the relativistic deviations of atomic spectral lines from the predictions of the Bohr model.

The interpretation of Bradford's law in terms of a geometric progression was suggested by V. Yatsko who introduced an additional constant and demonstrated that Bradford distribution can be applied to a variety of objects, not only to distribution of articles or citations across journals.

However, should this introduced coefficient contain a variable, while the original number has a constant meaning, this has no bearing if the new term stays constant as the introduced coefficient will always override the constant expression-for example, in when x is multiplied by 2, the result, 2x, is not constant ; while 1 *-2 is-2 and still a constant.

Additional instructions were supported via the Operate ( Opr ) instruction code, which decoded the constant operand as an extended zero-operand opcode, providing for almost endless and easy instruction set expansion as newer implementations of the transputer were introduced.

In the mid-1990s, Janssen Pharmaceutica developed and introduced into clinical trials the Duragesic patch, which is a formation of an inert alcohol gel infused with select fentanyl doses which are worn to provide constant administration of the opioid over a period of 48 to 72 hours.

Plato is said to have introduced Sophron's works into Athens and to have made use of them in his dialogues ; according to the Suda, they were Plato's constant companions, and he even slept with them under his pillow.

The original usage of the term, as introduced by Black, was applied to systems that were intentionally held at constant temperature.

The term latent heat was introduced into calorimetry around 1750 by Joseph Black when studying system changes, such as of volume and pressure, when the thermodynamic system was held at constant temperature in a thermal bath.

In general topological spaces, however, the different notions of compactness are not necessarily equivalent, and the most useful notion, introduced by Pavel Alexandrov and Pavel Urysohn in 1929, involves the existence of certain finite families of open sets that " cover " the space in the sense that each point of the space must lie in some set contained in the family.

Gauss also made important contributions to number theory with his 1801 book Disquisitiones Arithmeticae ( Latin, Arithmetical Investigations ), which, among things, introduced the symbol ≡ for congruence and used it in a clean presentation of modular arithmetic, contained the first two proofs of the law of quadratic reciprocity, developed the theories of binary and ternary quadratic forms, stated the class number problem for them, and showed that a regular heptadecagon ( 17-sided polygon ) can be constructed with straightedge and compass.

The concept of using a pair of axes was introduced in later work by commentators who were trying to clarify the ideas contained in Descartes ' La Géométrie.

It contained some of the new elements introduced in Black Tie White Noise, and also signalled a move towards alternative rock.

The 1995-7 Rainbow Coalition ( which contained parties of the centre right and the left ) introduced free third-level education to primary degree level.

The LSI-11 ( PDP-11 / 03 ), introduced in February, 1975 was the first PDP-11 model produced using large-scale integration ; the entire CPU was contained on four LSI chips made by Western Digital ( the MCP-1600 chip set ; a fifth chip could be added to extend the instruction set, as pictured on the right ).

In 1882 the Explosive Company of Stowmarket introduced the EC Powder, which contained nitro-cotton and nitrates of potassium and barium in a grain gelatinesed by ether alcohol.

One standard introduced by Prussia was the Reichsthaler, which contained one fourteenth of a Cologne mark of silver.

The Warner Bros. technology, named Vitaphone, was publicly introduced on August 6, 1926, with the premiere of the nearly three-hour-long Don Juan ; the first feature-length movie to employ a synchronized sound system of any type throughout, its soundtrack contained a musical score and sound effects, but no recorded dialogue — in other words, it had been staged and shot as a silent film.

In 1990, Kapor's new company ON Technology introduced their new product On Location, an application designed for the Macintosh that contained an indexing system that permit quick retrieval and display of text on the Mac's hard disk.

The term chrismation is used because the recipient of the sacrament is anointed with Chrism, which according to eastern Christan belief, the Apostles sanctified and introduced for all priests to use as a replacement for laying on of hands by the Apostles and consists of a " mixture of forty sweet-smelling substances and pure olive oil " sanctified by a bishop with some older Chrism added in, in the belief that some trace of the initial Chrism sanctified by the Apostles is contained therein.

* Cap ' n Crunch's Crunch Berries: Cap ’ n Crunch's Crunch Berries cereal was introduced in 1967 and contained, in addition to the yellow pieces found in the original Cap ' n Crunch, spherical red Crunch Berry pieces.

In 1955, McNeil Laboratories introduced Tylenol Elixir for children, which contained paracetamol as its sole active ingredient.

The controversial New Coke, introduced in 1985, used a version of the Diet Coke recipe that contained high fructose corn syrup and had a slightly different balance of ingredients.

In 1939, Hungarian engineer Peter Carl Goldmark introduced an electro-mechanical system while at CBS, which contained an Iconoscope sensor.

The idea contained within the Z-transform is also known in mathematical literature as the method of generating functions which can be traced back as early as 1730 when it was introduced by de Moivre in conjunction with probability theory.

The gold penny was the issue introduced, with a value of twenty pence, with the obverse showing the king enthroned, with the legend ( King Henry III ), while the reverse contained a long cross extending to the edge, with a flower in each quarter, and the moneyer's name in the legend, thus ( William of London ).

After inflation was contained as a result of the 1985 Economic Stabilization Plan, the new sheqel was introduced, replacing the old sheqel on January 1, 1986, at a rate of 1, 000 old sheqalim = 1 new sheqel.

Pratt introduced an innovative, new laugh track that contained more realistic, though less distinctive reactions.

It contained the main restrictions introduced by Iemitsu.

When introduced, the denarius contained nearly pure silver at a theoretical weight of approximately 4. 5 grams.

Aware that unprocessed vegetable oils frequently contained natural antioxidants such as lecithin that slowed their spoilage, he developed means of combining these compounds with salts and other materials so that they could be readily introduced to other foods.

The second season contained changes in the cast, as well as disputes between cast members and producers, while the third season introduced a new lead actor and title.

1E Premiere ( release: November, 1994 ) The first edition premiere set contained 363 cards and introduced the affiliations of the Federation, the Klingons, and the Romulans, along with Non-Aligned cards.